Robust iterative learning control method and device for permanent magnet synchronous motor

Abstract

The invention discloses a robust iterative learning control method and device for a permanent magnet synchronous motor. The method comprises the following steps: constructing a permanent magnet synchronous motor model; according to the permanent magnet synchronous motor model, constructing a nonlinear function used for estimating system external disturbance of the permanent magnet synchronous motor, and then according to the nonlinear function, constructing a finite time extended state observer used for estimating the system state and the system external disturbance of the permanent magnet synchronous motor; and constructing an iterative learning trajectory tracking control law of the permanent magnet synchronous motor according to the permanent magnet synchronous motor model and the finite time extended state observer, and then performing adaptive iterative learning control on the permanent magnet synchronous motor according to the iterative learning trajectory tracking control law to obtain a trajectory tracking control result of the permanent magnet synchronous motor. According to the invention, the control precision and robustness of tracking control of the permanent magnet synchronous motor can be improved.

Description

Technical Field

[0001] The present invention relates to the technical field of motor control, and in particular to a robust iterative learning control method and device for a permanent magnet synchronous motor. Background Art

[0002] With the continuous improvement of industrial automation level, permanent magnet synchronous motor (PMSM) has been widely used due to its small size, low loss and high efficiency. And with the rapid development of power electronics and microelectronics technology, as well as the emergence of rare earth permanent magnet materials, PMSM has been widely used in high-precision motion control system industries such as precision manufacturing, automobiles, aerospace, etc.

[0003] In these application scenarios, high-precision control of PMSM is crucial. Reducing control errors can not only reduce interruptions and delays in production, but also significantly improve the efficiency and flexibility of the production line. The performance of PMSM directly affects production efficiency and operating costs. Therefore, researching and developing high-precision PMSM output tracking control technology has important practical application value and economic benefits.

[0004] The existing PMSM output tracking control methods mainly include traditional PID control, fuzzy control, neural network control, model predictive control, etc. These PMSM tracking control methods can meet the actual application needs to a certain extent, but because the PMSM system has the characteristics of repeated operation and non-repetitive interference, these PMSM tracking control methods are easily affected by external non-repetitive interference when tracking and controlling the PMSM, and their control accuracy and robustness need to be improved. Summary of the invention

[0005] The present invention provides a robust iterative learning control method and device for a permanent magnet synchronous motor, so as to solve the technical problem that the existing PMSM tracking control method is easily affected by external non-repetitive interference when tracking and controlling the PMSM.

[0006] In order to solve the above technical problems, an embodiment of the present invention provides a robust iterative learning control method for a permanent magnet synchronous motor, comprising:

[0007] Construct a permanent magnet synchronous motor model;

[0008] According to the permanent magnet synchronous motor model, a nonlinear function for estimating a system external disturbance of the permanent magnet synchronous motor is constructed, and then according to the nonlinear function, a finite time extended state observer for estimating a system state of the permanent magnet synchronous motor and a system external disturbance is constructed;

[0009] According to the permanent magnet synchronous motor model and the finite time extended state observer, an iterative learning trajectory tracking control law of the permanent magnet synchronous motor is constructed, and then according to the iterative learning trajectory tracking control law, the permanent magnet synchronous motor is adaptively iteratively learned and controlled to obtain a trajectory tracking control result of the permanent magnet synchronous motor.

[0010] As a preferred solution, the permanent magnet synchronous motor model is:

[0011]

[0012] y k (t) = Cx k (t);

[0013]

[0014] Among them, x k (t) = [θ m,k ω m,k ] T ,θ m,k is the angular displacement of the permanent magnet synchronous motor rotor, ω m,k is the angular displacement of the permanent magnet synchronous motor rotor, is the state variable x k The first derivative of (t), y k (t) is the output of the permanent magnet synchronous motor, u k (t) is the control signal of the permanent magnet synchronous motor, w k (t) is the external disturbance to the permanent magnet synchronous motor system, l k (t) is the load disturbance of the permanent magnet synchronous motor, J is the moment of inertia of the permanent magnet synchronous motor, C e is the back electromotive force of the permanent magnet synchronous motor, K t is the torque coefficient of the permanent magnet synchronous motor, R s is the stator resistance of the permanent magnet synchronous motor, P n is the number of pole pairs of the permanent magnet synchronous motor, B n is the viscous friction coefficient of the permanent magnet synchronous motor, T f,k is the load torque of the permanent magnet synchronous motor.

[0015] As a preferred solution, the nonlinear function is:

[0016]

[0017]

[0018] in, and is a nonlinear function, and for The weight, and for The weight, for and specific manifestations, for and The specific form of k1>0, k1 is the adjustment parameter, j=1,2.

[0019] As a preferred solution, the finite time extended state observer is:

[0020]

[0021]

[0022] Where L1 and L2 are the gain matrices of the finite-time extended state observer, For x k The estimated value of (t), for l k (t)+w k The estimated value of (t), and They are and The first derivative of k is the control signal of the permanent magnet synchronous motor, e 1,k For x k The estimated error of (t), e 2,k for l k (t)+w k The estimated error of (t), e 1,k =[e 11,k ,e 12,k ] T ∈R 2 .

[0023] As a preferred solution, the tracking control module includes: a learning module, a feedback module and an interference compensation module.

