CN116505824A - Permanent magnet synchronous motor control method based on double-prediction control - Google Patents
Permanent magnet synchronous motor control method based on double-prediction control Download PDFInfo
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
- H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
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- G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
- G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
- G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance
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- H02P21/18—Estimation of position or speed
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- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
- H02P25/00—Arrangements or methods for the control of AC motors characterised by the kind of AC motor or by structural details
- H02P25/02—Arrangements or methods for the control of AC motors characterised by the kind of AC motor or by structural details characterised by the kind of motor
- H02P25/022—Synchronous motors
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- H02P27/00—Arrangements or methods for the control of AC motors characterised by the kind of supply voltage
- H02P27/04—Arrangements or methods for the control of AC motors characterised by the kind of supply voltage using variable-frequency supply voltage, e.g. inverter or converter supply voltage
- H02P27/06—Arrangements or methods for the control of AC motors characterised by the kind of supply voltage using variable-frequency supply voltage, e.g. inverter or converter supply voltage using dc to ac converters or inverters
- H02P27/08—Arrangements or methods for the control of AC motors characterised by the kind of supply voltage using variable-frequency supply voltage, e.g. inverter or converter supply voltage using dc to ac converters or inverters with pulse width modulation
- H02P27/12—Arrangements or methods for the control of AC motors characterised by the kind of supply voltage using variable-frequency supply voltage, e.g. inverter or converter supply voltage using dc to ac converters or inverters with pulse width modulation pulsing by guiding the flux vector, current vector or voltage vector on a circle or a closed curve, e.g. for direct torque control
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- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
- H02P2207/00—Indexing scheme relating to controlling arrangements characterised by the type of motor
- H02P2207/05—Synchronous machines, e.g. with permanent magnets or DC excitation
- H02P2207/055—Surface mounted magnet motors
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Abstract
The invention discloses a permanent magnet synchronous motor control method based on double prediction control, which comprises the following steps: the invention researches a current loop part, optimizes the motor current by using a dead beat prediction control algorithm, introduces a model prediction algorithm into a speed loop, determines a system state variable, a design sliding mode surface and an approach law function, solves corresponding control output, and finally proves the stability of the motor by using a Lyapunov equation; and introducing a model prediction control algorithm into the speed loop, performing discretization on the reference track, performing two-step prediction, adding model error correction, adopting a quadratic performance index as an evaluation function, and finally obtaining a control law. The invention controls the motor speed by using a model prediction algorithm aiming at the speed loop part to obtain better dynamic and static control effects, and the PMSM system has faster dynamic response and stronger load disturbance resistance.
Description
Technical Field
The invention relates to information and automatic control, in particular to a permanent magnet synchronous motor control method based on double prediction control.
Background
The permanent magnet synchronous motor is widely applied to various fields of railway traction, aerospace, machine tools, military and the like due to the advantages of high efficiency, high power density, high power factor and the like. Under the premise, the traditional control method is more difficult to meet the high-performance control requirement, and a high-performance alternating current motor control strategy is highly required to cope with the control occasion with higher requirements. Dead beat predictive control is widely used in the field of motor control in many advanced control techniques due to its simple structure and ease of handling complex nonlinear systems.
Disclosure of Invention
The invention aims to: the invention aims to provide a permanent magnet synchronous motor control method with good steady-state static difference performance and based on double prediction control, so that more general performance, faster dynamic response and stronger load disturbance resistance are provided.
The technical scheme is as follows: the invention discloses a permanent magnet synchronous motor control method based on double prediction control, which comprises the following steps:
(1) Establishing a mathematical model of the permanent magnet synchronous motor: in the PMSM control system, a surface-mounted permanent magnet synchronous motor is adopted as a research object, and related formulas are deduced from the voltage, the AC/DC speed, the torque and the mechanical motion equation 4 in a double synchronous rotation coordinate system.
