CN116582037A - Permanent magnet synchronous motor robust control method based on inequality constraint - Google Patents
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Classifications
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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
- H02P21/0003—Control strategies in general, e.g. linear type, e.g. P, PI, PID, using robust control
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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
- 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
Abstract
The invention discloses a permanent magnet synchronous motor robust control method based on inequality constraint, which comprises the following steps: s1: based on a Lagrangian energy method permanent magnet synchronous motor dynamic model, a state conversion function is constructed, and a constraint area in a state variable of the output permanent magnet synchronous motor is removed by the function; s2: introducing uncertainty parameters into a dynamics model in consideration of uncertainty in the system; s3: based on the model, a new robust controller is provided to obtain a more stable control effect of the permanent magnet synchronous motor; s4: carrying out stability analysis on a designed robust controller, and proving that the controller can ensure the requirements of consistent bouncy and consistent limit bouncy; s5: simulation and experimental verification are carried out by using a rapid controller prototype CSPACE and an actual permanent magnet synchronous motor platform, and a designed controller is adopted on the permanent magnet synchronous motor, so that more excellent dynamic performance can be obtained, and the safety performance is greatly improved.
Description
Technical Field
The invention relates to the technical field of motors and control, in particular to a permanent magnet synchronous motor robust control method based on inequality constraint.
Background
Permanent Magnet Synchronous Motor (PMSM) is widely applied to industries such as metallurgy, ceramics, petroleum and the like due to its simple structure and high efficiency.
Compared with an asynchronous motor, the permanent magnet synchronous motor does not need reactive exciting current, so that the efficiency is high and the power factor is high. Meanwhile, compared with a standard synchronous motor, the motor has the advantages of saving an excitation device, improving efficiency and simplifying the structure. Furthermore, it does not have the drawbacks of direct current motors, such as brushes and commutators. In recent years, with the development of the robot industry, the vector control system of the permanent magnet synchronous motor can realize speed control with large range, high dynamic performance and high precision, and therefore, the vector control system is widely paid attention to at home and abroad.
The key factors affecting permanent magnet synchronous motors are external disturbances and uncertainties, both time-varying and unknown. For example, the variation of phase and moment of inertia, the nonlinearity of the armature reaction, makes high performance trajectory tracking control a difficult task.
Meanwhile, in practical application, due to the existence of disturbance, the permanent magnet synchronous motor may exceed the working boundary of the motor, which not only affects the performance and service life of the motor, but also endangers the safety of workers, so that the working range of the permanent magnet synchronous motor needs to be limited, but also the working efficiency of the permanent magnet synchronous motor is low.
Therefore, we firstly construct a state transfer function to eliminate the constraint in the state variable in the working range of the output permanent magnet synchronous motor so that the output is strictly limited in the expected range, then we design a new robust controller based on the Lyapunov method to eliminate the influence of uncertainty on tracking performance and obtain more accurate track tracking, and therefore, in view of the fact that the existing structure is researched and improved, the robust control method of the permanent magnet synchronous motor based on inequality constraint is provided, so that the purpose of higher practical value is achieved.
Disclosure of Invention
In order to solve the technical problems, the invention provides the following technical scheme:
the invention discloses a robust control method of a permanent magnet synchronous motor based on inequality constraint, which comprises the following steps:
s1: based on a Lagrangian energy method permanent magnet synchronous motor dynamics model, a state conversion function is constructed, a constraint area in a state variable of the output permanent magnet synchronous motor is removed by the function, the constraint state variable is converted into an unconstrained state variable, and finally a new permanent magnet synchronous motor dynamics model is built;
s2: introducing uncertainty parameters into a dynamic model in consideration of uncertainty in the system, dividing a parameter matrix into a nominal part and an uncertainty part, and determining the upper bound of all uncertainties;
s3: based on the model, a new robust controller is provided to obtain a more stable control effect of the permanent magnet synchronous motor and reduce track tracking error to the maximum extent;
s4: carrying out stability analysis on a designed robust controller, and proving that the controller can ensure the requirements of consistent bouncy and consistent limit bouncy;
s5: and performing simulation and experimental verification by using a rapid controller prototype CSPACE and an actual permanent magnet synchronous motor platform.