[0024] Among them, the learning module is used to suppress the tracking error of the permanent magnet synchronous motor; the interference compensation module is used to suppress the non-repetitive interference of the permanent magnet synchronous motor and enhance the transient performance of the permanent magnet synchronous motor; the feedback module is used to control the permanent magnet synchronous motor system to maintain a stable state.

[0025] As a preferred solution, the iterative learning trajectory tracking control law of the permanent magnet synchronous motor is:

[0026]

[0027] in, For learning modules, For the feedback module, It is the interference compensation module.

[0028] As a preferred solution, the learning module is:

[0029]

[0030] Among them, α is the attenuation factor, 0<α<1, K2 is the gain matrix of the learning module, is the input of the previous iteration of the permanent magnet synchronous motor, y d (t) is the expected output of the permanent magnet synchronous motor, y k (t) is the actual output of the permanent magnet synchronous motor, e y,k (t) is the tracking error;

[0031] The feedback module is:

[0032]

[0033] Wherein, K1 is the gain matrix of the feedback module;

[0034] The interference compensation module is:

[0035]

[0036] in, for l k (t)+w k The estimated value of (t) is obtained according to the finite time extended state observer.

[0037] Based on the above embodiment, another embodiment of the present invention provides a robust iterative learning control device for a permanent magnet synchronous motor, comprising: a permanent magnet synchronous motor model building module, a finite time extended state observer building module and an iterative learning trajectory tracking control module;

[0038] The permanent magnet synchronous motor model building module is used to build a permanent magnet synchronous motor model;

[0039] The finite-time extended state observer construction module is used to construct a nonlinear function for estimating the system external disturbance of the permanent magnet synchronous motor according to the permanent magnet synchronous motor model, and then construct a finite-time extended state observer for estimating the system state and system external disturbance of the permanent magnet synchronous motor according to the nonlinear function;

[0040] The iterative learning trajectory tracking control module is used to construct an iterative learning trajectory tracking control law of the permanent magnet synchronous motor according to the permanent magnet synchronous motor model and the finite time extended state observer, and then perform adaptive iterative learning control on the permanent magnet synchronous motor according to the iterative learning trajectory tracking control law to obtain a trajectory tracking control result of the permanent magnet synchronous motor.

[0041] Based on the above embodiments, another embodiment of the present invention provides an electronic device, which includes a processor, a memory, and a computer program stored in the memory and configured to be executed by the processor, and when the processor executes the computer program, it implements the robust iterative learning control method of the permanent magnet synchronous motor described in the above invention embodiment.

[0042] Based on the above embodiments, another embodiment of the present invention provides a storage medium, which includes a stored computer program, wherein when the computer program is running, the device where the storage medium is located is controlled to execute the robust iterative learning control method of the permanent magnet synchronous motor described in the above invention embodiment.

[0043] Compared with the prior art, the embodiments of the present invention have the following beneficial effects:

[0044] The present invention provides a method for robust iterative learning control of a permanent magnet synchronous motor: first, a permanent magnet synchronous motor model is constructed; then, based on the permanent magnet synchronous motor model, a nonlinear function for estimating the system external disturbance of the permanent magnet synchronous motor is constructed, and then, based on the nonlinear function, a finite time extended state observer for estimating the system state and system external disturbance of the permanent magnet synchronous motor is constructed. Different from the existing extended state observer using a linear error function, the present invention constructs a nonlinear function to estimate the system external disturbance of the permanent magnet synchronous motor. By designing the error term as a nonlinear function, the constructed finite time extended state observer can suppress the non-repetitive disturbance of the permanent magnet synchronous motor, and realize the state estimation of the permanent magnet synchronous motor in a finite time, thereby reducing the observation time and improving the estimation accuracy.

[0045] Finally, according to the permanent magnet synchronous motor model and the finite time extended state observer, an iterative learning trajectory tracking control law of the permanent magnet synchronous motor is constructed, and then according to the iterative learning trajectory tracking control law, the permanent magnet synchronous motor is adaptively iteratively learned and controlled to obtain the trajectory tracking control result of the permanent magnet synchronous motor. The present invention aims at the problem that the permanent magnet synchronous motor has poor adaptive ability to non-repetitive environmental interference, and constructs an iterative learning trajectory tracking control law, which can fully utilize the repeatability of the system for learning while ensuring the trajectory tracking control accuracy, obtain the trajectory tracking control result of the permanent magnet synchronous motor, and improve the adaptive ability and robust performance of the permanent magnet synchronous motor to the environment. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 It is a flow chart of a robust iterative learning control method for a permanent magnet synchronous motor provided by an embodiment of the present invention;

[0047] Figure 2 It is a design flow chart of the PMSM trajectory tracking control method of the present invention;

[0048] Figure 3 It is a structural block diagram of the robust iterative learning trajectory tracking controller designed by the present invention;

[0049] Figure 4 It is a schematic diagram of the simulation results of PMSM angular displacement tracking using the traditional ESO combined with I LC method;

[0050] Figure 5 It is a schematic diagram of simulation results of PMSM angular displacement tracking using the FTESO and ILC combination method designed in the present invention;

[0051] Figure 6 It is a schematic diagram comparing the error curves of the two methods as the number of iterations changes;

[0052] Figure 7 It is a structural schematic diagram of a robust iterative learning control device for a permanent magnet synchronous motor provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0053] In order to make the purpose, technical solutions and advantages of this application clearer, the technical solutions in this application will be clearly and completely described below in conjunction with the drawings in the embodiments of this application. Obviously, the described embodiments are part of the embodiments of this application, not all of them. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0054] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by technicians in the technical field to which this application belongs; the terms used herein are only for the purpose of describing specific embodiments and are not intended to limit this application; the terms "including" and "having" in the specification and claims of this application and the above-mentioned figure descriptions and any variations thereof are intended to cover non-exclusive inclusions.

