CN117254734A

CN117254734A - PMSM (permanent magnet synchronous motor) multimode switching model prediction control method, system and storage medium

Info

Publication number: CN117254734A
Application number: CN202311262646.2A
Authority: CN
Inventors: 郭勇; 黄安; 张伟; 彭延峰; 彭稳升
Original assignee: Hunan University of Science and Technology
Current assignee: Hunan University of Science and Technology
Priority date: 2023-09-27
Filing date: 2023-09-27
Publication date: 2023-12-19

Abstract

The invention belongs to the technical field of vector control, and discloses a PMSM (permanent magnet synchronous motor) multi-mode switching model predictive control method, a PMSM multi-mode switching model predictive control system and a PMSM multi-mode switching model predictive control storage medium, wherein a RLS (dynamic random access memory) method is used for controlling a resistor R comprising a stator _s Inductance L _d,q Permanent magnet flux linkage ψ _f And identifying the motor parameters and using the identified parameters for calculating the predicted current value. This isIn addition, after one-beat delay compensation is carried out on the predicted current at the moment k, an improved Euler formula with a prediction-correction function is used for predicting and correcting the current at the next moment so as to improve the prediction accuracy of the current. The control performance of the motor is optimized to different degrees when the motor parameters are not matched, and the maximum torque pulsation is reduced from 0.63% to 0.22% when the flux linkage parameters are twice the standard values. The control parameters of the system are updated online, so that the steady-state control performance of the improved FCS-MPTC model under complex working conditions such as multistage rotating speed, variable load and the like is also improved.

Description

PMSM (permanent magnet synchronous motor) multimode switching model prediction control method, system and storage medium

Technical Field

The invention belongs to the technical field of vector control, and particularly relates to a PMSM multi-mode switching model predictive control method, a system and a storage medium.

Background

At present, a Permanent Magnet Synchronous Motor (PMSM) has the advantages of high power density, small volume, high efficiency and the like, and is widely applied to the fields of aerospace, electric automobiles, servo driving and the like. The selection of the motor control strategy directly affects the performance of the whole system, so that the research on the high-performance vector control scheme of the PMSM is critical for improving the overall performance of the driving system. Since PMSM is a complex system with multivariable, strong coupling characteristics, advanced control algorithms are required to maximize the performance of the motor. The most currently used PMSM control strategies mainly include two types, field Oriented Control (FOC) and Direct Torque Control (DTC). The FOC can realize accurate control on motor torque and speed, but has the defects of low dynamic response speed, more set PID parameters of the system and too complex mutual decoupling between controllers. DTCs have the advantage of fast response speed, but the torque ripple is large when the system reaches steady state, and the running performance is not ideal at low speed. Compared with the DTC, the advantage of the FOC is more obvious, so that the existing PMSM algorithms still adopt the basic framework of the FOC vector control, and the difference is that the original PID controller is replaced, and various parameters necessary in the vector control are acquired in other modes. Other types of high performance control strategies include: adaptive control, predictive control, sliding mode control, neural networks, and other various algorithms.

The non-linearity and time-lag phenomena of the system have been important issues of concern in PMSM control processes. As the motor is used as a complex coupling multi-factor control object, parameters such as the permanent magnet flux linkage of the inner rotor, the resistance, the inductance and the like of the stator are easy to be interfered by external environments, and thus, a nonlinear variation trend is presented. Existing control algorithms typically ignore non-linear factors in the motor and ideally model the PMSM. Meanwhile, when a Digital Signal Processor (DSP) is adopted for driving, a time lag effect exists, namely, the control signal output in the current period is obtained by calculation in the previous period, so that the output voltage is always delayed to be one control period of an actual waveform, when the carrier ratio is very low, the time lag effect can lead the phase lag of the output voltage of the driver to be very large, and when the carrier ratio is severe, the current loop is caused to vibrate, so that the motor is stopped in a step-out manner. System skew and nonlinearity are important issues to consider when performing precise control of PMSM.

The Model Predictive Control (MPC) has the advantages of simple structure, quick dynamic response, high steady-state control precision and the like, and can help solve the serious problems of multiple input and multiple output, large time lag, nonlinearity and the like in an actual industrial control system. The MPC controller is used for replacing a speed or current loop PI controller in a vector control structure, and the optimal voltage vector is selected to act on the motor by calculating the voltage vectors in different switch states in real time. The cost functions designed based on different emphasis points in the MPC control process can be expanded in control variables to realize multi-objective optimization of the performance of the control system, for example, limit variables can be added when the cost functions are designed to reduce the switching frequency of the inverter switches, so that the response speed of the system is increased and the energy consumption of the system is reduced. Compared with FOC vector control and direct torque control, MPC has more flexibility in the design of a PMSM control structure, so that MPC theory is used for a PMSM control link with multivariable, multi-objective and multi-constraint characteristics, and the multi-objective optimization control problem of the PMSM nonlinear time-varying system under complex working conditions can be effectively reduced. Two types of methods of current MPC control mainly include Dead Beat Control (DBC) and finite control set model predictive control (FCS-MPC). The implementation principle of the DBC is that the high-performance control of the PMSM is realized by predicting a reference voltage vector and generating a switch control signal of the inverter by means of SVPWM based on a mathematical model of the motor, and the algorithm has higher steady-state tracking precision and can effectively reduce the torque pulsation of the system. The FCS-MPC utilizes the discrete mathematical model of the PMSM and the switching state of the inverter, and the optimal inverter voltage vector applied to the motor at the next moment is obtained by continuously optimizing the cost function, so that the prediction control of the PMSM is completed. Depending on the control actions, MPC control strategies can be further divided into finite control set model predictive control (FCS-MPC) and continuous control set model predictive control (CCS-MPC). The two differ in that CCS-MPC does not take into account the discrete model of the inverter, but rather the optimal voltage vector is obtained by the auxiliary modulation technique to control the motor. FCS-MPC can be further classified into predicted rotational speed control (MPSC), predicted current control (MPCC), predicted torque control (MPTC), and predicted position control (MPPC) according to control objects. The cost function of the MPTC comprises a stator flux linkage and electromagnetic torque, and the dimensions of the stator flux linkage and the electromagnetic torque are different from each other, so that corresponding weight coefficients are required to be designed to evaluate the influence degree of the stator flux linkage and the electromagnetic torque on motor control performance. The torque ripple is calculated as a function of the weight coefficient and the weight coefficient is adjusted online by an optimization method. And (3) performing multi-objective optimization sorting by using the torque and flux linkage cost function instead of a single cost function in the traditional MPTC, and acting the obtained optimal voltage vector on the inverter. The torque and flux reference magnitudes are converted to equivalent reference vectors for the stator flux, thereby avoiding the design of the stator flux weight coefficients in conventional MPTCs.

Although MPC is an advanced control strategy widely applicable to complex system controller designs such as PMSM, the following two problems remain. Since the performance of MPC on system control depends largely on the accuracy of the system model, and the PMSM driving system is no exception, MPC control depends on the accurate discretized PMSM mathematical model, but the nonlinearity of the PMSM itself can cause the mathematical model to have time-varying characteristics, thereby affecting the control performance of the MPC. The common solution is to linearize the mathematical model of the PMSM to realize mutual decoupling of internal variables of the motor, and then apply MPC principle to model the linearized PMSM, but the system is more sensitive to parameter changes, and the parameter robustness of the system is reduced. Secondly, because the dynamic response time of the motor is close to the discrete control period, the capacity of the system for processing unknown disturbance is weaker, and the control performance of the MPC is affected when the system parameters are affected by external factors, so that a proper parameter disturbance estimation method is required to be selected for integral compensation to further improve the performance of the MPC. The common parameter disturbance estimation method is to predict the stator current and disturbance in real time by using a Stator Current and Disturbance Observer (SCDO), and compensate the disturbance estimation value into a controller to realize the prediction control of the PMSM. Because FCS-MPC is easily affected by model parameter mismatch, the parameter mismatch problem can be solved to a certain extent by constructing disturbance observer to carry out disturbance estimation on model parameters, but the method does not start from improving the anti-interference performance of the model itself, but passively reduces the influence of system parameter change on the model. In the research of the value function, the influence factors are weighted while more constraint variables are introduced into the function, so that the torque fluctuation of the system can be effectively restrained, and the steady-state performance of the control system is improved. However, too many variables increase the operation amount of the controller, so that the constructed cost function cannot obtain the optimal solution under the condition of multiple constraints, and the constructed cost function does not meet the definition of the lyapunov function in most cases. Meanwhile, the FCS-MPC does not contain a signal modulation process, so that the switching frequency of an inverter, voltage overshoot of an alternating current system, harmonic distortion of stator current and the like can influence the effect of the method in practical application. Although the prior art has considered combining modulation techniques with switching signal control sequences, the relationship between FCS-MPC and system control quantity is not truly addressed.

Another method for reducing the influence of PMSM model parameter variation on system performance is to perform on-line identification on system parameters in the control process, and simultaneously update and feed the identified parameters back to the PMSM model in real time, so that the control performance of FCS-MPC can be effectively improved, and the influence caused by parameter mismatch is reduced. For example, a model reference self-adaptive method is used for carrying out multi-parameter on-line identification on the PMSM, and a single-loop model predictive control system is used for replacing a traditional double-vector control system to simplify the system structure, so that the control performance of the system can be effectively improved. In addition, determining harmonic magnitudes of back EMF using a sliding mode observer and a recursive least squares estimator may reduce non-sinusoidal flux linkage torque ripple of the PMSM.

Through the above analysis, the prior art has drawbacks:

1) Model dependence and non-linearity:

MPC relies on an accurate mathematical model, and the nonlinearity of PMSM makes this model time-varying. This dependence and nonlinearity complicates controller design and is susceptible to system parameter variations.

2) Sensitivity to parameters:

even with linearization, the system is still more sensitive to parameter variations, resulting in lower parameter robustness.

3) The ability to dynamically respond and handle unknown disturbances is weak:

the dynamic response time of the motor approaches its discrete control period, resulting in a weaker ability to handle unknown disturbances.

4) The operation amount is large:

introducing too many variables into the construction of the value function increases the computational effort of the controller, which may result in an inability to find an optimal solution under multiple constraints.

5) Torque ripple and system effects:

since FCS-MPC does not include the modulation process of the signal, the switching frequency of the inverter, harmonic distortion of the stator current, and the like all affect the effect in practical applications.

6) Time lag and nonlinearity:

time lag and nonlinearity exist in the existing PMSM vector control process, so that the change of load and rotating speed cannot be well adapted under complex working conditions.

Technical problems to be solved urgently:

1) Model precision and robustness are improved:

there is a need to develop models that more accurately describe PMSM dynamics and improve the robustness of the parameters of the system.

2) Dynamic response and perturbation processing:

searching a more proper parameter disturbance estimation method to compensate, improving the capacity of the system for processing unknown disturbance and the adaptability to dynamic response.

3) Optimization of computational efficiency:

it is necessary to study how to reduce the number of variables and the computational complexity while maintaining the accuracy of the model, and optimize the computational efficiency.

4) Improving system performance:

new control strategies and algorithms need to be explored to improve issues with torque ripple, switching frequency, voltage overshoot, etc., and to improve overall system performance.

5) Solving the problems of nonlinearity and time lag:

aiming at the problems of nonlinearity and time lag in the conventional PMSM vector control process, new control strategies and technologies need to be developed, so that the system can maintain stable performance under the complex working conditions that the load and the rotating speed are continuously changed.

6) Self-adaption and online parameter identification:

it is necessary to develop a more efficient and accurate online parameter identification technique and an adaptive method to update and adjust model parameters in real time to adapt to system changes and reduce the influence caused by parameter mismatch.