As a preferable technical scheme of the invention, in the S1, a FOC (field oriented control) technology is adopted to carry out dynamic modeling on the permanent magnet synchronous motor, and the formula is as follows:
wherein W (·) is an inertia matrix, F (·) is a friction vector and other interference or measurement noise, C (·) is a centrifugal force/Coriolis force matrix, G (·) is a gravity matrix, u (t) is a generalized force vector, t ε R is time, x (·) ε Rn is generalized coordinates,representing generalized acceleration.
As a preferred technical solution of the present invention, in the step S1, because of structural limitation and safety consideration in the actual process, a state transition function is constructed to delete the constraint area in the output state variable and convert the constraint state variable into an unconstrained state variable, which comprises the following steps:
due to the factors of mechanical structure and engineering safety, in practical engineering, the rotation range q of the motor needs to be limited between qm and qm, namely:
q m ＜q＜q M
where qM represents the upper bound of the state variable q, qM represents the lower bound of q, and the inequality state constraint is designed as:
θ、and->Respectively represent the angular displacement, the angular velocity and the angular acceleration of the rotor under the condition of no state constraint, and theta d Indicating the expected angular displacement of the rotor. Thus, θ→θ d When q-q d θ - & gtinfinity is q- & gtq m θ - & gtand + & gtinfinity as q- & gtq M When qM<q<0 ε R at qM.
As a preferable technical scheme of the invention, after converting a constraint state variable into an unconstrained state variable in the S1, a new permanent magnet synchronous motor dynamics model is established, and the above formula is substituted into the model to obtain the permanent magnet synchronous motor dynamics model:
in the practical application of S2, because the parameters of the system are continuously changed, the system has uncertainty, and the values of W (·), F (·), C (·) and G (·) cannot be accurately known, so that they need to be divided into two parts, namely a nominal matrix and a non-deterministic part:
where W (-), F (-), C (-) and G (-) are nominal functions, ΔW, ΔF, ΔC and ΔG are uncertainty terms related to μ, μ is an uncertainty parameter over time in the system, and x is the actual motion profile.
As a preferable technical scheme of the invention, a new robust controller is provided in the step S3 based on a new model, and the formula is as follows:
。
as a preferable technical scheme of the invention, in the S4, stability analysis is performed by a Lyapunov method, and the controller is proved to ensure the requirements of consistent bouncy and consistent limit bouncy, and a Lyapunov function is selected, and the formula is as follows:
and proves to be positive and decremental.
As a preferred technical scheme of the invention, in the S5, a rapid controller prototype CSPACE and an actual permanent magnet synchronous motor platform are used for simulation and experimental verification, the CSPACE control platform provides a useful development environment for control algorithm verification, an algorithm is created in Matlab/Simulink by using a graphic method, codes can be automatically generated on line, and researchers can develop and test the algorithm by using the technology.
As a preferred technical solution of the present invention, in S5, in order to verify the track following control effect of the proposed method, taking a step signal as an example, several control algorithms under different situations are compared in simulation and experiment: PID (proportional-integral-derivative control), MPD (model-based proportional-derivative control), NMBRCS (model-based robust control with state transitions), NMBRCV (model-based robust control without state transitions).
The beneficial effects of the invention are as follows:
the NMBRCS (NMBRC) control algorithm of the designed permanent magnet synchronous motor has better control effect than PMBRCV (NMBRCV), MPD and PID without state transformation. The algorithm can realize accurate track tracking, so that control output is strictly limited in a desired range, and the dynamic performance and safety of the permanent magnet synchronous motor are improved. Meanwhile, the NMBRCS algorithm has certain universality in the design problem of an uncertain nonlinear system. In the future, the algorithm can be applied to other nonlinear mechanical systems, such as joint modules and aerospace, so as to verify the superiority of the algorithm in other practical projects, and has higher practical value.
Drawings
The accompanying drawings are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate the invention and together with the embodiments of the invention, serve to explain the invention. In the drawings:
FIG. 1 is a control flow diagram of the present invention;
FIG. 2 is a block diagram of a permanent magnet synchronous motor controller;
FIG. 3 is a graph of trace step signal contrast in simulation;
FIG. 4 is a graph of tracking step signal error versus in simulation;
FIG. 5 is a permanent magnet synchronous motor experimental platform;
FIG. 6 is a graph comparing trace step signals in an experiment;
FIG. 7 is a graph comparing tracking step signal errors in experiments.