[0055] In the description of the embodiments of the present application, the technical terms "first", "second", etc. are only used to distinguish different objects, and cannot be understood as indicating or implying relative importance or implicitly indicating the number, specific order or primary and secondary relationship of the indicated technical features. In the description of the embodiments of the present application, the meaning of "multiple" is more than two, unless otherwise clearly and specifically defined.

[0056] Reference to "embodiments" herein means that a particular feature, structure, or characteristic described in conjunction with the embodiments may be included in at least one embodiment of the present application. The appearance of the phrase in various locations in the specification does not necessarily refer to the same embodiment, nor is it an independent or alternative embodiment that is mutually exclusive with other embodiments. It is explicitly and implicitly understood by those skilled in the art that the embodiments described herein may be combined with other embodiments.

[0057] In the description of the embodiments of the present application, the term "and / or" is only a description of the association relationship of the associated objects, indicating that there may be three relationships. For example, A and / or B can represent: A exists alone, A and B exist at the same time, and B exists alone. In addition, the character " / " in this article generally indicates that the associated objects before and after are in an "or" relationship.

[0058] In the description of the embodiments of the present application, the term "multiple" refers to more than two (including two). Similarly, "multiple groups" refers to more than two groups (including two groups), and "multiple pieces" refers to more than two pieces (including two pieces).

[0059] In the description of the embodiments of the present application, unless otherwise clearly specified and limited, technical terms such as "installed", "connected", "connected", "fixed" and the like should be understood in a broad sense. For example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection or an indirect connection through an intermediate medium, and it can be the internal connection of two elements or the interaction relationship between two elements. For those of ordinary skill in the art, the specific meanings of the above terms in the embodiments of the present application can be understood according to the specific circumstances.

[0060] Embodiment 1

[0061] Please refer to Figure 1 , is a flow chart of a robust iterative learning control method for a permanent magnet synchronous motor provided by an embodiment of the present invention, comprising the following specific steps:

[0062] S1. Construct a permanent magnet synchronous motor model;

[0063] Preferably, the permanent magnet synchronous motor model is:

[0064]

[0065] y k (t) = Cx k (t);

[0066]

[0067] Among them, xk (t) = [θ m,k ω m,k ] T ,θ m,k is the angular displacement of the permanent magnet synchronous motor rotor, ω m,k is the angular displacement of the permanent magnet synchronous motor rotor, is the state variable x k The first derivative of (t), y k (t) is the output of the permanent magnet synchronous motor, u k (t) is the control signal of the permanent magnet synchronous motor, w k (t) is the external disturbance to the permanent magnet synchronous motor system, l k (t) is the load disturbance of the permanent magnet synchronous motor, J is the moment of inertia of the permanent magnet synchronous motor, C e is the back electromotive force of the permanent magnet synchronous motor, K t is the torque coefficient of the permanent magnet synchronous motor, R s is the stator resistance of the permanent magnet synchronous motor, P n is the number of pole pairs of the permanent magnet synchronous motor, B n is the viscous friction coefficient of the permanent magnet synchronous motor, T f,k is the load torque of the permanent magnet synchronous motor.

[0068] Specifically, the existing PMSM output tracking control methods mainly include traditional PID control, fuzzy control, neural network control, model predictive control, etc. These methods have their own advantages and disadvantages:

[0069] (1) The traditional PID control method is simple and easy to implement, but for complex control systems, it is difficult to meet the requirements of high-precision trajectory tracking and is easily affected by external disturbances. Its stability and robustness need to be improved.

[0070] (2) Fuzzy control methods can handle control problems in nonlinear systems and fuzzy environments and have certain robustness and adaptability, but they require a lot of experience and expertise to design fuzzy rules, and in some cases there may be problems with unstable performance.

[0071] (3) The neural network control method can learn the nonlinear characteristics of the system and has strong adaptability and generalization ability. However, the training process of the neural network is complicated and requires a large amount of data and computing resources. In some cases, there may be problems of overfitting and slow convergence.

[0072] (4) The model predictive control method can take into account the dynamic characteristics and constraints of the system and has good performance and robustness, but it has high computational complexity, poor real-time performance, and requires high model accuracy.

[0073] In summary, the existing PMSM tracking control methods can meet the needs of practical applications to a certain extent, but there are still problems in stability, robustness, computational complexity and real-time performance, which need further research and improvement. At the same time, these existing methods do not have learning capabilities, and their control performance remains unchanged when the dynamic system is repeatedly operated.

[0074] Based on the above problems, the present invention proposes a PMSM trajectory tracking control method with self-learning and strong robustness, which makes full use of the repeated operation characteristics of the PMSM system. On the basis of ensuring high-precision trajectory tracking control, a finite-time extended state observer (FTESO) is introduced to suppress non-repetitive interference, thereby improving the adaptability of PMSM to complex environments and enhancing its robustness to non-repetitive interference.