Solving these problems will help to improve the stability, accuracy and efficiency of PMSM control systems, thereby meeting more complex and diverse industrial application needs.

Disclosure of Invention

Aiming at the problems existing in the prior art, the invention provides a PMSM multi-mode switching model predictive control method, a PMSM multi-mode switching model predictive control system and a storage medium.

The invention is realized in such a way, a PMSM multi-mode switching model predictive control method is used for carrying out online identification on motor parameters by using a recursive least square (DFF-RLS) method capable of dynamically adjusting forgetting factors and updating the motor parameters into a system model in real time; identifying motor parameters including stator resistance, inductance and permanent magnet flux linkage by using an RLS method, and using the identification parameters for calculating a predicted current value; after one beat delay compensation is performed on the predicted current at the time k, the current at the next time is predicted and corrected by using an improved Euler formula with a prediction-correction function.

Further, the PMSM multimode switching model prediction control method comprises the following steps:

the first step: when the system is running stably, the dq-axis current i of the previous moment and the current moment is utilized _d (k-1),i _q (k-1) and i _d (k),i _q (k) The previous time dq axis voltage u _d (k-1),u _q (k-1) calculating a parameter matrix required for MPTC control

And a second step of: using the alpha-beta current i at the present moment _α (k),i _β (k) Sum voltage u _α (k),u _β (k) Identified parameter matrixCalculating a one-beat delay compensation current according to the following formula>

And a third step of: combining identification parameter matrixCurrent i at the present moment _α (k),i _β (k) Compensating current for one beat delay>Correcting to obtain the predicted current i at the next moment _α (k+1),i _β (k+1)；

Fourth step: using the predicted current i at the next instant _α (k+1),i _β (k+1) and identification parameter matrixCalculating the predicted value T of the torque and the flux linkage by combining _e (k+1),ψ _s (k+1); modulating different voltage vectors to obtain alpha beta axis voltage u under different switch sequences Sw (: i) _α,i (k),u _β,i (k) Repeating the calculation processes from the second step to the fourth step to obtain a torque and flux linkage prediction control set T under different voltage vectors _e,i (k+1),ψ _s,i (k+1)；

Fifth step: predictive control set T for linking torque and flux _e,i (k+1),ψ _s,i (k+1) and reference valueIs substituted into the following value function J (V _n ) Calculating;

sixth step: for the value function J (V _n ) Sequencing to obtain an optimal voltage vector V _opt The switch under action switches state and uses the switch as a control signal of the three-phase inverter;

V _opt ＝argminJ(V _n )。

further, the parameter sensitivity analysis of the PMSM multi-mode switching model prediction control method comprises three necessary motor parameters and a resistor R in an MPTC prediction model _s Inductance L _d ,L _q Rotor permanent magnet flux linkage ψ _f When the motor parameters are not matched, inaccuracy of the predicted current is directly caused, and the prediction performance of the model is finally affected; mathematical model of PMSM in dq coordinate systemThe prediction model for current obtained by discretization is as follows:

when the system is subjected to parameter disturbance, the model is changed into:

wherein: deltaR _s ,ΔL _d ,ΔL _q ,Δψ _f The deviation between the actual value and the reference value of the model resistance, the inductance and the flux linkage is respectively calculated, and the predicted current error under parameter disturbance is obtained as follows:

wherein: e (E) _d ,E _q The predicted current errors of the d axis and the q axis are respectively, and any parameter R can be known from the above _s ,L _s ,ψ _s Mismatch will have an effect on the predicted current;

predicted current with one beat delay compensation under parameter mismatch conditionsBy accurate current +.>And current prediction error E _d ,E _q The sum represents;

when parameter errors exist, a predicted current model with one-beat delay compensation is obtained as follows:

The predicted current error with one beat delay compensation is obtained by subtracting the actual model from the above:

wherein: e (E) _d ′,E _q ' the predicted current error with one beat delay compensation for the d-axis and q-axis, respectively.

Further, the improved euler method implementation process of the PMSM multimode switching model predictive control method comprises the following two steps:

the first step: estimating t using a display Euler method _i+1 Approximation of time of day

And a second step of: using predicted valuesAs the input of the right end equation of the trapezoid equation, and further calculates t _i+1 Final correction value +.>The pre-estimation and correction process is an improved Euler method;

in the above equationThe error of (2) can be further reduced by using a plurality of iterative modes, and the specific process is as follows:

the local truncation error due to the ordinary differential equation is defined as e _i ＝x _i -x(t _i ) Wherein x is _i And x (t) _i ) Respectively t _i Predicted and actual values of time of day, at t using modified Euler method _i+1 The time truncation error is:

for f (t) in the above formula _i+1 ,x _i+1 )，x(t _i+1 ) Taylor expansion is performed separately, and Δt, Δt·f (t _i ,x _i ) Seen as a binary function f (t _i ,x _i ) And for the binary function f (t _i ,x _i ) The method is characterized in that the method is obtained by only performing one unfolding treatment:

f(t _i+1 ,x _i+1 )＝f(t _i +Δt,x _i +Δt·f(t _i ,x _i ))

＝f(t _i ,x _i )+Δt·f _t ′(t _i ,x _i )+(Δt·f(t _i ,x _i ))f _x ′(t _i ,x _i )+Ο(Δt ² )

＝x′(t _i )+Δt·x″(t _i )+Ο(Δt ² )

the method comprises the following steps:

further, i is selected by the PMSM multi-mode switching model prediction control method _α ,i _β As a state variable and predicting it, the mathematical model of PMSM in the αβ coordinate system is:

wherein: u (u) _α ,u _β ,i _α ,i _β Sum phi _α ,ψ _β Stator voltage, current and flux linkage of alpha axis and beta axis respectively, p is differential operator, theta _e For the electrical angle of the rotor, due to u _s ＝u _α +ju _β ，i _s ＝i _α +ji _β Discretizing the voltage equation to obtain a current prediction model at the moment k+1, wherein the current prediction model comprises the following steps:

the predicted current is compensated by using an improved Euler method with a correcting function, and a current prediction equation at the moment k+1 after compensation is obtained as follows:

in the method, in the process of the invention,for the predicted value of the current at time k+1 using the Euler equation,/I>To use the current correction value, L, obtained by improving the Euler equation _s The inductances are d axis and q axis respectively; predicted current at time k+1 is obtained +.>Then, the linkage of the next control period can be predicted by combining the linkage equation of the PMSM and the torque equation>And torque->The method comprises the following steps of:

cost function J (V) _n ) The optimal matching of flux linkage and torque is considered, the flux linkage and torque error values under the action of different voltage vectors are compared and ordered, and the design is adoptedThe reasonable flux linkage weight coefficient is used for obtaining an inverter switching sequence corresponding to the optimal voltage vector, and the cost function is defined as:

V _opt ＝argminJ(V _n )

wherein:and- >Reference values for torque and flux linkage, respectively; ζ is defined as the flux linkage weight coefficient; v (V) _n (n=0,., 6) represents a voltage vector; v (V) _opt Is the optimal voltage vector. Wherein the initial value of ζ can be designed according to the weighting principles of torque, flux linkage and the like, namely, ζ=T _N /|ψ _sN |，T _N Is rated for torque, psi _sN Is the flux linkage amplitude under the rated condition; torque reference value->From the rotation speed error n _error Obtained by a PI controller, the flux linkage reference value +.>Based on the maximum torque current ratio MTPA:

substituting different voltage vectors into the equation respectively to obtain 8 groups of predicted currents at the moment k+1And calculating the corrected predicted current +.>Obtaining an optimal voltage vector V according to a calculation flow _opt 。

Further, what is saidThe PMSM multi-mode switching model prediction control method rewrites a mathematical model of the PMSM under a dq coordinate system into an RLS standard form based on Y=ΘX, wherein Θ is a parameter matrix to be recognized, and dq axis currents at the last moment and the current moment are calculatedAnd dq-axis voltage +.>Substituting matrix X, Y to calculate motor parameter identification result +.>And it is used for predicting the current +.>Is calculated;

a) The RLS basic principle is that the least square method is that the given data is { y ε R, x _i E R, i=1, 2,..n } solve the following formal problem:

Wherein: y=x ₁ θ ₁ +x ₂ θ ₂ +···+x _N θ _N On the basis of the measurement result at the previous moment, the result is corrected by utilizing the new data measured at the current moment, so that the calculation process is greatly simplified;

if k groups of X and Y data exist, identifying Θ= [ θ ] by the following form equation set ₁ θ ₂ ···θ _N ] ^T ∈R ^N×1 ：

Wherein:for the ith added data, it is converted into row vector form, i.eThe data matrix of the first k acquisitions is defined as +.> The above can be simplified as:

Y _k ＝X _k Θ

obtaining an estimated value of the equation solution by using a least square methodEstimated parameters->The more accurate the predicted output value of the model +.>The closer to Y _k Defining an error matrix->Whereas the objective of the least squares method is to make the square of the error matrix +.>Least, deriving the solution of the equation under the least square method is as follows:

parameter matrix to be identifiedThe problem of overlarge data volume caused by accumulation and iteration of data is solved, and the least square method is used for calculating again after new data is acquired, and the recursive least square method is used for identifying a matrix +_ of parameters at the previous moment>Correcting to obtain a current moment identification parameter matrix +.>

Definition of the definitionThen there are:

obtaining the productLet->Then there are:

the updated formula after the kth measurement data is obtained is:

matrix obtained by using the previous k-1 times of measurement data Sum vector B _k-1 I.e. calculate matrix +.>From the formulaKnow->Thereby get +.>And is composed ofThen it can be obtainedSubstituting it into the optimal approximate solution of the recursive least squares method is:

due to (A+BCD) ^-1 ＝A ^-1 -A ^-1 B(C ^-1 +DA ^-1 B) ^-1 DA ^-1 In the aboveSimplified intoLet K _k ＝P _k x _k The recursive least squares method can be expressed as:

wherein the method comprises the steps ofTo identify parameters, P _k As covariance matrix, K _k For the augmentation matrix, I is the identity matrix. Considering a recursive least square method of a fixed forgetting factor lambda, substituting the forgetting factor into an error square term for calculation, and obtaining an RLS formula as follows:

wherein: lambda is more than 0 and less than or equal to 1 and is a fixed forgetting factor introduced in RLS;

b) Calculating a Dynamic Forgetting Factor (DFF) function

Introducing a dynamic forgetting factor into the RLS, and outputting a difference epsilon according to a theoretical model and an actual model at the current moment _k Dynamic adjustment of forgetting factor, difference epsilon at time k _k Expressed as:

wherein: epsilon _k Representing the parameter identification error caused by noise at the current moment, when epsilon _k The convergence speed needs to be increased when the value is larger, and the convergence speed is equal to epsilon _k And if the dynamic forgetting factor is smaller, using a smaller forgetting factor, and establishing the following dynamic forgetting factor function as follows:

wherein: 0 < alpha < 1 is a positive adjustable factor, and gamma is greater than 0, when the error value epsilon _k Forgetting factor lambda at a large time _k Close to alpha, when epsilon _k Less forgetting factor lambda _k Then close to 1, the expression for the dynamic forgetting factor recursive least squares (DFF-RLS) is:

c) Implementation of DFF-RLS-FCS-MPTC

Will beSubstitution->The formula yields a discrete mathematical model of the PMSM in the dq coordinate system:

wherein the method comprises the steps of For the stator current at time k+1,/o>And->D-axis and q-axis currents and voltages at time k, respectively;

will be described inRewritten as a solution for RLS:

Y＝ΘX；

wherein:

comparing the formula y=xΘ of the DFF-RLS recursion, Y _k Representing one new data added at a time, x _k Representing that only one column vector is added at a time, the DFF-RLS recurrence formula of Y=ΘX formula is obtained as follows:

wherein: lambda (lambda) _k As a dynamic forgetting factor function, P _k For the covariance matrix at time k,for the parameter matrix to be identified at k moment, X _k ,Y _k And respectively adding new data at the moment k.