(1.1) dead beat predictive Current controller
Compared with the traditional current controller, the PI controller is replaced by the dead beat controller, and the method has the advantages of constant switching frequency, fast dynamic response, high bandwidth, small current fluctuation, easiness in implementation and the like; the most outstanding advantage is that dead beat tracking between the controlled object and the control expected value can be realized, and the relation between the input and the output of the controlled object is defined, so that a clear mathematical formula is established, and the system has quick response capability;
the current state equation is as follows:
the above is rewritten into a matrix form:
the Lawster transformation is carried out on the above materials to obtain:
wherein t is 0 For the sampling initial time, τ is the integration time constant; since the motor sampling period t=0.0001 s and the motor mechanical time constant is much larger than the current time constant, it can be considered that the motor rotation speed is unchanged in the adjacent sampling period, and thus the electromotive force is also unchanged; at this time, let t 0 =kt, t= (k+1) T, resulting in the following expression:
i(k+1)＝F(k)i(k)+A 0 -1 (F(k)-E)(B 0 u(k)+D 0 ) (4)
wherein,,
since the sampling period T is small, it can be considered that:cosω e T≈1、sinω e T≈ω e T、cosω e T≈1、sinω e T≈ω e T，
the moment after simplificationThe array F (k) is:
at this time, a discretized PMSM state equation is obtained as follows:
i(k+1)＝F(k)i(k)+Gu(k)+H(k)(5)
wherein,,
the control voltage can be obtained by solving:
u(k)＝G -1 (i(k+1)-F(k)i(k)-H(k))(6)
in a dead beat predictive current control algorithm, i is used to satisfy the requirement that current can follow a given value * (k+1) instead of i (k+1) in the above formula, the output voltage thereof is expressed as follows:
wherein i (k) is a current value obtained by sampling in the motor;
as the invention takes the surface-mounted permanent magnet synchronous motor as a research object, the motor meets the L requirement d ＝L q =l, so the electromagnetic torque equation at this point is:
wherein i is q And i s The included angle is beta;
for formula (8), wherein P n 、Ψ f Are all constant, so that the magnitude of the electromagnetic torque depends on the q-axis current, which in turn is equal to i s In relation to β, where sin β=1 is known, i.e. when β=90°, there is i q ＝i s That is, the torque current is entirely composed of the stator current, so that the operation efficiency of the motor reaches the maximum at this time; thus, when the high performance operation of the motor is desired, the torque is generatedThe flow ratio should be maximized to maximize the d-axis current, i.e. * d ＝0；
(1) Model predictive speed controller
Discrete state equation of the velocity prediction model:
t is the sampling period, k is the current time;
in order to facilitate the calculation of the influence of neglecting load disturbance, the speed prediction model equation at this time is:
i in the above q (k) The method can be written as follows:
i q (k)＝i q (k-1)+Δi q (k)(3)
for the convenience of calculation, the invention adopts two-step prediction, and the speeds at k+1 and k+2 predicted at k moment are respectively written as omega rm (k+1)、ω rm (k+2)；
The state equation obtained by combining the formulas (2) and (3) is as follows:
order the
Bringing (8) into (6) and (7) can be simplified to obtain:
let formula (9) rewrite to matrix form, namely:
the carry-over (9) according to formula (10) can be written as:
ω rm ＝ω r0 +GΔi q (11)
in order to reduce the model calculation error, model error correction is required to be added, and the prediction model is generally corrected approximately by adopting the deviation between the predicted value and the actual value at the previous moment; for omega after adding error correction term rm (k+1)、ω rm (k+2) are denoted as ω respectively rM (k+1)、ω rM (k+2) whose corresponding state equation is:
omega in the above formula (12) rm (k+1) is changed to ω rM (k+1), the correction term that can be obtained for the prediction model is:
for formula (13), let
According to formula (14), formula (13) may be written as:
ω rM ＝ω rm +e(15)
according to the commonly used performance index, a quadratic performance index is selected as an evaluation function, namely:
in the above formula, the first term is a constraint term of the deviation magnitude, the second term is a constraint term of the control quantity, q i 、r j Is a weight coefficient;
in equation (16), since the velocity is expected at the time of k+1, k+2Cannot be directly obtained, so that a first-order exponential form is adopted to obtain the reference track, namely:
in the formula (17), the amino acid sequence of the compound,wherein T is c Is a time constant;
solving the optimal delta i according to the principle of rolling optimization q It is necessary that the formula (16) satisfies:
solving for (18) to obtain Δi q The method comprises the following steps:
in the method, in the process of the invention,
combining the formula (5) with the formula (19), wherein the control law of the final surface-mounted PMSM model predictive controller is as follows:
(2) Load disturbance compensation
Because the second part model predicts the speed controller part and ignores the load disturbance, in order to improve the control precision, the load disturbance is compensated, and the torque equation and the motion equation of the permanent magnet synchronous motor are combined,
the q-axis current to be compensated for load disturbances is derived as:
load torque T L The current compensation can not be directly obtained, so that a fractional order integration method is adopted to carry out current compensation, and the aim is to reduce the system error by means of the integration effect and strengthen the system robustness; the invention adopts a caputo fractional order, and the expression is as follows:
in the above-mentioned (22),an alpha-order derivative or integral of the function f (t), alpha > 0 representing the derivative and alpha < 0 representing the integral; t is t 0 N is N and N-1 < alpha < N, which is the initial value of the variable t;
taking the deviation amount of the speed as an input quantity, obtaining q-axis compensation current after fractional integration action of a formula (22), namely:
finally, the control law of the model predictive speed controller is changed into after the compensation current is obtained by combining the formula (23) and the formula (20):
(2) Designing a current loop prediction controller: applying a dead beat prediction control strategy to the current internal control of the permanent magnet synchronous motor; the dead beat predictive current control is digital discrete control, the motor current obtained by sampling is compared with the given current through coordinate transformation, the comparison result is controlled by a dead beat current controller, the output voltage is subjected to coordinate transformation, the inverter generates a corresponding switching signal through a space vector pulse width modulation SVPWM modulator module, and the feedback current can follow the given current after the next switching period; because the current loop plays an important role in the performance of the motor control system, the dead current predictive controller replaces the PI controller in the traditional vector control in the inner loop, and the aim of the current loop is to improve the running performance and the response speed of the motor current loop;
(3) Designing an outer loop speed MPC controller: applying MPC to the speed loop to improve the control performance of the system; the MPC estimates the state of each moment in the future through a corresponding prediction model, takes an evaluation function as a criterion, adopts a rolling optimization mode to determine the optimal solution at the current moment, and adjusts the deviation between the output predicted value and the expected value through feedback correction; the MPC mainly comprises a reference track, a prediction model, feedback correction and rolling optimization, and a control structure of the MPC is shown in the figure;
(4) Establishing a simulation model of a control system: a double-model prediction strategy is adopted on the basis of a mathematical model of the permanent magnet synchronous motor, namely, a model prediction controller is applied to an outer ring of the system, namely, a speed ring, and a dead beat prediction controller is applied to an inner ring of the system, namely, a current ring.
A computer storage medium having stored thereon a computer program which, when executed by a processor, implements a permanent magnet synchronous motor control method based on a bi-predictive control as described above.
A computer device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, wherein the processor implements a permanent magnet synchronous motor control method based on double predictive control when executing the computer program.
The beneficial effects are that: compared with the prior art, the invention has the following advantages:
1. the invention combines the traditional vector control strategy and predictive control research to obtain the permanent magnet synchronous motor double-predictive control strategy method, researches the current loop part, optimizes the motor current by using dead beat predictive control algorithm, and obtains better dynamic and static control effects.