[0075] Please refer to Figure 2 , is a design flow chart of the PMSM trajectory tracking control method of the present invention, which mainly aims at the problem that PMSM has poor adaptability to non-repetitive environmental interference, and designs a robust adaptive iterative learning control algorithm, which can fully utilize the repeatability of the system for learning while ensuring the trajectory tracking control accuracy, thereby achieving the purpose of improving the adaptability and robust performance of PMSM to the environment. The specific design implementation steps are as follows:

[0076] Step 1: Establishment of PMSM model

[0077] First, start from the dq axis voltage equation of PMSM:

[0078]

[0079] Among them, u d ,u q ,i d ,i q , L d , L q They are dq axis voltage, dq axis current and dq axis inductance, R s is the stator resistance, P n is the pole pair number, C e is the back electromotive force, ω m is the mechanical angular velocity.

[0080] In order to obtain good control performance, the PMSM is subjected to field-oriented vector control. d = 0, so that the current vector and the permanent magnet magnetic field are orthogonal in space, then the torque equation of PMSM is:

[0081]

[0082] Among them, T e , ψ f , K t are electromagnetic torque, rotor permanent magnet flux and torque coefficient respectively.

[0083] The mechanical motion equation of PMSM is:

[0084]

[0085] Where J is the moment of inertia, T f is the load torque, B n is the viscous friction coefficient, θ m is the motor angular displacement.

[0086] The dynamic equation of PMSM can be derived from equations (1-1), (1-2) and (1-3):

[0087]

[0088] Here, the subscript k is used to indicate that the load on the motor changes with each iteration. The control goal is to drive the output angular displacement θ m Tracking the desired angular displacement θ in the presence of non-repeating disturbances ref We take the rotor’s angular displacement and angular velocity as state variables, i.e., θ m,k =x 1,k ,ω m,k =x 2,k , x k =[x 1,k ,x 2,k ] T , then equation (1-4) can be expressed in the form of a state equation:

[0089]

[0090] Among them, u k (t) is the control signal of PMSM, that is, u q , w k (t) is the external disturbance to the system, and C = [1 0], The specific meanings of some of the above PMSM parameters are shown in Table 1.

[0091] Table 1 PMSM parameters

[0092]

[0093]

[0094] Table 1 PMSM parameters

[0095] S2. According to the permanent magnet synchronous motor model, a nonlinear function for estimating the system external disturbance of the permanent magnet synchronous motor is constructed, and then according to the nonlinear function, a finite time extended state observer for estimating the system state and the system external disturbance of the permanent magnet synchronous motor is constructed;

[0096] Preferably, the nonlinear function is:

[0097]

[0098]

[0099] in, and is a nonlinear function, and for The weight, and for The weight, for and specific manifestations, for and The specific form of , κ1>0, κ1 is the adjustment parameter, j=1,2.

[0100] Preferably, the finite-time extended state observer is:

[0101]

[0102]

[0103]

[0104] Where L1 and L2 are the gain matrices of the finite-time extended state observer, For x k The estimated value of (t), for l k (t)+w k The estimated value of (t), and They are and The first derivative of k is the control signal of the permanent magnet synchronous motor, e 1,k For x k The estimated error of (t), e 2,k for l k (t)+w k The estimated error of (t), e 1,k =[e 11,k ,e12,k ] T ∈R 2 .

[0105] Step 2: Design of finite-time extended state observer

[0106] make Then the system (1-5) can be re-expressed as follows:

[0107]

[0108] Let z 2,k =ftotal,k(t),z 1,k =x k (t), the system (2-1) can be expressed as an extended state model:

[0109]

[0110] For this system, FTESO is designed to estimate the state and interference of the system. The specific design is as follows:

[0111]

[0112] Where L1 and L2 are the observer gain matrices to be designed, e 1,k =[e 11,k ,e 12,k ] T ∈R 2 , nonlinear function and The design is as follows:

[0113]

[0114] Among them, κ1>0, j=1,2.

[0115] In order to better illustrate the effect of the FTESO designed by the present invention, we provide the design of the traditional ESO for comparison. The design of the ESO is as follows:

[0116]

[0117] Compared with the traditional ESO using linear error function e 1,k Different from the above, the FTESO (2-3) proposed in the present invention adopts an appropriate nonlinear function and To estimate the total disturbance, a nonlinear function is cleverly constructed and The following relationship is satisfied, namely:

[0118]

[0119] in:

[0120]

[0121] Furthermore, the proposed Lyapunov function can construct an inequality form that converges in finite time Thus, the estimation accuracy and convergence speed of the observer are improved. The characteristics of the FTESO proposed in the present invention are that they can give an estimate of the state within a finite time and ensure that the error is within a certain acceptable range during this time. The traditional ESO converges asymptotically over infinite time. Considering the limited operating time interval of the ILC system, if the ESO cannot estimate the disturbance within a finite time, the control performance of the entire system will be significantly reduced. Therefore, the introduction of FTESO improves the development of ESO in the ILC system.

[0122] The error equation of FTESO state estimation is obtained by subtracting (2-2) and (2-3):

[0123]

[0124] Compared with the traditional extended state observer, the error term in equation (2-3) is and The design is nonlinear, which enables FTESO to achieve state estimation in a finite time, thereby reducing the observation time to a certain extent and improving the estimation accuracy. Specifically, equation (2-4) introduces the nonlinear term and the linear term e 1j,k When the estimation error is far away from the origin, the linear term e 1j,k The estimated error converges quickly near the origin. On the contrary, when the estimated error is near the origin, the nonlinear term in equation (2-4) ensures that the error remains near the origin.