It is a further object of the present invention to provide a computer device comprising a memory and a processor, the memory storing a computer program which, when executed by the processor, causes the processor to perform the PMSM multimode switching model predictive control method.

It is another object of the present invention to provide a computer-readable storage medium storing a computer program which, when executed by a processor, causes the processor to perform the PMSM multimode switching model predictive control method.

Another object of the present invention is to provide an information data processing terminal for implementing the PMSM multimode switching model predictive control method.

Another object of the present invention is to provide a PMSM multimode switching model predictive control system based on the PMSM multimode switching model predictive control method, the PMSM multimode switching model predictive control system comprising:

the model updating module is used for carrying out online identification on motor parameters by a recursive least squares method DFF-RLS capable of dynamically adjusting forgetting factors and updating the motor parameters to a system model in real time;

the current calculation module is used for identifying motor parameters including stator resistance, inductance and permanent magnet flux linkage by using an RLS method and calculating a predicted current value by using the identification parameters;

and the prediction correction module is used for predicting and correcting the current at the next moment by using an improved Euler formula with a prediction-correction function after performing one-beat delay compensation on the predicted current at the moment k.

In combination with the technical scheme and the technical problems to be solved, the technical scheme to be protected has the following advantages and positive effects:

firstly, the invention provides a PMSM Robust Model Predictive Control (RMPC) method based on dynamic forgetting factor recursive least square method parameter identification for time lag and nonlinearity problems in a PMSM vector control process. To reduce the inherent delay of PMSM digital control systems, one beat delay compensation is introduced based on conventional finite control set model predictive torque control (FCS-MPTC), and the controller design is performed using an improved euler equation with a predictive-corrective function to improve the current prediction accuracy. In addition, as the control performance of MPTC is also affected by the change of motor parameters, in order to reduce the sensitivity of system parameters, a recursive least square (DFF-RLS) method capable of dynamically adjusting forgetting factors is used for carrying out online identification on the motor parameters and updating the motor parameters into a system model in real time so as to improve the robustness of the system parameters. Secondly, in order to check the control precision and steady-state performance of the PMSM under the complex working condition, a PMSM multi-mode switching controller is built by utilizing a Stateflow toolbox in MATLAB/Simulink, so that the system can select optimal control parameters according to the current working condition and update the optimal control parameters into a system model. Finally, the parameter identification performance of the PMSM model prediction control method with parameter identification is analyzed under static and dynamic conditions, and the influence of different parameter changes on the system performance is simulated. Compared with the traditional FCS-MPTC method, the control model can adapt to complex working conditions which continuously change along with load and rotating speed, meanwhile, total Harmonic Distortion (THD) of current and torque pulsation are obviously reduced, and the influence of load and rotating speed changes on system performance is also obviously reduced.

Secondly, aiming at the problems of parameter mismatch and system nonlinearity in the PMSM control process, the invention provides an online parameter identification method based on dynamic forgetting factor (RLS), which is used for establishing a forgetting factor dynamic function according to the difference between the actual output and the theoretical output of a system model when carrying out iterative calculation on new data, thereby improving the system convergence rate while ensuring the algorithm identification accuracy. For the inherent delay problem of the PMSM driving system, the invention introduces one beat delay compensation based on the traditional MPTC control, and uses an improved Euler formula with a prediction-correction function to design a controller so as to improve the current prediction precision. In addition, in order to verify the steady-state control performance of the PMSM under different working conditions, a PMSM multi-mode switching controller is built through a Stateflow toolbox, so that the current working condition can be identified, and the optimal controller parameters can be updated into an MPTC model. Finally, the PMSM model prediction control method based on DFF-RLS parameter identification provided by the invention analyzes the parameter identification performance under static and dynamic conditions, and the current THD value and torque pulsation under motor parameter, load and rotating speed changes. The invention mainly contributes to the following:

(1) Based on the traditional MPTC control, an improved Euler formula with a prediction-correction function is used for designing a controller, and one-beat delay compensation is carried out to reduce the inherent delay of a digital system, and meanwhile, the accuracy of model prediction current is improved;

(2) Carrying out online identification on motor parameters by using an RLS algorithm with a dynamic forgetting factor, and updating an identification result into an FCS-MPTC controller in real time to reduce the sensitivity of system parameters;

(3) Verifying the dynamic and steady state performance of the PMSM under the complex working condition by constructing a multi-mode switching controller;

(4) The parameter identification performance of the DFF-RLS algorithm under static and dynamic working conditions is analyzed, and the influences of different motor parameters, load and rotation speed changes on the current THD value and the torque pulsation are compared.

Thirdly, the technical scheme of the invention fills the technical blank in the domestic and foreign industries:

the technical scheme of the invention is that on the basis of the traditional FCS-MPTC, an improved Euler formula is used for carrying out one-beat delay compensation on the predicted current at the next moment, and the predicted current is corrected to improve the current prediction precision. Most of the current PMSM prediction control schemes directly adopt a forward Euler formula to discretize a motor mathematical model so as to acquire a predicted current at the next moment, compared with the improved Euler formula of the invention, the forward Euler formula has only first-order identification precision, and the improved Euler formula is obtained by combining the forward Euler formula and a trapezoidal formula, so that the method has second-order precision and is more accurate in calculating the predicted current;

Because the parameter change of the PMSM directly affects the control performance of the MPC, the invention uses the recursive least square method of the dynamic forgetting factor to identify the motor parameters on line and load the motor parameters into the DFF-FCS-MPTC model in real time, thereby reducing the influence of parameter mismatch on the control performance of the system and reducing the robustness of the system parameters;

the multi-mode switching control strategy provided by the invention can effectively improve the running performance of the traditional FCS-MPTC method under complex working conditions, avoid the situation that the PMSM model predictive control cannot adapt to the complex working conditions which change along with the load and the rotating speed in multiple stages, and load the optimal controller parameters into the PMSM model through the active recognition of the working conditions so as to obtain the optimal control effect under different working conditions.

Fourth, the present invention combines online identification and real-time updating of motor parameters using a recursive least squares (DFF-RLS) method that dynamically adjusts forgetting factors. The method can identify motor parameters including stator resistance, inductance and permanent magnet flux linkage, and can also use the identification parameters for calculating a predicted current value.

The improved euler equation with the prediction-correction function helps to predict and correct the current at the next moment. This is critical to ensuring stability and performance of the system. The method further includes a time stepping scheme of the system that uses the shaft current, shaft voltage and parameter matrix to calculate predicted values of torque and flux linkage and orders the value functions to obtain an optimal voltage vector. This time stepping scheme provides great flexibility and adaptability to the control system.

In terms of parameter sensitivity analysis, this approach also accounts for motor parameter mismatch issues that may affect the predicted performance. The current prediction model obtained by discretizing the mathematical model of the PMSM under the coordinate system can more accurately predict the current value, and the prediction performance of the model is further improved.

In general, the PMSM multimode switching model predictive control method has high practical value, can realize remarkable technical progress in industrial application, and improves the performance and stability of the system.

Drawings

FIG. 1 is a flowchart of a PMSM multimode switching model predictive control method provided by an embodiment of the present invention;

fig. 2 is a schematic diagram of a conventional FCS-MPTC control provided by an embodiment of the present invention;

fig. 3 is a flowchart of a conventional FCS-MPTC control provided by an embodiment of the present invention;

FIG. 4 is a schematic diagram of an improved FCS-MPTC control principle with parameter identification according to an embodiment of the present invention;

FIG. 5 is a schematic diagram showing the relationship between the parameter error and the current prediction error in different degrees according to the embodiment of the present invention: (a) E (E) _d And DeltaR _s ,ΔL _s The relationship between them; (b) E (E) _q And DeltaR _s ,ΔL _s The relationship between them; (c) E (E) _q And delta phi _s The relationship between them;

FIG. 6 is a schematic diagram showing the relationship between the parameter errors and the prediction errors with one-beat delay compensation according to the embodiment of the present invention: (a) E (E) _d ' and DeltaR _s ,ΔL _s The relationship between them; (b) E (E) _q ' and DeltaR _s ,ΔL _s The relationship between them; (c) E (E) _q ' and Deltapsi _s The relationship between them;

FIG. 7 is a flow chart of a multiple iteration modified Euler method control provided by an embodiment of the present invention;

FIG. 8 is a flow chart of an improved FCS-MPTC control provided by an embodiment of the present invention;

fig. 9 is a schematic diagram of a control structure based on DFF-RLS-FCS-MPTC according to an embodiment of the present invention;

FIG. 10 is a flow chart of selection of an optimal voltage vector in an improved FCS-MPTC provided by an embodiment of the present invention;

FIG. 11 is a schematic diagram of a function implementation of a DFF-RLS parameter identification algorithm provided by an embodiment of the present invention;

fig. 12 is a schematic diagram of a DFF-RLS-FCS-MPTC control time sequence provided by an embodiment of the present invention;

FIG. 13 is a schematic diagram of a simulation model of a conventional FCS-MPTC and a modified FCS-MPTC provided by an embodiment of the present invention;

FIG. 14 is a graph showing a comparison of the performance of a conventional FCS-MPTC and a modified FCS-MPTC system based on DFF-RLS parameter identification when inductance and flux linkage parameters are mismatched, as provided by an embodiment of the present invention;

FIG. 15 is a schematic diagram of a Stateflow implementation detail of a multimode switching controller operating mode identification and parameter update subsystem under Matlab according to an embodiment of the present invention;

FIG. 16 is a simulation result (T) of a step change in rotational speed according to an embodiment of the present invention _L =0.2 Nm) schematic diagram: (a) reference, general and proposed rotational speeds; (b) dq axis stator current; (c) measured torque and error; (d) three-phase current;

FIG. 17 is a simulation result (T) of the dynamic change of the rotational speed according to the embodiment of the present invention _L =0.2 Nm) schematic diagram: (a) Reference, general and proposed rotational speeds; (b) dq axis stator current; (c) measured torque and error; (d) three-phase current;

FIG. 18 is a graph showing a comparison of the results of ramp-up of rotational speed (T) _L =0.2 Nm) schematic diagram: (a) reference, general and proposed rotational speeds; (b) dq axis stator current; (c) measured torque and error; (d) three-phase current;

FIG. 19 is a simulation result (n) of the dynamic load change according to the embodiment of the present invention _ref =1000 rpm) schematic diagram: (a) reference, general and proposed rotational speeds; (b) dq axis stator current; (c) measured torque and error; (d) three-phase current;

FIG. 20 is a graph showing performance analysis (T) of dynamic change of rotational speed according to an embodiment of the present invention _L =0.2 Nm) schematic diagram: (a) general and proposed d-axis currents; (b) general and proposed q-axis currents; (c) general and proposed three-phase currents; (d) general and proposed torque and load;

FIG. 21 is a schematic diagram of a simulation model of parameter identification performance analysis based on DFF-FCS-MPTC provided by an embodiment of the present invention;

FIG. 22 is a schematic diagram of the static parameter identification result under the working conditions of 1000rpm and 0.1Nm according to the embodiment of the present invention;

FIG. 23 is a graph showing the identification result of static parameters under the working conditions of 1500rpm and 0.2Nm according to the embodiment of the present invention;

fig. 24 is a schematic diagram of parameter identification performance analysis of the DFF-RLS based method under different rotation speeds and loads according to an embodiment of the present invention: (a) (b) comparing the average parameter identification error with the maximum parameter identification error at a rotational speed in the range of 500-1500 rpm; (c) (d) comparing the average parameter identification error with the maximum parameter identification error for a load in the range of 0.1-0.2 Nm;

fig. 25 is a graph showing the result of parameter identification when the load is changed from 0.1Nm to 0.15Nm at 0.025s at n=1000 rpm according to the embodiment of the present invention;

FIG. 26 is a diagram of a T-cell according to an embodiment of the present invention _L Parameter identification results for a rotation speed of 1000rpm to 1050rpm at 0.025 s=0.1 Nm;

FIG. 27 is a graph of T at 0.025s provided by an embodiment of the present invention _L The parameter identification result is shown in a schematic diagram when the rotation speed n is changed from 1000rpm to 1050rpm from 0.1Nm to 0.15 Nm;

FIG. 28 shows the parameters set to k times the standard value for the current THD and torque ripple T in the DFF-RLS method according to the embodiment of the present invention _ri Is a schematic diagram of the influence of (a);

fig. 29 is a schematic diagram showing a comparison of performance of the DFF-RLS-FCS-MPTC and FCS-MPTC based methods provided by the embodiments of the present invention;

FIG. 30 shows the current THD and torque ripple T of the DFF-RLS-FCS-MPTC and FCS-MPTC methods at different speeds and loads according to an embodiment of the present invention _ri Comparing the schematic diagrams;

fig. 31 is a block diagram of a PMSM multimode switching model predictive control system provided by an embodiment of the invention.