2. The invention controls the motor speed by using a model prediction algorithm aiming at the speed loop part, and the obtained PMSM system has faster dynamic response and stronger load disturbance resistance.
3. Simulation analysis proves that the double MPC strategy has good control performance, and compared with the traditional control method, the PMSM control system has almost no obvious overshoot and has good quality of sine wave output phase current.
Drawings
FIG. 1 is a flow chart of the steps of the method of the present invention;
FIG. 2 is a block diagram of a dual model predictive control strategy;
FIG. 3 is a comparison graph of rotational speed waveforms; wherein fig. 3 (a) is a waveform diagram of a PMSM rotational speed for dual-model predictive control, and fig. 3 (b) is a waveform diagram of a PMSM rotational speed for PI control;
FIG. 4 is a graph of PI control dq axis current waveforms;
FIG. 5 is a graph of a bi-modal predictive control dq-axis current waveform;
FIG. 6 is a graph of electromagnetic torque waveforms for a conventional PID algorithm;
FIG. 7 is a dual model predictive algorithm electromagnetic torque map.
Fig. 8 is a technical route for dual model predictive control PMSM.
Detailed Description
The technical scheme of the invention is further described below with reference to the accompanying drawings.
A permanent magnet synchronous motor control method based on double prediction control comprises the following steps:
(1) Establishing a mathematical model of the permanent magnet synchronous motor: in the PMSM control system, a surface-mounted permanent magnet synchronous motor is adopted as a research object, and related formulas are deduced from the voltage, the AC/DC speed, the torque and the mechanical motion equation 4 in a double synchronous rotation coordinate system.
(1.1) dead beat predictive Current controller
Compared with the traditional current controller, the PI controller is replaced by the dead beat controller, and the method has the advantages of constant switching frequency, fast dynamic response, high bandwidth, small current fluctuation, easiness in implementation and the like; the most outstanding advantage is that dead beat tracking between the controlled object and the control expected value can be realized, and the relation between the input and the output of the controlled object is defined, so that a clear mathematical formula is established, and the system has quick response capability;
the current state equation is as follows:
the above is rewritten into a matrix form:
the Lawster transformation is carried out on the above materials to obtain:
wherein t is 0 For the sampling initial time, τ is the integration time constant; since the motor sampling period t=0.0001 s and the motor mechanical time constant is much larger than the current time constant, it can be considered that the motor rotation speed is unchanged in the adjacent sampling period, and thus the electromotive force is also unchanged; at this time, let t 0 ＝kT、t＝(k+1) T, giving the following expression:
i(k+1)＝F(k)i(k)+A 0 -1 (F(k)-E)(B 0 u(k)+D 0 ) (4)
wherein,,
since the sampling period T is small, it can be considered that:cosω e T≈1、sinω e T≈ω e T、cosω e T≈1、sinω e T≈ω e T，
the matrix F (k) after simplification is:
at this time, a discretized PMSM state equation is obtained as follows:
i(k+1)＝F(k)i(k)+Gu(k)+H(k)(5)
wherein,,
the control voltage can be obtained by solving:
u(k)＝G -1 (i(k+1)-F(k)i(k)-H(k))(6)
in a dead beat predictive current control algorithm, i is used to satisfy the requirement that current can follow a given value * (k+1) instead of i (k+1) in the above formula, the output voltage thereof is expressed as follows:
u(k)＝G -1 (i * (k+1)-F(k)i(k)-H(k))(7)
wherein i (k) is a current value obtained by sampling in the motor;
as the invention takes the surface-mounted permanent magnet synchronous motor as a research object, the motor meets the L requirement d ＝L q =l, so the electromagnetic torque equation at this point is:
wherein i is q And i s The included angle is beta;
for formula (8), wherein P n 、Ψ f Are all constant, so that the magnitude of the electromagnetic torque depends on the q-axis current, which in turn is equal to i s In relation to β, where sin β=1 is known, i.e. when β=90°, there is i q ＝i s That is, the torque current is entirely composed of the stator current, so that the operation efficiency of the motor reaches the maximum at this time; it is thus obtained that, if high performance operation of the motor is desired, the torque-to-current ratio thereof should be maximized to maximize the d-axis current thereof, i.e., i * d ＝0；
(1) Model predictive speed controller
Discrete state equation of the velocity prediction model:
t is the sampling period, k is the current time;
in order to facilitate the calculation of the influence of neglecting load disturbance, the speed prediction model equation at this time is:
i in the above q (k) The method can be written as follows:
i q (k)＝i q (k-1)+Δi q (k)(3)
for the convenience of calculation, the invention adopts two-step prediction, and the speeds at k+1 and k+2 predicted at k moment are respectively written as omega rm (k+1)、ω rm (k+2)；
The state equation obtained by combining the formulas (2) and (3) is as follows:
order the
Bringing (8) into (6) and (7) can be simplified to obtain:
let formula (9) rewrite to matrix form, namely:
the carry-over (9) according to formula (10) can be written as:
ω rm ＝ω r0 +GΔi q (11)
in order to reduce the model calculation error, model error correction is required to be added, and the prediction model is generally corrected approximately by adopting the deviation between the predicted value and the actual value at the previous moment; for omega after adding error correction term rm (k+1)、ω rm (k+2) are denoted as ω respectively rM (k+1)、ω rM (k+2) whose corresponding state equation is:
omega in the above formula (12) rm (k+1) is changed to ω rM (k+1), the correction term that can be obtained for the prediction model is:
for formula (13), let
According to formula (14), formula (13) may be written as:
ω rM ＝ω rm +e(15)
according to the commonly used performance index, a quadratic performance index is selected as an evaluation function, namely:
in the above formula, the first term is a constraint term of the deviation magnitude, the second term is a constraint term of the control quantity, q i 、r j Is a weight coefficient;
in equation (16), since the velocity is expected at the time of k+1, k+2Cannot be directly obtained, so that a first-order exponential form is adopted to obtain the reference track, namely:
in the formula (17), the amino acid sequence of the compound,wherein T is c Is a time constant;
solving the optimal delta i according to the principle of rolling optimization q It is necessary that the formula (16) satisfies:
solving for (18) to obtain Δi q The method comprises the following steps:
in the method, in the process of the invention,
combining the formula (5) with the formula (19), wherein the control law of the final surface-mounted PMSM model predictive controller is as follows:
(2) Load disturbance compensation
Because the second part model predicts the speed controller part and ignores the load disturbance, in order to improve the control precision, the load disturbance is compensated, and the torque equation and the motion equation of the permanent magnet synchronous motor are combined,
the q-axis current to be compensated for load disturbances is derived as:
load torque T L The current compensation can not be directly obtained, so that a fractional order integration method is adopted to carry out current compensation, and the aim is to reduce the system error by means of the integration effect and strengthen the system robustness; the invention adopts a caputo fractional order, and the expression is as follows:
in the above-mentioned (22),an alpha-order derivative or integral of the function f (t), alpha > 0 representing the derivative and alpha < 0 representing the integral; t is t 0 N is N and N-1 < alpha < N, which is the initial value of the variable t;
taking the deviation amount of the speed as an input quantity, obtaining q-axis compensation current after fractional integration action of a formula (22), namely:
finally, the control law of the model predictive speed controller is changed into after the compensation current is obtained by combining the formula (23) and the formula (20):
(2) Designing a current loop prediction controller: applying a dead beat prediction control strategy to the current internal control of the permanent magnet synchronous motor; the dead beat predictive current control is digital discrete control, the motor current obtained by sampling is compared with the given current through coordinate transformation, the comparison result is controlled by a dead beat current controller, the output voltage is subjected to coordinate transformation, the inverter generates a corresponding switching signal through a space vector pulse width modulation SVPWM modulator module, and the feedback current can follow the given current after the next switching period; because the current loop plays an important role in the performance of the motor control system, the dead current predictive controller replaces the PI controller in the traditional vector control in the inner loop, and the aim of the current loop is to improve the running performance and the response speed of the motor current loop;
(3) Designing an outer loop speed MPC controller: applying MPC to the speed loop to improve the control performance of the system; the MPC estimates the state of each moment in the future through a corresponding prediction model, takes an evaluation function as a criterion, adopts a rolling optimization mode to determine the optimal solution at the current moment, and adjusts the deviation between the output predicted value and the expected value through feedback correction; the MPC mainly comprises a reference track, a prediction model, feedback correction and rolling optimization, and a control structure of the MPC is shown in the figure;
(4) Establishing a simulation model of a control system: a double-model prediction strategy is adopted on the basis of a mathematical model of the permanent magnet synchronous motor, namely, a model prediction controller is applied to an outer ring of the system, namely, a speed ring, and a dead beat prediction controller is applied to an inner ring of the system, namely, a current ring.