[0125] By adjusting the parameters L1, L2 and κ1, the observer (2-3) will converge within a finite time and can effectively estimate the state and disturbance of the system.

[0126] S3. According to the permanent magnet synchronous motor model and the finite time extended state observer, an iterative learning trajectory tracking control law of the permanent magnet synchronous motor is constructed, and then according to the iterative learning trajectory tracking control law, adaptive iterative learning control is performed on the permanent magnet synchronous motor to obtain a trajectory tracking control result of the permanent magnet synchronous motor.

[0127] Preferably, the tracking control module includes: a learning module, a feedback module and an interference compensation module.

[0128] Among them, the learning module is used to suppress the tracking error of the permanent magnet synchronous motor; the interference compensation module is used to suppress the non-repetitive interference of the permanent magnet synchronous motor and enhance the transient performance of the permanent magnet synchronous motor; the feedback module is used to control the permanent magnet synchronous motor system to maintain a stable state.

[0129] Preferably, the iterative learning trajectory tracking control law of the permanent magnet synchronous motor is:

[0130]

[0131] in, For learning modules, For the feedback module, It is the interference compensation module.

[0132] Preferably, the learning module is:

[0133]

[0134] Among them, α is the attenuation factor, 0<α<1, K2 is the gain matrix of the learning module, is the input of the previous iteration of the permanent magnet synchronous motor, y d (t) is the expected output of the permanent magnet synchronous motor, y k (t) is the actual output of the permanent magnet synchronous motor, e y,k (t) is the tracking error;

[0135] The feedback module is:

[0136]

[0137] Among them, K1 is the gain matrix of the feedback module;

[0138] The interference compensation module is:

[0139]

[0140] in, for l k (t)+w k The estimated value of (t) is obtained according to the finite time extended state observer.

[0141] Step 3: Design of robust iterative learning trajectory tracking control method

[0142] For system (2-1), the following FTESO-based iterative learning trajectory tracking control law is designed:

[0143]

[0144] in, For learning modules, For the feedback module, For the interference compensation module, the three modules are as follows:

[0145] Learning modules:

[0146]

[0147] Among them, 0<α<1 is the attenuation factor, K2 is the gain matrix to be designed, represents the input of the previous iteration,

[0148] Feedback module:

[0149]

[0150] Among them, K1 is the gain matrix to be designed, which represents the gain of the feedback controller;

[0151] Interference compensation module:

[0152]

[0153] in, Obtained by the designed FTESO.

[0154] Please refer to Figure 3 , which is a block diagram of the robust iterative learning trajectory tracking controller designed by the present invention. As shown in formulas (3-1) to (3-4), the control algorithm (3-1) integrates three different modules: the feedforward module Designed to minimize tracking errors, the interference rejection module Effectively suppress non-repeatable interference and enhance transient performance. At the same time, the feedback module It plays a key role in ensuring the stability of the system. The control algorithm (3-1) shows the integration of key control information, including the data of the previous iteration, the output feedback of the current iteration and the disturbance estimation. This control scheme improves the overall performance of the system.

[0155] Finally, we can draw the following conclusions: For the PMSM system (1-4) in a complex environment, the proposed learning control schemes (3-1) to (3-4) can ensure the tracking error e y,k (t) When k→∞, it gradually converges to the neighborhood of zero.

[0156] Step 4: Implementation and application of the proposed control method

[0157] This step will verify the effectiveness of the proposed FTESO-based robust iterative learning trajectory tracking control method through numerical simulation. The specific application steps are as follows:

[0158] Given a reference trajectory:

[0159] Assume the reference trajectory is:

[0160]

[0161] Set PMSM parameters:

[0162] To verify the effectiveness of the proposed scheme, by substituting the parameters of PMSM in Table 1, we can get a = -16213, b = 320000. Assume that the state disturbance in the system is time-varying, specifically w k (t) = cos(2t) + 0.5sin(200πt), the second term in this expression represents the influence of high-frequency noise. k (t) depends on the load of the PMSM ( T f,k is the load torque, J is the moment of inertia, so l k (t) depends on the iteratively changing load torque T f,k , T f,k The value range of is 0.122N·m~0.490N·m). Assume that the PMSM is unloaded. k (t)=-348.6 / s 2 , l when fully loaded k (t)=-1398.6 / s 2 The simulation assumes that the load on the motor varies with the iteration number k, given by the following equation:

[0163] l k (t) = -348.6*(k%4) (4-2)

[0164] Select controller parameters:

[0165] According to the PMSM system parameters, the controller parameters need to be selected to ensure the convergence of the algorithm. The controller parameters can be selected as follows:

[0166] K1=3.6×10 4 , K2=1,

[0167] k1=0.6,α=0.1,

[0168]

[0169] Control law comparison:

[0170] In order to verify the feasibility of the control method proposed in the present invention, the traditional ESO is used for experimental comparison under the ILC control framework. The observer parameters are set the same, which facilitates the demonstration of the performance of the control method proposed in the present invention. The traditional ESO is shown below:

[0171]

[0172] The controller executes and obtains the control result:

[0173] Please refer to Figure 4 , is a schematic diagram of the simulation results of PMSM angular displacement tracking under the traditional ESO and ILC combination method, showing the system output trajectory under the 1st, 5th and 60th iteration learning respectively. Please refer to Figure 5 , which is a schematic diagram of the simulation results of PMSM angular displacement tracking under the FTESO and ILC combination method designed by the present invention, respectively showing the system output trajectory under the 1st, 5th and 60th iteration learning. Please refer to Figure 6 , which is a schematic diagram of the error curve comparison of the two methods as the number of iterations changes. It can be seen that when the FTESO-I LC method is used, the initial error of the system is smaller and the convergence speed is faster, while when the traditional I LC method is used, the initial error is larger, the convergence speed is slower, and the tracking performance is reduced.