Detailed Description

The present invention will be described in further detail with reference to the following examples in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention.

As shown in fig. 1, the PMSM multimode switching model prediction control method provided by the embodiment of the invention includes the following steps:

s101: carrying out online identification on motor parameters by using a recursive least square method DFF-RLS capable of dynamically adjusting forgetting factors and updating the motor parameters to a system model in real time;

s102: identifying motor parameters including stator resistance, inductance and permanent magnet flux linkage by using an RLS method, and using the identification parameters for calculating a predicted current value;

S103: after one beat delay compensation is performed on the predicted current at the time k, the current at the next time is predicted and corrected by using an improved Euler formula with a prediction-correction function.

Example 1:

1. PMSM model and legacy FCS-MPTC control

1.1 mathematical model of Motor

The mathematical model of the PMSM under a three-phase coordinate system has more variables, and is not suitable for directly carrying out mathematical modeling. The mathematical model of the motor under the three-phase coordinate system is subjected to equivalent transformation by utilizing coordinate transformation, so that a voltage equation under the dq coordinate system is obtained, and a stator flux linkage, an electromagnetic torque and a mechanical motion equation can be further obtained, wherein the voltage equation is as follows:

T _e ＝1.5p _n (ψ _d i _q -ψ _q i _d ) (3)

wherein L is _d ,L _q ,i _d ,i _q ,ψ _d ,ψ _q And u _d ,u _q Stator inductance, current, permanent magnet flux linkage and voltage of d axis and q axis respectively; omega _e For rotor electrical angular velocity; t (T) _e ,T _L Electromagnetic torque and load torque, respectively; p is p _n The pole pair number of the motor is; psi phi type _f Is a rotor permanent magnet flux linkage; j is moment of inertia; r is R _s Is the stator resistance; b (B) _m Is the adhesion damping coefficient.

1.2 MPC control general principle

The MPC control is mainly used for realizing model prediction control of a linear time-varying PMSM system under discrete time, and the general expression form of the discrete system is as follows:

the constraint conditions are satisfied: y is _min ≤y _k ≤y _max ,u _min ≤u _k ≤u _max . Wherein k is the kth sampling period of the system; x is x _k Is a state vector of the system, u _k Is the system input vector, y _k Is the output vector.

The cost function of a discrete system can be defined as:

wherein E is a systematic error matrix; q, R, F are the weight matrix of the present error, control input and final error of the system respectively; e (E) _N Representing the systematic terminal error.

The MPC rolling optimization implementation steps are as follows:

(1) The first step: at time k, the current state y of the system is measured or estimated _k ；

(2) And a second step of: u is obtained by calculation _k ,u _k+1 ,u _k+2 ,...,u _k+N-1 Further obtain the estimated value y of the system in the future state _k+1 ,y _k+2 ,y _k+3 ,...,y _k+N Then, performing optimization control;

(3) And a third step of: after the optimal control input sequence is obtained, only u is taken at the moment k _k As a control input;

(4) Fourth step: the above process is repeated when the prediction of the k+1 time is performed, thereby realizing the rolling optimization.

Calculating a cost function by using a quadratic programming method, defining u (k|k), x (k|k) being model input and system state based on k moment prediction, N _p For predicting the interval length. To simplify the calculation process, assuming that the desired reference input R is zero and the system output vector is equal to the state vector, the error matrix E _k ＝x _k The system cost function obtainable from equation (6) is:

the first term is the error weighted square sum, the second term is the input weighted square sum, the last term is the weighted square of the terminal error, Q, R is the weighted diagonal matrix of the current state and control input.

Let the initial value of the state vector at time k be x (k|k) =x _k The combination of formula (5) can be obtained:

to facilitate matrix calculation, letThe above is changed to:

X _k ＝Mx _k +CU _k (9)

wherein:

the cost function may be converted into the following form according to the above conversion process:

in the method, in the process of the invention,the error weight matrix and the augmentation matrix of the input weight matrix are respectively.

Substituting the formula (9) into the formula (11) can eliminate the state quantity X _k The method comprises the following steps of:

order theA simplified form of the cost function is obtained:

at this time, the cost function is only equal to the initial state x of the system _k Control input U _k Related is a multiparameter quadratic programming (MPQP) problem. The optimal solution of the above problem can be solved by modern control theory.

1.3 legacy FCS-MPTC control implementation

The traditional FCS-MPTC adopts a two-level three-phase inverter to drive, and has 8 voltage vectors in total and a limited voltage control set of u _s ∈{V ₀ ,V ₁ ,V ₂ ,V ₃ ,V ₄ ,V ₅ ,V ₆ ,V ₇ }, wherein V ₁ -V ₆ Is the effective voltage vector, and V ₀ ,V ₇ Is a zero voltage vector. The control principle of FCS-MPTC is shown in FIG. 2. The system state variable is x= [ ψ ] _d ψ _q ] ^T The output variable is equal to the input variable y=x= [ ψ ] _d ψ _q ] ^T The control input is u= [ u ] _d u _q ] ^T Since only one-step prediction is performed, i.e. N _p =1, and the cost function considers only the error term, and ignores the two latter terms, resulting inWherein E is _k ＝y _k -r＝y _k -r＝x _k -r, wherein- >There is->Predicted +.>Conversion to the corresponding torque and flux linkage amplitude +.>Let->The cost function becomes +.>

The prediction equations for flux linkage, current and torque obtained by discretizing the above equations (1) to (3) by using a forward Euler equation are as follows:

wherein T is _s Is a discrete sampling period. FIG. 3 shows a voltage vector selection process by the conventional FCS-MPTC method for three-phase stator currents i _abc Clark-Park conversion is carried out to obtain sampling current at k moment under dq coordinate systemSubstituting it into flux linkage equation (2) and torque equation (3) to obtain d-axis and q-axis stator flux linkage of k moment>Component and torque->And the basic voltage vector at time k +.>Then is made up of DC bus voltage V _dc And the method is obtained after the modulation and the coordinate transformation of the inverter switch. Bringing the stator flux at the kth time and the voltage vector into the formula (14) to obtain the stator flux predicted value at the k+1 time +.>From this, the stator flux linkage amplitude at time k+1 is calculated to be +.>The flux linkage predicted value obtained by the same method>By taking equation (15), the current prediction value +.1 at time k+1 can be obtained>And then bringing this into the expression (16) to obtain the predicted torque value +.1 at time k->At the moment of obtaining k+1, 8 stator flux and torque predictive valuesAfter (i=0-7), it is compared with the reference value- >Carry-in cost function->The switching sequence for minimizing the cost function is obtained and used as the control signal of the inverter IGBT, thereby realizing the model predictive torque control of the PMSM.

Example 2:

1. FCS-MPTC implementation based on DFF-RLS parameter identification

In order to solve the problem of parameter sensitivity of the conventional FCS-MPTC control, the invention proposes an online identification of motor parameters based on a parameter identification method of DFF-RLS, and uses the motor parameters in the calculation of the prediction current in the improved FCS-MPTC, and the control basic principle of the improved FCS-MPTC with parameter identification is shown in figure 4. To reduce the impact of PMSM parameter mismatch on FCS-MPTC control performance, the RLS method is first used to control the phase current including the stator resistance R _s Inductance L _d,q Permanent magnet flux linkage ψ _f And identifying the motor parameters and using the identified parameters for calculating the predicted current value. In addition, after one-beat delay compensation is performed on the predicted current at the time k, the current at the next time is fed by using an improved Euler formula with a prediction-correction functionPrediction and correction are performed to improve the prediction accuracy of the current.

1.1, parameter sensitivity analysis

According to MPTC control principles, the MPTC predictive model includes the necessary three motor parameters (resistance R _s Inductance L _d,q Rotor permanent magnet flux linkage ψ _f ) Inaccuracy of the predicted current is directly caused when motor parameters are mismatched, and the prediction performance of the model is finally affected, so that analysis of parameter sensitivity of MPTC control is necessary. Analysis shows that the influence of inductance and flux linkage on the predicted current is larger, and the influence of resistance on the predicted current is second.

Substituting the formula (2) into the formula (1) and taking L into consideration _d ＝L _q And discretizing the current to obtain a prediction model of the current, wherein the prediction model comprises the following steps:

when a system is subjected to parameter disturbance, the model is changed into:

wherein: deltaR _s ,ΔL _d ,ΔL _q ,Δψ _f The model resistance, inductance, and the deviation between the actual and reference values of the flux linkage, respectively. To simplify the analysis, take a surface-mounted PMSM as an example, there is ΔL _d ＝ΔL _q ＝ΔL _s The predicted current error under the parameter perturbation from equations (17) and (18) is:

wherein: e (E) _d ,E _q The predicted current errors of the d axis and the q axis are respectively, and any parameter R can be known from the above _s ,L _s ,ψ _s Mismatch will have an effect on the predicted current. FIG. 5 shows the parameter error (ΔR) to varying degrees _s ,ΔL _s ,Δψ _s ) With current prediction error (E _d ,E _q ) The relationship between the resistance error change to 3Ω, the inductance error change to 0.01H, and the flux linkage error change to 0.3Wb. As can be seen from fig. 5, the resistance error Δr _s Less influence on the predicted current error, while the inductance error DeltaL _s The influence on the prediction current error is maximum, and the flux linkage error delta phi is the largest _f Only affects the prediction error of the q-axis current, and can cause the given value of the q-axis currentAnd feedback value i _q An inherent offset between them. So that the sensitivity of the motor parameters is L from high to low _s ＞ψ _f ＞R _s 。

Predicted current with one beat delay compensation under parameter mismatch conditionsThe available accurate current +.>And current prediction error E _d ,E _q And the sum represents.

Substituting the above formula into (18) to obtain a predicted current model with one-beat delay compensation when the parameter error exists, wherein the predicted current model is as follows:

wherein: e (E) _d ′,E _q ' predicted current errors with one beat delay compensation for d-axis and q-axis, respectively, are given in FIG. 6Parameter error (ΔR) under the same conditions _s ,ΔL _s ,Δψ _s ) With current prediction error (E _d ′,E _q ' s relation between the two components).