Detailed Description
The preferred embodiments of the present invention will be described below with reference to the accompanying drawings, it being understood that the preferred embodiments described herein are for illustration and explanation of the present invention only, and are not intended to limit the present invention.
Examples: as shown in fig. 1 to 7, the robust control method of the permanent magnet synchronous motor based on inequality constraint of the invention comprises the following steps of S1: based on a Lagrangian energy method permanent magnet synchronous motor dynamics model, a state conversion function is constructed, a constraint area in a state variable of the output permanent magnet synchronous motor is removed by the function, the constraint state variable is converted into an unconstrained state variable, and finally a new permanent magnet synchronous motor dynamics model is built;
s2: introducing uncertainty parameters into a dynamic model in consideration of uncertainty in the system, dividing a parameter matrix into a nominal part and an uncertainty part, and determining the upper bound of all uncertainties;
s3: based on the model, a new robust controller is provided to obtain a more stable control effect of the permanent magnet synchronous motor and reduce track tracking error to the maximum extent;
s4: carrying out stability analysis on a designed robust controller, and proving that the controller can ensure the requirements of consistent bouncy and consistent limit bouncy;
s5: and performing simulation and experimental verification by using a rapid controller prototype CSPACE and an actual permanent magnet synchronous motor platform.
In the step S1, we use FOC (field oriented control) technology to model the permanent magnet synchronous motor dynamically. The formula is as follows:
wherein W (·) is an inertia matrix, F (·) is a friction vector and other interference or measurement noise, C (·) represents a centrifugal force/Coriolis force matrix, G (·) represents a gravity matrix, u (t) represents a generalized force vector,t.epsilon.R represents time, x (. Cndot.). Cndot.epsilon.Rn represents generalized coordinates,representing generalized acceleration.
In said S1, since we need to limit the range of motion of the motor in practical process, due to structural limitations and safety considerations, we will construct a state transfer function that deletes the constraint areas in the output state variables and transfers the constraint state variables to unconstrained state variables, as follows:
due to the factors of mechanical structure and engineering safety, in practical engineering, we need to limit the rotation range q of the motor between qm and qm, namely:
q m ＜q＜q M
where qM represents the upper bound of the state variable q, qM represents the lower bound of q, and the inequality state constraint is designed as:
θ、and->Respectively represent angular displacement, angular velocity and angular acceleration, θ, under no state constraint d Indicating the expected angular displacement of the rotor. Thus, θ→θ d When q-q d θ - & gtinfinity is q- & gtq m θ - & gtand + & gtinfinity as q- & gtq M When qM<q<At qM θ∈r.
Thus, we can obtain:
in the step S1, after the constraint state variable is converted into the unconstrained state variable, a new permanent magnet synchronous motor dynamics model is built. Substitution of the above formula into modeling can therefore result in:
thus, the nominal matrix may be represented as follows
The relevant parameters of the permanent magnet synchronous motor are shown in table 1;
in the S2, in practical application, since the parameters of the system are continuously changed, the system has uncertainty, and we cannot accurately know the values of W (·), F (·), C (·) and G (·), so we divide them into two parts, namely a nominal matrix and a non-deterministic part, with the following formula:
where W (-), F (-), C (-) and G (-) are nominal functions, ΔW, ΔF, ΔC and ΔG are uncertainty terms related to μ. μ is an uncertainty parameter that varies with time in the system, and x is the actual motion profile.
In the step S3, a new robust controller is proposed based on the new model, which comprises the following steps:
s31: the output tracking error formula is as follows:
let:
in order for the controller to work properly, our goal is to makeThe agreement is bounded and the agreement is ultimately bounded.
S32: ρ is used to estimate the hypothetical boundary of uncertainty and external interference such that for a given S >0, the function ρ is chosen as follows:
wherein:
phi is the sum of the uncertainties. Obviously, if φ≡0, all uncertainties disappear.