[0174] From the control results, it can be seen that the beneficial effects of the robust adaptive learning trajectory tracking control method proposed in the present invention include:

[0175] (1) Compared with the traditional trajectory tracking control, the present invention can make full use of the repeated operation characteristics of the PMSM system for learning, gradually improve the PMSM trajectory tracking control accuracy, and enhance the ability to adapt to the environment;

[0176] (1) The extended state model characterization method proposed in the present invention can regard the unknown model and disturbance of the system as the total disturbance, which is convenient for controller design and state estimation;

[0177] (1) The control method proposed in the present invention can effectively deal with the uncertainty factors of the system, which is beneficial to improving the robustness of the PMSM system.

[0178] In a specific embodiment, in order to verify the above beneficial effects, the convergence of the finite time extended state observer (2-3) and the convergence of the controller are proved as follows:

[0179] 1. Prove the convergence of the finite-time extended state observer (2-3):

[0180] Define the following Lyapunov function:

[0181]

[0182] in, P e is a positive definite matrix, let but:

[0183]

[0184] For η k Derivative:

[0185]

[0186] in,

[0187]

[0188] ∥h k ∥2≤D, D is unknown but bounded, since |T(e 1j,k )|≥1, so Select appropriate L1, L2, k1 so that is a Hurwitz matrix. Then, for any positive definite matrix Q e , there exists a corresponding positive definite matrix P e satisfy:

[0189]

[0190] Obviously, there exists a positive constant μ such that Negative determination, that is

[0191]

[0192] Before proving it, we give the following lemma:

[0193] Lemma 1: If a continuously differentiable non-negative function V(x) satisfies where α * >0,β * > 0, 0<γ<1, for the scalar τ(0<τ<β * ) There exists a finite time T L > 0, for all t ≥ T L ,have:

[0194]

[0195] The time limit is:

[0196]

[0197] Derivative (5-3):

[0198]

[0199] in as well as:

[0200]

[0201] According to the determinant operation rule of block matrix, the determinant operation of the following matrix is ​​calculated as:

[0202]

[0203] Existence α e >0, μ>0, so that the following matrix is ​​semi-negative definite:

[0204]

[0205] Then, (5-7) can be further simplified as:

[0206]

[0207] From (5-1), we can get the following inequality:

[0208]

[0209] and:

[0210]

[0211] From (5-12) and (5-13), we can get:

[0212]

[0213] Based on the above formula, we can get:

[0214]

[0215] Substituting the above formula into (5-11), we get:

[0216]

[0217] in, b1=μ,c1=α e D 2 According to formula (5-16), the inequality exist Then, according to Lemma 1, the estimated error η k Converges from the initial error η0 to the region The finite time T c for:

[0218]

[0219] Among them, η0 represents the initial value of the error. Therefore, the observer error e 1,k 、e 2,k will converge to a bounded region in finite time. This completes the proof of convergence of FTESO.

[0220] 2. To prove the convergence of the controller, the reference trajectory is y d Indicates that, assuming there is a corresponding control input u d , so that the output generated by the following system is y d :

[0221]

[0222] Subtract (2-1) from (6-1) and substitute it into (3-1) to obtain the error equation:

[0223]

[0224] in, e -1 (t) = 0. We use the composite energy function CEF for analysis. First, establish CEF as follows:

[0225]

[0226] Convergence analysis can be divided into two parts, including the convergence of difference and tracking errors between two consecutive iterations:

[0227] ① Difference of CEF in two iterations

[0228] The difference of CEF in two iterations can be expressed as:

[0229]

[0230] In each iteration, the initial state of the system can be reset to the same position as the reference state, i.e. The above formula can be rearranged as:

[0231]

[0232] Calculate the second term on the right side of equation (6-5):

[0233]

[0234] Calculate the third term on the right side of equation (6-5):

[0235]

[0236] Using the controller's learning law (3-2), we can transform Then the second term on the right side of equation (6-7) is simplified to:

[0237]

[0238] And the third term on the right side of equation (6-7) is simplified to:

[0239]

[0240] The formula uses the inequality -(a+b) 2 ≤-2ab-b 2 Combining (6-8) and (6-9), we get:

[0241]

[0242] Substituting the above formula into (6-7) we get:

[0243]

[0244] Substituting (6-8) and (6-11) into (6-7), we obtain:

[0245]

[0246] because:

[0247]

[0248] Let K2 = Γ1Γ2, there exists P = P T >0, Q=Q T ≥0, so that the following conditions hold:

[0249]

[0250] Then (6-5) can be simplified to:

[0251]

[0252] In the formula, According to the estimated error δ of FTESO k Convergence, that is, ‖δ k ‖≤δ M , where δ M Unknown but bounded.

[0253] make Then we have:

[0254]

[0255] So (6-15) can be written as

[0256]

[0257] Where 0<α<1.