As can be seen from fig. 6, when one beat delay compensation is introduced, the dq-axis current prediction error after the mismatch of the inductance and resistance parameters is further increased, and the q-axis current prediction error after the mismatch of the flux linkage parameters is also increased. Thus, after one beat delay compensation, the overall current prediction error E of the system _d ′,E _q ' both are further expanded, indicating that the predictive performance of the system is degraded, and therefore it is necessary to propose a control method with strong parameter robustness.

1.2 improving FCS-MPTC implementation procedures

Since one beat delay compensation is introduced in the MPTC control process, the system delay is reduced, but the sensitivity of the system to parameter errors is also increased. In order to reduce the influence of parameter mismatch on the prediction performance in the control process, an improved Euler formula is used for correcting the prediction current, and meanwhile, the motor parameters are identified on line so as to reduce the sensitivity of the system parameters.

1.2.1, modified Euler theory

Explicit or implicit Euler methods are common methods for solving PMSM ordinary differential discrete mathematical models, although the calculation amount is small, the precision is low, and the trapezoidal formula can improve the precision, but unknown variables are introduced. The two ideas are combined in actual calculation to obtain an improved Euler formula with a prediction-correction function.

Taking a first-order differential equation x' =f (t, x) as an example, the implementation process of the improved euler method with the pre-estimation-correction function mainly comprises the following two steps:

And a second step of: using predicted values Right end etc. as trapezoid formulaInput and then calculate t _i+1 Final correction value +.>The above pre-estimated-corrected process is the improved Euler method.

the local truncation error due to the ordinary differential equation is defined as e _i ＝x _i -x(t _i ) Wherein x is _i And x (t) _i ) Respectively t _i A predicted value and an actual value of the time instant. So modified Euler method is used at t _i+1 The time truncation error is:

substituting the formula (25) into the formula (24) to obtain:

the improved euler method has second-order precision according to the definition of the local truncation error of the ordinary differential equation, so that the prediction precision can be effectively improved when the improved euler method is used for correcting the PMSM by compensating the prediction current through one beat of delay, and fig. 7 shows an improved euler method control flow for carrying out multiple iterations, and the number of iterations N=1 adopted by the invention is because the calculated amount is increased by the multiple iterations and the secondary iteration precision is similar to that of the first iteration.

1.2.2 improved FCS-MPTC function implementation

In order to reduce the actual calculation amount in the PMSM prediction control process, i is selected in the invention _α ,i _β As state variables and predicts them. Similar to the conventional FCS-MPTC control method, the state variable of the system is x= [ i ] _α i _β ] ^T The output variable is equal to the input variable y=x= [ i ] _α i _β ] ^T The control input is u= [ u ] _α u _β ] ^T Only one-step prediction of N is performed _p =1, parameters to be predictedConversion to the corresponding torque->And stator flux linkage magnitude +.>The cost function is

While the mathematical model of PMSM in the αβ coordinate system can be expressed as:

wherein: u (u) _α ,u _β ,i _α ,i _β Sum phi _α ,ψ _β Stator voltage, current and flux linkage of alpha axis and beta axis respectively, p is differential operator, theta _e Is the electrical angle of the rotor. Due to u _s ＝u _α +ju _β ，i _s ＝i _α +ji _β Discretizing the voltage equation (27) to obtain kThe current prediction model at time +1 is:

in the method, in the process of the invention,for the predicted value of the current at time k+1 using the Euler equation,/I>To use the current correction value, L, obtained by improving the Euler equation _s The inductances of d-axis and q-axis. Predicted current at time k+1 is obtained +.>Then, the flux linkage of the next control period can be predicted by combining the flux linkage equation (29) and the torque equation >And torque->The method comprises the following steps of: />

Cost function J (V) _n ) The optimal matching of flux linkage and torque is mainly considered, flux linkage and torque error values under the action of different voltage vectors are compared and ordered, and an inverter switching sequence corresponding to the optimal voltage vector is obtained through reasonably designed flux linkage weight coefficients. The cost function is defined as:

V _opt ＝argminJ(V _n ) (33)

wherein:and->Reference values for torque and flux linkage, respectively; ζ is defined as the flux linkage weight coefficient; v (V) _n (n=0,., 6) represents a voltage vector; v (V) _opt Is the optimal voltage vector. Wherein the initial value of ζ can be designed according to the weighting principles of torque, flux linkage and the like, namely, ζ=T _N /|ψ _sN |，T _N Is rated for torque, psi _sN Is the flux linkage amplitude under the rated condition; torque reference value->From the rotation speed error n _error Obtained by a PI controller, the flux linkage reference value +.>Based on maximum torque to current ratio (MTPA), it is:

fig. 8 is a modified FCS-MPTC control flow chart, and table 1 shows inverter switching states and phase voltage values corresponding to 8 basic voltage vectors. Substituting different voltage vectors into equation (29) respectively to obtain 8 groups of predicted currents at k+1 timeAnd calculating the corrected predicted current +.>Then obtaining the optimal voltage vector V according to the general calculation flow _opt 。

Table 1 switch switching states and inverter voltage vectors and corresponding phase voltages

1.3, parameter identification method

The traditional RLS method uses a fixed forgetting factor to perform on-line identification on motor parameters, and the speed and the precision of parameter identification cannot be ensured at the same time. The smaller forgetting factor can obtain faster recognition speed, but the accuracy and noise resistance of parameter recognition are reduced, and the larger forgetting factor can improve the accuracy of parameter recognition but also increase the calculated amount so as to reduce the recognition speed. The invention introduces a dynamic forgetting factor based on the traditional RLS method, dynamically adjusts the forgetting factor by utilizing the output difference value of the actual model and the theoretical model, uses a smaller forgetting factor to obtain a faster convergence speed when the output difference value is larger, and uses a larger forgetting factor when the output difference value is smaller so as to improve the accuracy of parameter identification and the noise immunity of the system. The specific method comprises the following steps: rewriting a mathematical model of the PMSM in a dq coordinate system into an RLS standard form of Y=ΘX, wherein Θ is a parameter matrix to be identified, and the dq axis currents of the previous moment and the current momentAnd dq-axis voltage +.>Substituting matrix X, Y to calculate motor parameter identification result +.>And it is used for predicting the current +. >Is calculated by the computer.

wherein: y=x ₁ θ ₁ +x ₂ θ ₂ +···+x _N θ _N . After new data are obtained each time, the least square method is needed to calculate all the data, when the measurement times are increased, the calculated amount is large, the calculated amount in the process can be reduced by the recursive least square method, and on the basis of the measurement result at the last moment, the result is corrected by using the new data measured at the current moment, so that the calculation process is greatly simplified.

Assuming that k sets of X and Y data exist, Θ= [ θ ] is identified by the following set of formal equations ₁ θ ₂ ···θ _N ] ^T ∈R ^N×1 ：

Wherein:for the ith added data (column vector) it is converted into row vector form for easy calculation, i.e +.>Defining the data matrix acquired for the previous k times as(row vector group),>the above can be simplified as:

Y _k ＝X _k Θ (37)

obtaining an estimated value of the equation solution by using a least square methodEstimated parameters->The more accurate the predicted output value of the model +.>The closer to Y _k A corresponding error matrix can be obtained>Whereas the objective of the least squares method is to make the square of the error matrix +.>Minimum. Deriving it can result in the solution of the equation under the least squares method:

/>

Parameter matrix to be identified in the above methodThe problem of excessive data volume is caused by accumulation and iteration of the data, and the least square method needs to be recalculated after new data is acquired. To avoid repeated computation of data, a recursive least squares method is used to identify the matrix of parameters at the previous moment +.>Correcting to obtain identification parameter matrix +.>

Definition of the definitionThen there are:

is obtained by the above methodLet->Then there are:

the updated formula after the kth measurement data is obtained is:

matrix obtained by using the previous k-1 times of measurement dataSum vector B _k-1 I.e. calculate matrix +.>From (41), it can be seen thatObtain->And +.about.39 can be obtained from the formula (39)>Substituting it into the above formula yields the best approximation solution for the recursive least squares method:

due to (A+BCD) ^-1 ＝A ^-1 -A ^-1 B(C ^-1 +DA ^-1 B) ^-1 DA ^-1 In the aboveCan be simplified intoLet K _k ＝P _k x _k ThenThe recursive least squares method is expressed as:

wherein: lambda is more than 0 and less than or equal to 1, and is a fixed forgetting factor introduced in RLS. When lambda is smaller, the weight of the data at the current moment is increased in the iterative process, and the weight of the data at the previous moment is reduced, so that the data iterative process is quickened. When lambda is larger, the data of the last moment is considered more, the convergence speed of the algorithm is slower, and the parameter identification process is more stable.

b) Calculating a dynamic forgetting factor function

In order to solve the problem that the RLS parameter identification method can not ensure the convergence rate and the identification precision at the same time, a dynamic forgetting factor is introduced into the RLS, and the difference epsilon outputted by the theoretical model and the actual model at the current moment is used _k The forgetting factor is dynamically adjusted. The difference epsilon at time k _k Can be expressed as:

wherein: epsilon _k Indicating the parameter identification error caused by noise at the current time. When epsilon _k The convergence speed needs to be increased when the value is larger, so that a larger forgetting factor is used, and the value is epsilon _k Smaller forgetting factors are used to improve the accuracy of the recognition algorithm and noise immunity. Establishing the following dynamic forgetting factor function as：

Wherein: 0 < alpha < 1 is a positive adjustable factor, and gamma > 0. When the error value epsilon _k Forgetting factor lambda at a large time _k Close to alpha, when epsilon _k Less forgetting factor lambda _k Then it is close to 1. The expression thus derived is the dynamic forgetting factor recursive least squares (DFF-RLS) as:

c) DFF-RLS-FCS-MPTC implementation

Substituting the formula (2) into the formula (1) can obtain a discrete mathematical model of the PMSM in the dq coordinate system:

wherein the method comprises the steps of For the stator current at time k+1,/o>And->The d-axis and q-axis currents and voltages at time k, respectively.

To achieve R _s ,L _d ,L _q Psi-shaped material _f Identification of the isoparameter, rewrite (48) to the solution form applicable to RLS:

Y＝ΘX (49)

wherein:

comparing the formula y=xΘ of the DFF-RLS recursion, Y _k Representing one new data added at a time, x _k Representing that only one column vector is added at a time, Y is added two new data at a time in equation (49), and X is added only one column vector at a time, so Y is used _k Representing two new data added simultaneously each time, X _k Representing one column vector added at a time, a DFF-RLS recurrence formula of formula (49) can be obtained as:

Fig. 9 shows the basic control structure of DFF-RLS-FCS-MPTC, including signal measurement, coordinate transformation, PID calculation, RLS parameter identification, current prediction and correction, and optimal voltage vector modulation. Wherein the RLS parameter identification link is performed before the current prediction and correction link, and the current value of the last moment and the current moment is utilizedAnd the voltage value of the last moment +.>Identifying the parameter R _s ,L _d ,L _q Sum phi _f Current for predicting the next time instant>And correcting the predicted current.