S33: then, fromIt will be appreciated that a controller needs to be designed to ensure that the track following error is below a predetermined range. Thus, we propose a nonlinear system controller as follows:
where scalars P >0, D >0, and γ >0, which are variables that can be changed.
A robust control block diagram of a permanent magnet synchronous motor with uncertainty and disturbance compensation is shown in fig. 2:
in the step S4, stability analysis is performed by a Lyapunov method, and the controller is proved to be capable of guaranteeing the requirements of consistent bouncy and consistent limit bouncy. The method comprises the following steps:
s41: selecting Lyapunov candidate functions:
in order to prove that V is an acceptable candidate for the Lyapunov function, it must prove positive and decremental.
S42: proof V is positive:
since the inertia matrix W (·) in a mechanical system has uniformly positive characteristics, the scalar constant δ (δ > 0) exists as follows:
so that:
wherein:
easily demonstratedThus, V is positive.
S43: proof V is decreasing:
next we have to prove that V is decreasing, that is to say thatTaking the derivative of V with respect to time, the following equation is derived:
substituting the algorithm of the robust controller to obtain:
simplifying and obtaining:
and is further composed ofThe method can obtain:
i.e. if it is to be provedOnly prove +.>That is, by adjusting the parameter variables P, D and γ in the equation, it can be proved that this is true.
In said S5 we use the fast controller prototype cspue and the actual permanent magnet synchronous motor platform for simulation and experimental verification. The CSPACE control platform provides a useful development environment for control algorithm validation. These algorithms are created using a graphical method in Matlab/Simulink, which can automatically generate code on-line. Researchers can develop and test algorithms using the techniques described above. In order to verify the track following control effect of the proposed method, we take step signals as an example, and compare control algorithms under several different conditions in simulation and experiment: PID (proportional-integral-derivative control), MPD (model-based proportional-derivative control), NMBRCS (model-based robust control with state transitions), NMBRCV (model-based robust control without state transitions). The method comprises the following steps:
s51: response to the step; fig. 3 and 4 show the result of setting the amplitude of the step signal θd to 28.3642.
From the comparison of the figures, MPD and NMBRCS (banding transitionModel-based robust control of the trade) and NMBRCV (model-based robust control of the stateless transition) reach steady state within 0.2s, the PID response time is slow, the final error is significant, the final error of the NMBRCV control algorithm and MPD control is about 0.02 °, and the NMBRCS is used to control the absolute error to 4×10 -10 Inside. The simulation result of the controller is superior to MPD and a robust control algorithm based on a model. Table 2 shows the controller parameters in the simulation.
S52: next, we have further validated the applicability of this algorithm through experimentation. Fig. 5 is a permanent magnet synchronous motor experimental platform. For the step response, the amplitude of the step signal θd was set to 60 °, and the same amplitude as the numerical simulation was maintained, and the results are shown in fig. 6 and 7 below.
From the graph comparison, it can be concluded that the step control signal under NMBRCV control has a maximum error of 2 ° while exceeding the constraint range, while the output under NMBRCS control is strictly limited to the desired range, with the error remaining within 0.2 °.
Table 1: parameter values of permanent magnet synchronous motor
| Control algorithm | Control parameters |
| PID | P＝89,I＝5,D＝17 |
| MPD | P＝4,D＝0.1 |
| NMBRCV | P＝4,D＝0.1,γ＝3.3128，S＝1 |
| NMBRCS | P＝4,D＝0.1,γ＝3.3128，S＝1 |
Table 2: controller parameters in simulation
The foregoing description is only a preferred embodiment of the present invention, and the present invention is not limited thereto, but it is to be understood that modifications and equivalents of some of the technical features described in the foregoing embodiments may be made by those skilled in the art, although the present invention has been described in detail with reference to the foregoing embodiments. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (9)
1. The robust control method of the permanent magnet synchronous motor based on inequality constraint is characterized by comprising the following steps of:
s1: based on a Lagrangian energy method permanent magnet synchronous motor dynamics model, a state conversion function is constructed, a constraint area in a state variable of the output permanent magnet synchronous motor is removed by the function, the constraint state variable is converted into an unconstrained state variable, and finally a new permanent magnet synchronous motor dynamics model is built;
s2: introducing uncertainty parameters into a dynamic model in consideration of uncertainty in the system, dividing a parameter matrix into a nominal part and an uncertainty part, and determining the upper bound of all uncertainties;
s3: based on the model, a new robust controller is provided to obtain a more stable control effect of the permanent magnet synchronous motor and reduce track tracking error to the maximum extent;
s4: carrying out stability analysis on a designed robust controller, and proving that the controller can ensure the requirements of consistent bouncy and consistent limit bouncy;
s5: and performing simulation and experimental verification by using a rapid controller prototype CSPACE and an actual permanent magnet synchronous motor platform.