[0258] ②Convergence of tracking error

[0259] According to formula (6-17), it is not difficult to draw the following conclusion. The difference can be written as:

[0260]

[0261] It can be seen that if V0 is bounded, then:

[0262]

[0263] And because:

[0264]

[0265] so:

[0266]

[0267] The proof that V0 is bounded is as follows:

[0268]

[0269] Taking the derivative of V0, we have:

[0270]

[0271] The above formula applies the FTESO-based ILC schemes (3-1) and (3-2)-(3-4), and uses and Equation (6-23) shows that Bounded, which means that V0 remains bounded in the interval [0,T], that is, it can be finally proved that convergence.

[0272] Embodiment 2

[0273] Please refer to Figure 7 , is a structural schematic diagram of a robust iterative learning control device for a permanent magnet synchronous motor provided by an embodiment of the present invention, the device comprising: a permanent magnet synchronous motor model building module, a finite time extended state observer building module and an iterative learning trajectory tracking control module;

[0274] The permanent magnet synchronous motor model building module is used to build a permanent magnet synchronous motor model;

[0275] The finite-time extended state observer construction module is used to construct a nonlinear function for estimating the system external disturbance of the permanent magnet synchronous motor according to the permanent magnet synchronous motor model, and then construct a finite-time extended state observer for estimating the system state and system external disturbance of the permanent magnet synchronous motor according to the nonlinear function;

[0276] The iterative learning trajectory tracking control module is used to construct an iterative learning trajectory tracking control law of the permanent magnet synchronous motor according to the permanent magnet synchronous motor model and the finite time extended state observer, and then perform adaptive iterative learning control on the permanent magnet synchronous motor according to the iterative learning trajectory tracking control law to obtain a trajectory tracking control result of the permanent magnet synchronous motor.

[0277] It should be noted that the device embodiments described above are merely schematic, wherein the units described as separate components may or may not be physically separated, and the components displayed as units may or may not be physical units, that is, they may be located in one place, or they may be distributed on multiple network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the scheme of this embodiment. In addition, in the accompanying drawings of the device embodiments provided by the present invention, the connection relationship between the modules indicates that there is a communication connection between them, which may be specifically implemented as one or more communication buses or signal lines. A person of ordinary skill in the art may understand and implement it without paying any creative effort.

[0278] Those skilled in the art can clearly understand that, for the sake of convenience and brevity, the specific working process of the device described above can refer to the corresponding process in the aforementioned method embodiment, and will not be repeated here.

[0279] Embodiment 3

[0280] Accordingly, an embodiment of the present invention provides an electronic device, comprising a processor, a memory, and a computer program stored in the memory and configured to be executed by the processor, wherein when the processor executes the computer program, the robust iterative learning control method for the permanent magnet synchronous motor described in the above-mentioned embodiment of the invention is implemented.

[0281] The electronic device may be a computing device such as a desktop computer, a notebook, a palmtop computer, a cloud server, etc. The device may include, but is not limited to, a processor and a memory.

[0282] The processor may be a central processing unit (CPU), other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field-programmable gate arrays (FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor may be a microprocessor or any conventional processor, etc. The processor is the control center of the device, and various interfaces and lines are used to connect various parts of the entire device.

[0283] Embodiment 4

[0284] Accordingly, an embodiment of the present invention provides a storage medium, which includes a stored computer program, wherein when the computer program is running, the device where the storage medium is located is controlled to execute the robust iterative learning control method of the permanent magnet synchronous motor described in the above-mentioned embodiment of the invention.

[0285] The memory can be used to store the computer program, and the processor realizes various functions of the device by running or executing the computer program stored in the memory and calling the data stored in the memory. The memory can mainly include a program storage area and a data storage area, wherein the program storage area can store an operating system, at least one application required for a function, etc.; the data storage area can store data created according to the use of the mobile phone, etc. In addition, the memory can include a high-speed random access memory, and can also include a non-volatile memory, such as a hard disk, a memory, a plug-in hard disk, a smart memory card (Smart Med ia Card, SMC), a secure digital (Secure Digital, SD) card, a flash card (Flash Card), at least one disk storage device, a flash memory device, or other volatile solid-state storage devices.

[0286] The storage medium is a computer-readable storage medium, and the computer program is stored in the computer-readable storage medium. When the computer program is executed by the processor, the steps of each method embodiment described above can be implemented. Among them, the computer program includes computer program code, and the computer program code can be in source code form, object code form, executable file or some intermediate form, etc. The computer-readable medium may include: any entity or device capable of carrying the computer program code, recording medium, USB flash drive, mobile hard disk, disk, optical disk, computer memory, read-only memory (ROM, Read-On l yMemory), random access memory (RAM, Random Access Memory), electric carrier signal, telecommunication signal and software distribution medium, etc. It should be noted that the content contained in the computer-readable medium can be appropriately increased or decreased according to the requirements of legislation and patent practice in the jurisdiction. For example, in some jurisdictions, according to legislation and patent practice, computer-readable media do not include electric carrier signals and telecommunication signals.

[0287] The above is a preferred embodiment of the present invention. It should be pointed out that a person skilled in the art can make several improvements and modifications without departing from the principle of the present invention. These improvements and modifications are also considered to be within the scope of protection of the present invention.