The calculation process mainly comprises the following 6 steps:

the first step: when the system is running stably, the dq-axis current i of the previous moment and the current moment is utilized _d (k-1),i _q (k-1) and i _d (k),i _q (k) The previous time dq axis voltage u _d (k-1),u _q (k-1) in combination with (50) calculating a parameter matrix required for MPTC control

And a second step of: using the alpha-beta current i at the present moment _α (k),i _β (k) Sum voltage u _α (k),u _β (k) Identified parameter matrixCalculating a one-beat delay compensation current +.>

And a third step of: identification parameter matrix using equation (30) in combinationCurrent i at the present moment _α (k),i _β (k) Compensating current for one beat delay>Correcting to obtain the predicted current i at the next moment _α (k+1),i _β (k+1)。

Fourth step: using the predicted current i at the next instant _α (k+1),i _β (k+1) and identification parameter matrixCalculating the predicted value T of the torque and flux linkage in combination with equation (31) _e (k+1),ψ _s (k+1). Modulating different voltage vectors to obtain alpha beta axis voltage u under different switch sequences Sw (: i) _α,i (k),u _β,i (k) Repeating the calculation processes from the second step to the fourth step to obtain a torque and flux linkage prediction control set T under different voltage vectors _e,i (k+1),ψ _s,i (k+1)。

Fifth step: predictive control set T for linking torque and flux _e,i (k+1),ψ _s,i (k+1) and reference value T _e ^ref ,Substituting (32) the value-pair function J (V _n ) And (5) performing calculation.

Sixth step: for the value function J (V _n ) Sequencing, and obtaining the optimal voltage vector V according to the step (33) _opt The switch under action switches state and uses the switch as a control signal of the three-phase inverter.

The fifth and sixth steps in the above process can realize the optimum voltage vector V _opt Switching voltage sequence j _opt FIG. 10 shows the optimum voltage vector V in the improved FCS-MPTC control _opt Is selected according to the selection process. First using alpha beta axis current i _α (k),i _β (k) Different voltage vector groups V _j (j=0,., 6) corresponding αβ axis voltage u _α,j (k),u _β,j (k) Calculating the predicted current i corresponding to different voltage vectors at the next moment _α,j (k+1),i _β,j (k+1). The obtained predicted current i _α,j (k+1),i _β,j (k+1) and motor parameter R obtained by DFF-RLS method _s ,L _d ,L _q ,ψ _f Substituting into flux linkage and torque equation to calculate to obtain multiple groups of predicted values T of torque and flux linkage _e,j (k+1),ψ _s,j (k+1). Predictive value T using torque and flux linkage _e,j (k+1),ψ _s,j (k+1) calculating a cost function J (V) _j ) And comparing and sorting them to obtain a voltage vector V for minimizing the cost function _opt Switching voltage sequence j _opt The optimal voltage vector V to be obtained after the complete calculation of the voltage vector _opt Optimal switching voltage sequence j _opt Minimum value J of cost function _min And outputting.

The function implementation of the DFF-RLS parameter identification algorithm is shown in fig. 11 below. The first step is to define the local variable matrix at the last moment used in the DFF-RLS parameter identification process, including the parameter identification matrix Covariance matrix P (k-1), dq axis voltage matrix i _dq (k-1) dq-axis voltage matrix u corresponding to different voltage vectors _dq (k-1); the second step is to assign values to the matrix variables defined at the last moment, and simultaneously to the dq-axis current and voltage matrix i at the current moment _dq (k),u _dq (k) Initializing and setting positive adjustable parameters alpha, gamma, and sampling period T of the system _s Is set to 5 multiplied by 10 ^-5 s; the third step is to calculate the matrices X and Y and the dynamic forgetting factor lambda (k) according to formulas (48) - (50) to obtain the error matrix P (k) and the parameter matrix ∈in the recursive expression>The fourth step is to use the identification parameter matrix +.>Extracting motor parameters R from matrices A, B, C _s ,L _d ,L _q Psi-shaped material _f The method comprises the steps of carrying out a first treatment on the surface of the The fifth step is to add the parameter matrix of the current moment after the system is in the steady state>P(k),i _dq (k) U _dq (k) Initialization matrix +.>P(k-1),i _dq (k-1) and u _dq (k-1) facilitating the iterative computation of the next function; the sixth step is to identify the motor parameter +.>And judging that the motor parameter is set to zero when the identification parameter is invalid, so that the influence of an error parameter identification result on the subsequent FCS-MPTC control process is avoided.

d) Update condition for parameter identification

The fifth step of the DFF-RLS parameter identification algorithm needs to judge the running state of the motor, and when the system is running stably, the identification parameters are updated, so that the next time is realized Iterative calculation; when the system is in the running stage of dynamic change of rotating speed and load, the identification result R at the last moment is continuously used _s (k-1),L _d (k-1),L _q (k-1) and ψ _f (k-1) controlling the motor. The invention utilizes the rated rotation speed n _ref The difference value with the feedback rotating speed n is used for judging whether the PMSM is in a stable running state or not, and the running state function E of the system _n The expression is:

wherein: η is a PMSM steady operation judgment threshold to be designed, and when the rotation speed error is smaller than the threshold, the motor is indicated to be in a steady operation state, and at this time E _n =1; when the rotating speed error is larger than the threshold value, the motor is in a dynamic running state, and the DFF-RLS parameter identification algorithm does not update the parameters any more, but continues to control the motor by using the previous identification result.

Fig. 12 shows a time series distribution diagram of DFF-RLS-FCS-MPTC control. First using i _α (k-1),i _β (k-1)，u _α (k-1),u _β (k-1) and i _α (k),i _β (k) Obtaining a parameter matrixThen utilize i _α (k),i _β (k)，u _α (k),u _β (k) And +.>Predicting the compensation current at time k+1 +.>And correcting the current to obtain correction current i at time k+1 _α (k+1),i _β (k+1) and finally correcting the current i _α (k+),i _β (k+1) and matrix->Substituting into flux linkage and torque equation to calculate T _e (k+1),ψ _s (k+1)。

The PMSM multi-mode switching model prediction control system provided by the embodiment of the invention comprises:

The embodiment of the invention has a great advantage in the research and development or use process, and has the following description in combination with data, charts and the like of the test process.

1. Simulation results of control method

To examine the control performance of the improved FCS-MPTC with parameter identification, a simulation model of the conventional FCS-MPTC and the improved FCS-MPTC based on DFF-RLS parameter identification were respectively built in MATLAB/Simulink. And analyzing the system response of the traditional FCS-MPTC and the improved FCS-MPTC under parameter mismatch and the steady-state performance of the controller under different working conditions, and simultaneously verifying the parameter identification performance of the proposed DFF-RLS algorithm and the system parameter robust performance when the motor parameter change is large. Table 2 gives the specific parameters of the PMSM used in the simulation process.

Table 2 PMSM parameters used in simulation model

1.1 System response under parameter mismatch

For comparing the traditional FCS-MPTC control method with the improved FCS-MPTC control method with parameter identification provided by the invention, the control performance of the improved FCS-MPTC control method under the condition of motor parameter mismatch is improvedThe same controller parameters can be used in the simulation model, wherein the proportional and integral gains of the PI controller are set to k, respectively _p ＝0.02，k _i The upper and lower limits of the output saturator are set to ± 90 =0.3. The discrete sampling period of the system is T _s ＝5×10 ^-6 s, the flux linkage weight coefficient in the cost function is ζ=20, the positive adjustable parameter alpha=0.96 and gamma=2 in the dynamic forgetting factor function, and the steady operation judgment threshold in the state function is set to be η=0.02.

Fig. 13 shows a simulation model of a conventional FCS-MPTC and an improved FCS-MPTC with parameter identification as proposed by the present invention. When the system is in a stable running state, the inductor L is improved in the FCS-MPTC due to the introduction of the DFF-RLS parameter identification algorithm _d ,L _q Magnetic linkage psi _f On-line identification is carried out, and current i is predicted at the next moment _α (k+1),i _β And (k+1) is calculated, so that the influence of model parameter mismatch on system performance is reduced to a great extent.

FIG. 14 is a comparison of the system performance of a conventional FCS-MPTC and the improved FCS-MPTC method with parameter identification according to the present invention under constant operating conditions and with different degrees of parameter mismatch. Because the parameter identification algorithm is introduced, the current prediction of the improved FCS-MPTC control method is more accurate, and the stator inductance L is improved _d ,L _q Permanent magnet flux linkage ψ _f The problem of system performance degradation caused by parameter mismatch is also optimized to different degrees. Dq-axis current i obtained by using the conventional FCS-MPTC method under a simulation condition in which the reference rotation speed is fixed at 1000rpm and the system load is 0.2Nm _d ,i _q Three-phase current i of system _a ,i _b ,i _c System rotational speed n and electromagnetic torque T _e As shown in fig. 14 (a) - (d), and fig. 14 (e) - (h) are simulation results obtained by the improved FCS-MPTC method with parameter identification according to the present invention under the same working conditions. Comparing fig. 14 (c) with fig. 14 (g), it can be seen that the steady-state rotational speed error (SSE) of the conventional FCS-MPTC method is 10rpm, whereas the rotational speed error of the improved FCS-MPTC method proposed by the present invention in steady state is only-1.5 rpm, and the steady-state tracking error of the latter is significantly reduced. Comparing FIG. 14 (b) with FIG. 14 (f) it is known that the three-phase current Total Harmonic Distortion (THD) obtained using the modified FCS-MPTC method is much smaller than that obtained using the conventional FCS-MPTC method. The torque observations of the two methods under rated load are shown in fig. 14 (d) and 14 (h), respectively, and it can be seen that the torque response curve obtained by using the method of the present invention does not oscillate at the initial stage of the system, and the torque error after the system is stabilized is smaller than that of the conventional FCS-MPTC method. Fig. 14 (i) -fig. 14 (L) are the inductance L using the conventional FCS-MPTC and the modified FCS-MPTC methods, respectively _d ,L _q Magnetic linkage psi _f Current THD and torque ripple T at a nominal value of k times _ri Is a comparison result of (a). The THD value of the current can be calculated by the formula (52), the current waveforms under different inductances and flux linkage parameters are subjected to FFT analysis within the range of 0.01s-0.025s after the system is stable in operation, and the fundamental frequency and the maximum frequency are respectively set to 66.6Hz and 5000Hz. Torque ripple T _ri Can be calculated from formula (53), wherein T _max ,T _min Maximum and minimum values of torque in 0.01s-0.025s respectively, T _ref The average value of the reference torque over the same time is taken. As can be seen from fig. 14 (i) -14 (L), the proposed improved FCS-MPTC method with parameter identification is applied to the inductor L as the k value increases _d ,L _q Magnetic linkage psi _f Current THD and system torque ripple T at parameter mismatch _ri Are smaller than the conventional FCS-MPTC method, indicating that the proposed control method has varying degrees of suppression of current and torque ripple caused by parameter mismatch.

The current THD value may be used to describe the magnitude of the current ripple and may be expressed as:

wherein: i _hmn Representing harmonic components; i _fdm Represents a fundamental frequency component; i _n Representing the nth harmonic.

Also torque ripple T _ri The following formal definition may be used:

wherein: t (T) _max Is the maximum value of torque observation; t (T) _min Observing a minimum value for torque; t (T) _ref Then it is the torque reference.

Table 3 shows the current THD values and torque ripple T of the conventional FCS-MPTC and the improved FCS-MPTC method of the present invention under mismatch of inductance parameters _ri And table 4 shows the numerical comparison obtained under mismatch of flux linkage parameters using two types of methods.

TABLE 3 specific results of current THD values and torque ripple for inductance parameter mismatch

TABLE 4 specific results of current THD values and torque ripple for flux linkage parameter mismatch

1.2 steady-state Performance analysis of a controller under multiple conditions

In order to verify the control performance of the improved FCS-MPTC method with parameter identification under complex working conditions such as multi-stage rotating speed, variable load and the like, a multi-mode switching controller is built by using a Stateflow toolbox in Simulink for switching the complex working conditions, and meanwhile, the parameters of the controller are adjusted on line, so that the steady-state performance of the system under the multi-working condition running condition is further improved. The multi-mode switching controller can adjust the model reference rotating speed and the load in real time according to the type of the input signal, so that model reference input under complex working conditions is obtained, and the optimal controller parameters under different working conditions are different, so that the multi-mode switching controller can write the optimal controller parameters into the model after actively identifying the working conditions, and the online updating of the parameters is realized. Fig. 15 is a state flow implementation detail of the PMSM multimode switching controller operating mode identification and parameter update subsystem under Matlab. In order to test the system performance of the improved FCS-MPTC method provided by the invention after the multi-mode switching controller is introduced, simulation results of the FCS-MPTC model based on the multi-mode switching controller under different working conditions are respectively provided.