A computer storage medium having stored thereon a computer program which, when executed by a processor, implements a permanent magnet synchronous motor control method based on a bi-predictive control as described above.
A computer device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, wherein the processor implements a permanent magnet synchronous motor control method based on double predictive control when executing the computer program. Simulation results:
in order to verify the feasibility and effectiveness of the control method provided by the invention, the control performance of the two strategies under the conditions of sudden load, speed regulation and the like is discussed by comparing the traditional PI control method with the strategy provided by the invention. Table 1 gives the values of the parameters simulated in MATLAB/Simulink for the permanent magnet synchronous motor, with a simulation time selection tmax=1.0 s.
Table 1 parameters of permanent magnet synchronous motor
| Parameters of the motor | Numerical value |
| Rated rotation speed (r/min) | 1000 |
| Rated load (N.m) | 3 |
| Polar pair number (P) | 4 |
| Stator resistor (omega) | 0.35 |
| Permanent magnet flux linkage (Wb) | 0.1827 |
| Inductance (mH) | 8.5 |
The simulation process of the motor starts no-load operation at the rated speed of 1000r/min, the load is suddenly increased to be 3 N.m in 0.2s, and the whole simulation time is 0.5s. A comparison of the speed waveforms for PI control and bi-predictive model control is shown in fig. 3. The simulation result of fig. 3 shows that when the motor starts in a no-load state, the PI control algorithm generates obvious overshoot and vibration, the rising and adjusting time becomes long, the suddenly increased load decreases the speed due to the excessively long response time, the starting speed of the dual prediction model control mode is higher, and the performance is improved compared with PI control. Almost no overshoot, fast response speed, and seamless reaching of rated speed. When the load suddenly increases and the speed decreases, the response speed of the system is increased, the speed decreases, the adaptability is enhanced, and the reliability and the stability of the system are further improved.
As shown in fig. 4, it can be intuitively seen that the dq-axis current error range under the conventional PI control method is wider, the id of the system is not maintained at a level close to zero after the load is applied under PI control, and the response time of the q-axis current under the PMSM system is relatively faster, but the fluctuation is more obvious.
As shown in FIG. 5, the q-axis current tracking error range is better optimized in the dual-mode pre-measurement control method, the range is narrower, the q-axis can track the given value more accurately, the system has higher precision and better dynamic and static control effects, and the dual-mode prediction system optimizes the value range of id and maintains the value range to be close to zero.
As shown in fig. 6, there is a significant overshoot and jitter in the PMSM electromagnetic torque waveform under PI control, and there is a large torque ripple overall.
As shown in fig. 7, although a certain response time is required in the initial stage, the waveform is gentle, and there is no large overshoot and buffeting. Therefore, the output phase current of the method provided by the invention has better sinusoidal quality, and can maintain the normal state of the current control, thereby further improving the dynamic performance of the current control.