2. The robust control method of permanent magnet synchronous motor based on inequality constraint according to claim 1, wherein the step S1 adopts FOC (field oriented control) technology to dynamically model the permanent magnet synchronous motor, and the formula is as follows:
wherein W (·) is an inertia matrix, F (·) is a friction vector and other interference or measurement noise, C (·) is a centrifugal force/Coriolis force matrix, G (·) is a gravity matrix, u (t) is a generalized force vector, t ε R is time, x (·) ε Rn is generalized coordinates,representing generalized acceleration.
3. The robust control method of permanent magnet synchronous motor based on inequality constraint according to claim 1, wherein in S1, since the motor' S motion range needs to be limited due to structural limitation and safety consideration in the actual process, a state transition function is constructed, which deletes the constraint area in the output state variable and converts the constraint state variable into an unconstrained state variable, and the steps are as follows:
due to the factors of mechanical structure and engineering safety, in practical engineering, the rotation range q of the motor needs to be limited between qm and qm, namely:
q m ＜q＜q M
where qM represents the upper bound of the state variable q, qM represents the lower bound of q, and the inequality state constraint is designed as:
θ、and->Respectively represent the angular displacement, the angular velocity and the angular acceleration of the rotor under the condition of no state constraint, and theta d Indicating the expected angular displacement of the rotor. Thus, θ→θ d When q-q d θ - & gtinfinity is q- & gtq m θ - & gtand + & gtinfinity as q- & gtq M When qM<q<0 ε R at qM.
4. The robust control method of permanent magnet synchronous motor based on inequality constraint according to claim 1, wherein after converting constraint state variable into unconstrained state variable in S1, a new permanent magnet synchronous motor dynamics model is built, and the above formula is substituted into the model to obtain:
5. the robust control method of permanent magnet synchronous motor based on inequality constraint according to claim 1, wherein in the practical application in S2, because the system has uncertainty due to the continuous variation of parameters of the system, the values of W (·), F (·), C (·) and G (·) cannot be known accurately, so they need to be divided into two parts, namely a nominal matrix and a non-deterministic part:
where W (-), F (-), C (-) and G (-) are nominal functions, ΔW, ΔF, ΔC and ΔG are uncertainty terms related to μ, μ is an uncertainty parameter over time in the system, and x is the actual motion profile.
6. The robust control method of permanent magnet synchronous motor based on inequality constraint according to claim 1, wherein a new robust controller is provided in S3 based on a new model, and the formula is as follows:
7. the robust control method of permanent magnet synchronous motor based on inequality constraint according to claim 1, wherein in S4, stability analysis is performed by Lyapunov method, and it is proved that the controller can ensure the requirements of consistent constraint and consistent limit constraint, and the Lyapunov function is selected according to the following formula:
and proves to be positive and decremental.
8. The robust control method of permanent magnet synchronous motor based on inequality constraint according to claim 1, wherein in S5, simulation and experimental verification are performed by using a fast controller prototype CSPACE and an actual permanent magnet synchronous motor platform, the CSPACE control platform provides a useful development environment for control algorithm verification, the algorithm is created in Matlab/Simulink using a graphic method, codes can be automatically generated online, and researchers can develop and test the algorithm using the above-mentioned technology.
9. The robust control method of permanent magnet synchronous motor based on inequality constraint according to claim 1, wherein in S5, in order to verify the track following control effect of the proposed method, taking step signals as an example, control algorithms under several different conditions are compared in simulation and experiment: PID (proportional-integral-derivative control), MPD (model-based proportional-derivative control), NMBRCS (model-based robust control with state transitions), NMBRCV (model-based robust control without state transitions).
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