1.2.1 rotor speed step Change under multimode switching controller

FIG. 16 is a graph showing the speed tracking performance of the proposed modified FCS-MPTC method at a step change in rotational speed at 0.2Nm load torque, with a sudden change from 1000rpm to 1500rpm at 0.025 s. As can be seen from fig. 6 (a), when the rotation speed is suddenly changed, the multimode switching controller can load the optimal PI parameter into the FCS-MPTC model according to the change of the current reference rotation speed, so that the system rotation speed can better track the change of the reference rotation speed, and a larger speed tracking error and overshoot occur in the system rotation speed adopting the constant PI parameter. Fig. 16 (b) shows dq-axis stator current obtained by using a multi-mode switching controller at the time of a rotation speed step change. Fig. 16 (c) shows the tracking result of the system electromagnetic torque and the corresponding torque tracking error (maximum tracking error at the time of the rotation speed step change, mte=0.18 Nm). The system three-phase currents with phase sequence acceleration at different rotational speed stages are shown in fig. 16 (d).

1.2.2 dynamic changes in rotor speed under multimode switching controller

The speed tracking performance at a dynamic change in rotational speed under a load of 0.2Nm is shown in FIG. 17, where the reference rotational speed is suddenly changed to 1500rpm at 0.01s, returned to 1000rpm at 0.025s, and reduced to 600rpm at 0.04 s. The proposed rotational speed and the general rotational speed can accurately track dynamic changes of the speed, but tracking performance of the proposed rotational speed is significantly better than that of the general rotational speed (see (a) of fig. 17). Fig. 17 (b) shows dq-axis stator current when the rotational speed is dynamically changed. Fig. 17 (c) shows the torque tracking result and the torque tracking error (mte= -0.27Nm at 0.025 s). The three phase currents of the system with phase sequence deceleration at different rotational speed stages are shown in fig. 17 (d).

1.2.3 rotor speed ramp under multimode switching controller

The speed tracking performance of the proposed speed and the general speed following the reference speed ramp at the rated load of 0.2Nm is shown in fig. 18. The error of the proposed rotation speed when the reference rotation speed reaches 1500rpm is smaller than the general rotation speed (see (a) of fig. 18, the rotation speed tracking error is-4 rpm). Fig. 18 (b) shows the dq-axis current tracking result when the reference rotation speed is ramped. Torque tracking performance and tracking error (mte=0.3 Nm at 0.035 s) are shown in fig. 18 (c). The system three-phase current with phase sequence acceleration after the increase in rotational speed is shown in fig. 18 (d). Increasing the reference speed from 1000rpm to 1500rpm at a constant load of 0.2Nm accelerates the phase sequence of the three-phase current, but the overall tracking performance meets the system requirements.

1.2.4 dynamic load Change under multimode switching controller

The speed tracking performance of the proposed rotational speed and the general rotational speed following the dynamic change of the load at the reference rotational speed of 1000rpm is shown in fig. 19 (a), the load is increased from 0Nm to 0.2Nm at 0.01s, the load is decreased to 0.1Nm at 0.025s, and the load is removed at 0.04 s. As is clear from fig. 19 (a), the normal rotation speed cannot normally track the reference rotation speed (the rotation speed tracking error reaches-28 rpm) when the load increases to 0.2 Nm. Fig. 19 (b) gives good dq-axis current tracking characteristics. Fig. 19 (c) shows torque tracking performance and tracking error (mte= -0.15Nm at 0.01 s). Fig. 19 (d) is a system three-phase current, the current amplitude is reduced from 7A to 4.5A due to the load being reduced from 0.2Nm to 0.1 Nm.

1.2.5 comparison of Performance at dynamic Change of reference speed

When the reference rotation speed dynamically changes, the dq-axis current, the system three-phase current and the torque tracking performance corresponding to a general FCS-MPTC method adopting fixed PI control parameters and the proposed FCS-MPTC method using a multi-mode switching controller are compared. Fig. 20 shows a comparison of simulation results of the above two cases when the rotational speed is dynamically changed. As can be seen from the graph, the dq-axis current, the three-phase current and the torque ripple are smaller than those of the simulation results under the general condition when the rotation speed of 0.025s suddenly changes. Tables 5 and 6 respectively show dynamic response parameters of the two methods under different working conditions, including a rotational speed Steady State Error (SSE) and a Maximum Torque Error (MTE), and the results show that the dynamic response speed of the proposed FCS-MPTC method under different working conditions is higher, no abrupt change occurs in the rotational speed, and the fluctuation of load torque is smaller.

TABLE 5 dynamic response parameters of general FCS-MPTC methods under different conditions

Table 6 shows dynamic response parameters of FCS-MPTC method under different working conditions

1.3, parameter identification Performance analysis

In order to study the parameter identification performance of the proposed DFF-RLS method under static and dynamic working conditions, a system simulation model based on the DFF-RLS parameter identification method shown in figure 21 is built. The static parameter identification performance when the load and the rotating speed are constant and the dynamic parameter identification performance when the load and the rotating speed are suddenly changed are researched. At the same time, for the traditional FCS-MPTC method and the DFF-RLS-FCS-MPTC method proposed by the invention, the current THD value and the torque ripple T under the changes of motor parameters, load and rotating speed _ri Analysis was performed.

1.3.1 static parameter identification Performance of DFF-RLS

The parameter identification performance of the DFF-RLS-FCS-MPTC was analyzed in steady state. FIGS. 22 and 23 show the stator resistance R at 1000rpm, 0.1Nm load and 1500rpm load, respectively _s Inductance L _d ,L _q Magnetic linkage psi _f Is a parameter identification curve of (a).

To analyze static parameter identification performance of the DFF-RLS method, average parameter identification error P is used _aer And maximum parameter identification error P _mer And evaluating the identification result. Average parameter identification error P _aer Can be given by the formula (54):

maximum parameter identification error P _mer Then it is derived from the following equation:

wherein P represents the motor parameter R to be identified _s ,L _d ,L _q Sum phi _f ；P _ref Is the standard value of the identification parameter;is an estimate of the identification parameter.

As can be seen from FIGS. 22 and 23, the identification result of the DFF-RLS method provided by the present invention on the parameters within 0.025s-0.05s is basically consistent with the standard value, the identification curve in steady state does not have larger fluctuation, and the average parameter identification error P of the system _aer And maximum parameter identification error P _mer All less than 0.5%. Resistance R under two working conditions _s And magnetic linkage psi _f The parameter identification performance is better than that of the inductance L _d ,L _q Wherein the flux linkage parameter ψ _f Preferably at 1000rpm and 0.1Nm (ψ) _f ) _aer 0.00098%, and a maximum parameter identification error (ψ) at 1500rpm and 0.2Nm _f ) _mer Only 0.25%. Inductance L _d ,L _q Is relatively stable, and the average parameter identification error (L _d ,L _q ) _aer Maximum parameter identification error (L) _d ,L _q ) _mer Both 0.43%.

The parameter identification performance of the proposed DFF-RLS parameter identification method under different rotating speeds and load working conditions is researched, and a comparison result of static parameter identification performance under different levels of rotating speeds and loads is shown in a figure 24. At load T _L The motor parameter identification performance when the rotation speed n is varied from 500rpm to 1500rpm is shown in (a) (b) of fig. 4. As can be seen from fig. 24 (a), the resistance R increases with increasing rotation speed _s The average parameter identification error of (a) is continuously increased, and the flux linkage ψ in (b) of fig. 24 _f Is subject to maximum parameter identification errorThe effect of the rotational speed variation is most pronounced, its maximum parameter identification error (ψ _f ) _mer Up to 0.5538%, and the parameter identification error (L) _d ,L _q ) _aer Sum (L) _d ,L _q ) _mer Substantially stabilized at about 0.43% when the rotational speed was varied. Fig. 24 (c) (d) shows the load T at a rotational speed n=1000 rpm _L From the motor parameter identification performance at the time of 0.1Nm to 0.2Nm variation, the average identification error P of the DFF-RLS algorithm to the motor parameter can be known from FIG. 24 (c) _aer Less affected by load variations, wherein the average parameter of the inductance identifies errors (L _d ) _aer Up to 0.43296%, while in (d) of fig. 24 (ψ) _f ) _mer Sum (L) _q ) _mer With increasing load, there is an increase in the degree of maximum parameter identification error (ψ) of flux linkage _f ) _mer Up to 0.7155%.

1.3.2 dynamic parameter identification of DFF-RLS analysis of the dynamic parameter identification performance of the proposed DFF-RLS method under load and speed abrupt changes, FIG. 25 shows that at speed n=1000 rpm, load T _L The motor parameter identification curve when 0.025s is changed from 0.1Nm to 0.15Nm, and the change of the load has little influence on the identification result of the motor parameter, wherein the identification error delta R of the resistance parameter _so At most only 0.007 omega. Fig. 26 shows the load T _L As can be seen from comparison of fig. 25, the parameter identification curve at a rotation speed n of 0.025s from 1000rpm to 1050rpm at 0.1Nm, and the resistance R is caused by the abrupt change of the rotation speed _s Inductance L of q axis _q Magnetic linkage psi _f The identification curves of the resistance parameters can generate a certain fluctuation and still can quickly recover to the standard value in a short time, wherein the maximum identification error delta R of the resistance parameters _so Up to 0.8187 Ω, while the identification curve of d-axis inductance is minimally affected by the change in rotational speed, ΔL _do Only 2.6X10 ^-6 H. FIG. 27 shows the load T at 0.025s _L As can be seen from comparison of FIG. 25 and FIG. 26, all the motor parameter identification curves have different degree of fluctuation when the rotation speed n is suddenly changed, wherein the identification result of the resistance parameter is equal to the standard value R _s Error Δr between =1.02Ω _so Reaches 33.49 omega, and the identification error delta phi of the flux linkage parameter _fo And also to 0.305Wb. From the above results, although the identification result of the motor parameter is affected by the change of the rotation speed and the load, the motor parameter can quickly return to the standard value in a short time, and a certain identification accuracy is ensured.

1.3.3 comparison of Performance of FCS-MPTC and DFF-RLS-FCS-MPTC

To analyze the effect of motor parameter mismatch on system performance in the DFF-RLS method, motor parameter R is calculated _s ,L _d ,L _q ,ψ _f Are all set to be k times standard value, and the current THD value and the torque ripple T are set under the same operation condition _ri A comparison is made. Reference speed n=1000 rpm, load T _L =0.2 Nm, the coefficient k varies from 0.5 to 1.5 every 0.1. FIG. 28 shows the current THD and torque ripple T when the motor parameter is k times the standard value _ri Is a comparison result of (a). Wherein the current THD value is i in the range of 0.025s to 0.04s _a The waveform is calculated with a base frequency of 66.6Hz and a maximum frequency of 5000Hz, and torque ripple T _ri Then according to a torque T within 0.005 s-0.05 s _e Reference value T of _ref Obtained. As can be seen from fig. 28, the flux linkage parameter ψ _f The variation of (1) versus current THD and torque ripple T _ri The effect of (2) is greatest when ψ _f The maximum value of the current THD is 12.32% at 0.5 times the standard value, and the torque ripple T _ri Also reaches 23.49%. Resistance parameter R _s Varying the pair current THD and torque ripple T _ri The influence of (2) is small, and as the k value increases, the current THD and the torque ripple T show an ascending trend _ri The maximum values of (2) are 4.24% and 1.399%, respectively.