Claims

1. A robust iterative learning control method for a permanent magnet synchronous motor, characterized in that: include: Construct a permanent magnet synchronous motor model; According to the permanent magnet synchronous motor model, a nonlinear function for estimating a system external disturbance of the permanent magnet synchronous motor is constructed, and then according to the nonlinear function, a finite time extended state observer for estimating a system state of the permanent magnet synchronous motor and a system external disturbance is constructed; According to the permanent magnet synchronous motor model and the finite time extended state observer, an iterative learning trajectory tracking control law of the permanent magnet synchronous motor is constructed, and then according to the iterative learning trajectory tracking control law, the permanent magnet synchronous motor is adaptively iteratively learned and controlled to obtain a trajectory tracking control result of the permanent magnet synchronous motor.

2. The method for robust iterative learning control of a permanent magnet synchronous motor according to claim 1, characterized in that: The permanent magnet synchronous motor model is: y k (t)=Cx k (t); Among them, x k (t) = [θ m,k ω m,k ] T ,θ m,k is the angular displacement of the permanent magnet synchronous motor rotor, ω m,k is the angular displacement of the permanent magnet synchronous motor rotor, is the state variable x k The first derivative of (t), y k (t) is the output of the permanent magnet synchronous motor, u k (t) is the control signal of the permanent magnet synchronous motor, w k (t) is the external disturbance to the permanent magnet synchronous motor system, l k (t) is the load disturbance of the permanent magnet synchronous motor, J is the moment of inertia of the permanent magnet synchronous motor, C e is the back electromotive force of the permanent magnet synchronous motor, K t is the torque coefficient of the permanent magnet synchronous motor, R s is the stator resistance of the permanent magnet synchronous motor, P n is the number of pole pairs of the permanent magnet synchronous motor, B n is the viscous friction coefficient of the permanent magnet synchronous motor, T f,k is the load torque of the permanent magnet synchronous motor.

3. The robust iterative learning control method for a permanent magnet synchronous motor according to claim 2, characterized in that: The nonlinear function is: in, and is a nonlinear function, and for The weight, and for The weight, for and specific manifestations, for and The specific form of , κ1>0, κ1 is the adjustment parameter, j=1,2.

4. The method for robust iterative learning control of a permanent magnet synchronous motor according to claim 3, characterized in that: The finite-time extended state observer is: Where L1 and L2 are the gain matrices of the finite-time extended state observer, For x k The estimated value of (t), for l k (t)+w k The estimated value of (t), and They are and The first derivative of k is the control signal of the permanent magnet synchronous motor, e 1,k For x k The estimated error of (t), e 2,k for l k (t)+w k The estimated error of (t), e 1,k =[e 11,k ,e 12,k ] T ∈R 2 .

5. The method for robust iterative learning control of a permanent magnet synchronous motor according to claim 4, characterized in that: The tracking control module includes: a learning module, a feedback module and an interference compensation module. Among them, the learning module is used to suppress the tracking error of the permanent magnet synchronous motor; the interference compensation module is used to suppress the non-repetitive interference of the permanent magnet synchronous motor and enhance the transient performance of the permanent magnet synchronous motor; the feedback module is used to control the permanent magnet synchronous motor system to maintain a stable state.

6. The method for robust iterative learning control of a permanent magnet synchronous motor according to claim 5, characterized in that: The iterative learning trajectory tracking control law of the permanent magnet synchronous motor is: in, For learning modules, For the feedback module, It is the interference compensation module.

7. The method for robust iterative learning control of a permanent magnet synchronous motor according to claim 7, characterized in that: The learning modules are: Among them, α is the attenuation factor, 0<α<1, K2 is the gain matrix of the learning module, is the input of the previous iteration of the permanent magnet synchronous motor, y d (t) is the expected output of the permanent magnet synchronous motor, y k (t) is the actual output of the permanent magnet synchronous motor, e y,k (t) is the tracking error; The feedback module is: Wherein, K1 is the gain matrix of the feedback module; The interference compensation module is: in, for l k (t)+w k The estimated value of (t) is obtained according to the finite time extended state observer.

8. A robust iterative learning control device for a permanent magnet synchronous motor, characterized in that: include: Permanent magnet synchronous motor model building module, finite time extended state observer building module and iterative learning trajectory tracking control module; The permanent magnet synchronous motor model building module is used to build a permanent magnet synchronous motor model; The finite-time extended state observer construction module is used to construct a nonlinear function for estimating the system external disturbance of the permanent magnet synchronous motor according to the permanent magnet synchronous motor model, and then construct a finite-time extended state observer for estimating the system state and system external disturbance of the permanent magnet synchronous motor according to the nonlinear function; The iterative learning trajectory tracking control module is used to construct an iterative learning trajectory tracking control law of the permanent magnet synchronous motor according to the permanent magnet synchronous motor model and the finite time extended state observer, and then perform adaptive iterative learning control on the permanent magnet synchronous motor according to the iterative learning trajectory tracking control law to obtain a trajectory tracking control result of the permanent magnet synchronous motor.

9. An electronic device, characterized in that: The method comprises a processor, a memory, and a computer program stored in the memory and configured to be executed by the processor, wherein the processor implements the robust iterative learning control method for a permanent magnet synchronous motor as claimed in any one of claims 1 to 7 when executing the computer program.

10. A storage medium, characterized in that: The storage medium includes a stored computer program, wherein when the computer program is executed, the device where the storage medium is located is controlled to execute the robust iterative learning control method for the permanent magnet synchronous motor according to any one of claims 1 to 7.

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