According to simulation results and analysis, the double MPC strategy has good control performance, and compared with the traditional control method, the PMSM control system has almost no obvious overshoot, and the quality of sine wave output phase current is good. In addition, the dual MPC strategy provides more versatile performance, faster dynamic response and greater load disturbance rejection.
Claims (5)
1. The control method of the permanent magnet synchronous motor based on the double-prediction control is characterized by comprising the following steps of:
(1) Establishing a mathematical model of the permanent magnet synchronous motor: in a PMSM control system, a surface-mounted permanent magnet synchronous motor is adopted as a research object, and a related formula is deduced from 4 aspects of voltage, AC/DC speed, torque and mechanical motion equation in a double synchronous rotation coordinate system;
(2) Designing a current loop prediction controller: applying a dead beat prediction control strategy to the current internal control of the permanent magnet synchronous motor; the dead beat predictive current control is digital discrete control, the motor current obtained through sampling is compared with a given current through coordinate transformation, the comparison result is controlled by a dead beat current controller, the output voltage is subjected to coordinate transformation, and the space vector pulse width modulation SVPWM modulator module is used for enabling the inverter to generate a corresponding switching signal, so that the click feedback current in the next switching period can follow the given current;
(3) Designing an outer loop speed MPC controller: applying MPC to the speed loop to improve the control performance of the system; the MPC estimates the state of each moment in the future through a corresponding prediction model, takes an evaluation function as a criterion, adopts a rolling optimization mode to determine the optimal solution at the current moment, and adjusts the deviation between the output predicted value and the expected value through feedback correction;
(4) Establishing a simulation model of a control system: a double-model prediction strategy is adopted on the basis of a mathematical model of the permanent magnet synchronous motor, a model prediction controller is applied to an outer ring of the system, namely a speed ring, and a dead beat prediction controller is applied to an inner ring of the system, namely a current ring.
2. The method for controlling a permanent magnet synchronous motor based on double predictive control according to claim 1, wherein the step (1) is specifically:
(1.1) dead beat predictive Current controller
The current state equation is as follows:
the formula (1) is rewritten into a matrix form:
the Lawster transformation of formula (2) can be obtained:
wherein t is 0 For the sampling initial time, τ is the integration time constant; motor sampling period t=0.0001 s andthe mechanical time constant of the motor is far greater than the current time constant, so that the motor rotating speed is unchanged in the adjacent sampling period, and the electromotive force is unchanged; at this time, let t 0 =kt, t= (k+1) T, resulting in the following expression:
i(k+1)＝F(k)i(k)+A 0 -1 (F(k)-E)(B 0 u(k)+D 0 ) (4)
wherein,,
since the sampling period T is small, it is considered that:cosω e T≈1、sinω e T≈ω e T、/>cosω e T≈1、sinω e T≈ω e T；
the matrix F (k) after simplification is:
at this time, a discretized PMSM state equation is obtained as follows:
i(k+1)＝F(k)i(k)+Gu(k)+H(k) (5)
wherein,,
the control voltage can be obtained by solving:
u(k)＝G -1 (i(k+1)-F(k)i(k)-H(k))(6)
in a dead beat predictive current control algorithm, i is used to satisfy the requirement that current can follow a given value * (k+1) instead of i (k+1) in the above formula, the output voltage thereof is expressed as follows:
u(k)＝G -1 (i * (k+1)-F(k)i(k)-H(k)) (7)
wherein i (k) is a current value obtained by sampling in the motor;
as the invention takes the surface-mounted permanent magnet synchronous motor as a research object, the motor meets the L requirement d ＝L q =l, so the electromagnetic torque equation at this point is:
wherein i is q And i s The included angle is beta;
for formula (8), wherein P n 、Ψ f Are all constant, so that the magnitude of the electromagnetic torque depends on the q-axis current, which in turn is equal to i s In relation to β, where sin β=1 is known, i.e. when β=90°, there is i q ＝i s That is, the torque current is entirely composed of the stator current, so that the operation efficiency of the motor reaches the maximum at this time; it is thus obtained that, if high performance operation of the motor is desired, the torque-to-current ratio thereof should be maximized to maximize the d-axis current thereof, i.e., i * d ＝0；
(1.2) model predictive speed controller
Discrete state equation of the velocity prediction model:
t is the sampling period, k is the current time;
in order to facilitate the calculation of the influence of neglecting load disturbance, the speed prediction model equation at this time is:
i in the above q (k) The method can be written as follows:
i q (k)＝i q (k-1)+Δi q (k) (3)
for the convenience of calculation, the invention adopts two-step prediction, and the speeds at k+1 and k+2 predicted at k moment are respectively written as omega rm (k+1)、ω rm (k+2)；
The state equation obtained by combining the formulas (2) and (3) is as follows:
order the
Bringing (8) into (6) and (7) can be simplified to obtain:
let formula (9) rewrite to matrix form, namely:
the carry-over (9) according to formula (10) can be written as:
ω rm ＝ω r0 +GΔi q (11)
in order to reduce the model calculation error, model error correction is required to be added, and the prediction model is generally corrected approximately by adopting the deviation between the predicted value and the actual value at the previous moment; for omega after adding error correction term rm (k+1)、ω rm (k+2) are denoted as ω respectively rM (k+1)、ω rM (k+2) whose corresponding state equation is:
omega in the above formula (12) rm (k+1) is changed to ω rM (k+1), the correction term that can be obtained for the prediction model is:
for formula (13), let
According to formula (14), formula (13) may be written as:
ω rM ＝ω rm +e (15)
according to the commonly used performance index, a quadratic performance index is selected as an evaluation function, namely:
in the above formula, the first term is a constraint term of the deviation magnitude, the second term is a constraint term of the control quantity, q i 、r j Is a weight coefficient;
in equation (16), since the velocity is expected at the time of k+1, k+2Cannot be directly obtained, so that a first-order exponential form is adopted to obtain the reference track, namely:
in the formula (17), the amino acid sequence of the compound,wherein T is c Is a time constant;
solving the optimal delta i according to the principle of rolling optimization q It is necessary that the formula (16) satisfies:
solving for (18) to obtain Δi q The method comprises the following steps:
in the method, in the process of the invention,
combining the formula (5) with the formula (19), wherein the control law of the final surface-mounted PMSM model predictive controller is as follows:
(2) Load disturbance compensation
Because the second part model predicts the speed controller part and ignores the load disturbance, in order to improve the control precision, the load disturbance is compensated, and the torque equation and the motion equation of the permanent magnet synchronous motor are combined,
the q-axis current to be compensated for load disturbances is derived as:
load torque T L Cannot be directly obtained, so thatThe current compensation is carried out by a fractional order integration method, so that the system error is reduced by means of the integration effect, and the system robustness is enhanced; the invention adopts a caputo fractional order, and the expression is as follows:
in the above-mentioned (22),an alpha-order derivative or integral of the function f (t), alpha > 0 representing the derivative and alpha < 0 representing the integral; t is t 0 N is N and N-1 < alpha < N, which is the initial value of the variable t;
taking the deviation amount of the speed as an input quantity, obtaining q-axis compensation current after fractional integration action of a formula (22), namely:
finally, the control law of the model predictive speed controller is changed into after the compensation current is obtained by combining the formula (23) and the formula (20):
3. the method of claim 1, wherein the MPC in step (3) includes reference trajectory, prediction model, feedback correction and rolling optimization.
4. A computer storage medium having stored thereon a computer program which, when executed by a processor, implements a bi-predictive control based permanent magnet synchronous motor control method according to any one of claims 1-3.
5. A computer device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, characterized in that the processor implements a bi-predictive control based permanent magnet synchronous motor control method according to any of claims 1-3 when executing the computer program.
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