The current THD and the torque ripple T are related to the change of the flux linkage and the inductance _ri The influence of the method is large, and the resistor R is used for comparing the system performance of the traditional FCS-MPTC method and the DFF-RLS-MPTC method proposed by the invention _s Set to 0.5 times the standard value and compare the current and torque responses of the two methods. At rotational speed n=1000 rpm, load T _L Current i of FCS-MPTC and DFF-RLS-MPTC methods at 0.1Nm _a And torque T _e And standard ofThe values are compared and FIG. 29 shows current and torque waveforms based on the DFF-RLS-MPTC and conventional FCS-MPTC methods. And switching from FCS-MPTC to DFF-RLS-FCS-MPTC for control by adopting a DFF-RLS parameter identification algorithm at 0.025 s. As can be seen from the graph, the performance of the DFF-RLS-MPTC is better than that of the traditional FCS-MPTC method, and the current THD value is reduced from 2.89% to 2.85%, and the torque ripple T is generated at the same time _ri From 0.18% to 0.12%.

FIG. 30 shows the current THD and torque ripple T of the FCS-MPTC and DFF-RLS-MPTC methods at more speeds and loads _ri Wherein (a) (b) of FIG. 30 is applied to the load T for both methods _L =0.1 Nm, current THD and torque ripple T at every 100rpm change of rotation speed n from 800rpm to 1200rpm _ri In comparison, it is clear from FIG. 30 (a) that the current THD values for the two methods under the same load and rotational speed operating conditions differ little, but the torque ripple for the DFF-RLS-MPTC is significantly smaller, with a current THD value of only 2.58% at 1000 rpm. The current THD value and the torque ripple T obtained by the two methods are used for controlling the current THD value and the torque ripple T _ri And (3) respectively comparing the difference value with the corresponding standard value under the rated working condition to obtain the relative error value of the current THD and the torque pulsation. Fig. 30 (c) and (d) shows two methods at a rotational speed of n=1000 rpm, load T _L Current THD and torque ripple T at every 0.02Nm variation from 0.11Nm to 0.19Nm _ri Is a comparison result of (a). As can be seen from (c) and (d) of fig. 30, as the load increases, the current THD values of both methods are continuously reduced, but the current THD values of DFF-RLS-MPTC are smaller than those of the conventional FCS-MPTC method, and the torque ripple T of both methods is smaller _ri The DFF-RLS-MPTC method is more stable on fluctuation of torque pulsation, which shows that the proposed DFF-RLS method has better dynamic performance.

The foregoing is merely illustrative of specific embodiments of the present invention, and the scope of the invention is not limited thereto, but any modifications, equivalents, improvements and alternatives falling within the spirit and principles of the present invention will be apparent to those skilled in the art within the scope of the present invention.

Claims

1. The PMSM multimode switching model prediction control method is characterized in that a recursive least square method DFF-RLS is utilized to conduct online identification on motor parameters and update the motor parameters to a system model in real time; identifying motor parameters including stator resistance, inductance and permanent magnet flux linkage by using an RLS method, and using the identification parameters for calculating a predicted current value; after one beat delay compensation is performed on the predicted current at the time k, the current at the next time is predicted and corrected by using an improved Euler formula with a prediction-correction function.

2. The PMSM multimode switching model predictive control method of claim 1, wherein the PMSM multimode switching model predictive control method comprises the steps of:

And a second step of: using the alpha-beta current i at the present moment _α (k),i _β (k) Sum voltage u _α (k),u _β (k) Identified parameter matrixCalculating one beat delay compensation current by combining formula>

And a third step of: identifying parameter matrices using equalityCurrent i at the present moment _α (k),i _β (k) Compensating current for one beat delay>Correcting to obtain the predicted current i at the next moment _α (k+1),i _β (k+1)；

Fourth step: using the predicted current i at the next instant _α (k+1),i _β (k+1) and identification parameter matrixCalculation of the predicted value T of the torque and flux linkage in combination with the equation _e (k+1),ψ _s (k+1); modulating different voltage vectors to obtain alpha beta axis voltage u under different switch sequences Sw (: i) _α,i (k),u _β,i (k) Repeating the calculation processes from the second step to the fourth step to obtain a torque and flux linkage prediction control set T under different voltage vectors _e,i (k+1),ψ _s,i (k+1)；

Fifth step: predictive control set T for linking torque and flux _e,i (k+1),ψ _s,i (k+1) and reference valueSubstituted intermediate value function J (V _n ) Calculating;

sixth step: for the value function J (V _n ) Performing rowAcquiring an optimal voltage vector V according to the sequence _opt The switch under action switches state and uses the switch as a control signal of the three-phase inverter;

V _opt ＝argminJ(V _n )。

3. The PMSM multimode switching model predictive control method of claim 2, wherein the parameter sensitivity analysis of the PMSM multimode switching model predictive control method includes three necessary motor parameters, resistance R, in the MPTC predictive model _s Inductance L _d,q Rotor permanent magnet flux linkage ψ _f When the motor parameters are not matched, inaccuracy of the predicted current is directly caused, and the prediction performance of the model is finally affected; the prediction model for the current obtained by discretization is as follows:

wherein: deltaR _s ,ΔL _d ,ΔL _q ,Δψ _f The deviation between the actual value and the reference value of the model resistance, the inductance and the magnetic linkage are respectively obtained, and the predicted current error under parameter disturbance is as follows:

Wherein: e's' _d ,E′ _q The predicted current errors for d-axis and q-axis with one beat delay compensation, respectively.

4. The PMSM multimode switching model predictive control method of claim 2, wherein the modified euler method implementation procedure of the PMSM multimode switching model predictive control method includes the following two steps:

And a second step of: using predicted valuesAs the input of the right end equation of the trapezoid equation, and further calculates t _i+1 Final correction of time of dayValue->The pre-estimation and correction process is an improved Euler method;

f(t _i+1 ,x _i+1 )＝f(t _i +Δt,x _i +Δt·f(t _i ,x _i ))

＝f(t _i ,x _i )+Δt·f _t ′(t _i ,x _i )+(Δt·f(t _i ,x _i ))f′ _x (t _i ,x _i )+Ο(Δt ² )

＝x′(t _i )+Δt·x″(t _i )+Ο(Δt ² )

the method comprises the following steps:

5. the PMSM multimode switching model predictive control method of claim 2, wherein the PMSM multimode switching model predictive control method is selected from i _α ,i _β As a state variable and predicting it, the mathematical model of PMSM in the αβ coordinate system is expressed as:

in the method, in the process of the invention,for the predicted value of the current at time k+1 using the Euler equation,/I>To use the current correction value, L, obtained by improving the Euler equation _s The inductances are d axis and q axis respectively; predicted current at time k+1 is obtained +.>Then, the flux linkage ++of the next control period can be predicted by combining the flux linkage equation and the torque equation>And torque->The method comprises the following steps of:

cost function J (V) _n ) Considering the optimal matching of flux linkage and torque, comparing and sequencing flux linkage and torque error values under the action of different voltage vectors, and obtaining an inverter switching sequence corresponding to the optimal voltage vector through reasonably designed flux linkage weight coefficients, wherein a cost function is defined as follows:

V _opt ＝argminJ(V _n )

wherein:and->Reference values for torque and flux linkage, respectively; ζ is defined as the flux linkage weight coefficient; v (V) _n (n=0,., 6) represents a voltage vector; v (V) _opt Is the optimal voltage vector. Wherein the initial value of ζ can be designed according to the weighting principles of torque, flux linkage and the like, namely, ζ=T _N /|ψ _sN |，T _N Is rated for torque, psi _sN Is the flux linkage amplitude under the rated condition; torque reference value->From the rotation speed error n _error Obtained by a PI controller, the flux linkage reference value +.>Based on the maximum torque current ratio MTPA:

substituting different voltage vectors into the equation respectively to obtain 8 groups of predicted currents at the time of k+1And calculating the corrected predicted current +.>Obtaining an optimal voltage vector V according to a calculation flow _opt 。

6. The PMSM multimode switching model predictive control method of claim 2, wherein the PMSM multimode switching model predictive control method rewrites a mathematical model of the PMSM in a dq coordinate system to an RLS standard form of y=Θx, wherein Θ is a parameter matrix to be recognized, and dq axis currents of a previous time and a current time are calculatedAnd dq-axis voltage +.>Substituting matrix X, Y to calculate motor parameter identification result +.>And it is used for predicting the current +.>Is calculated;

there are k sets of X and Y data, and Θ= [ θ ] is identified by the following set of formal equations ₁ θ ₂ ··· θ _N ] ^T ∈R ^N×1 ：

Wherein:for the ith added data, the calculation converts it into row vector form, i.eThe data matrix of the first k acquisitions is defined as +.> The above can be simplified as:

Y _k ＝X _k Θ

obtaining an estimated value of the equation solution by using a least square methodEstimated parameters->The more accurate the predicted output value of the modelThe closer to Y _k Obtaining a corresponding error matrix->Whereas the objective of the least squares method is to make the square of the error matrix +.>Least, deriving the solution of the equation under the least square method is as follows:

parameter matrix to be identifiedThe problem of overlarge data volume caused by accumulation and iteration of data is solved, and the least square method is used for calculating again after new data is acquired, and the recursive least square method is used for identifying a matrix +_ of parameters at the previous moment>Correcting to obtain identification parameter matrix +.>

Definition of the definitionThen there are:

obtaining the productLet->Then there are:

the updated formula after the kth measurement data is obtained is:

Matrix obtained by using the previous k-1 times of measurement dataSum vector B _k-1 I.e. calculate matrix +.>From the formulaKnow->Obtain->And is composed ofObtainingSubstituting it into the optimal approximate solution of the recursive least squares method is:

due to (A+BCD) ^-1 ＝A ^-1 -A ^-1 B(C ^-1 +DA ^-1 B) ^-1 DA ^-1 In the aboveSimplified intoLet K _k ＝P _k x _k The recursive least squares method is expressed as:

b) Calculating a dynamic forgetting factor DFF function

Introducing a dynamic forgetting factor into the RLS, and outputting a difference epsilon according to a theoretical model and an actual model at the current moment _k Dynamically adjusting forgetting factor, difference epsilon at time k _k Expressed as:

wherein: 0 < alpha < 1 is a positive adjustable factor, and gamma is greater than 0, when the error value epsilon _k Forgetting factor lambda at a large time _k Close to alpha, when epsilon _k Less forgetting factor lambda _k Then close to 1, the expression for obtaining the dynamic forgetting factor recursive least squares method DFF-RLS is:

c) DFF-RLS-FCS-MPTC implementation

will be%Formula (ii) is rewritten as a solution for RLS:

Y＝ΘX；

wherein:

7. A computer device comprising a memory and a processor, the memory storing a computer program which, when executed by the processor, causes the processor to perform the PMSM multimode switching model predictive control method of any one of claims 1 to 6.

8. A computer-readable storage medium storing a computer program which, when executed by a processor, causes the processor to perform the PMSM multimode switching model predictive control method of any one of claims 1 to 6.

9. An information data processing terminal, characterized in that the information data processing terminal is configured to implement the PMSM multimode switching model predictive control method according to any one of claims 1 to 6.

10. A PMSM multimode switching model predictive control system based on the PMSM multimode switching model predictive control method according to any one of claims 1 to 6, characterized in that said PMSM multimode switching model predictive control system includes: