Optimal trajectory tracking control method and device for nonlinear motor servo system

Abstract

The present application proposes an optimal trajectory tracking control method and device for a nonlinear motor servo system, which relates to the field of artificial intelligence technology, wherein the method includes: establishing an error dynamic model for motor system tracking control, introducing new state variables to convert them into an augmented system model, and determining the description form of the optimal tracking control problem under state inequality constraints; based on the augmented system model, using the function approximation method to establish an identification model of the unknown dynamic system; using the parallel learning method, using online data and historical data to estimate the unknown parameters in the identification model; based on the identification model, updating the control input through an iterative algorithm, solving the optimal tracking control problem under state inequality constraints, and obtaining the optimal tracking control strategy. The present application using the above scheme does not rely on the precise model of the motor system, and achieves minimization of the tracking error and control energy consumption in a limited time domain while ensuring that the state of the motor system meets the existing constraints.

Description

Technical Field

[0001] The present application relates to the technical field of control theory, and in particular to an optimal trajectory tracking control method and device for a nonlinear motor servo system. Background Art

[0002] Trajectory tracking control aims to design a control strategy that enables the controlled system to track a predefined trajectory. Traditional control methods, such as PID controllers, rely on accurate modeling and parameter setting of the system. However, actual systems usually have complex dynamic characteristics, such as nonlinearity, which makes it difficult for traditional methods to achieve ideal tracking performance. As an important branch of modern control theory, optimal tracking control tracks the system trajectory by minimizing a specified cost function under given constraints. The cost function usually includes tracking error and control input. The generation of control strategy must not only ensure the minimization of tracking error, but also take into account the rationality of control input and avoid excessive resource consumption. It is of great significance in the field of control.

[0003] The main methods for solving the optimal tracking control problem are variational method and dynamic programming method. However, since the actual motor system is highly nonlinear and the accurate model is difficult to obtain, the solution of these two methods is often extremely difficult. Summary of the invention

[0004] The present application aims to solve one of the technical problems in the related art at least to some extent.

[0005] To this end, the first purpose of the present application is to propose an optimal trajectory tracking control method for a nonlinear motor servo system, which is independent of the precise model of the system and can handle the optimal tracking control problem of any nonlinear system state subject to inequality constraints.

[0006] The second objective of the present application is to provide an optimal trajectory tracking control device for a nonlinear motor servo system.

[0007] To achieve the above-mentioned purpose, the first embodiment of the present application proposes an optimal trajectory tracking control method for a nonlinear motor servo system, comprising:

[0008] Establish the error dynamic model of motor system tracking control, introduce new state variables to transform the error dynamic model into an augmented system model, and determine the description form of the optimal tracking control problem under state inequality constraints;

[0009] Based on the augmented system model, the identification model of the unknown dynamic system is established using the function approximation method;

[0010] Through parallel learning methods, online data and historical data are used to estimate unknown parameters in the identification model;

[0011] Based on the identification model, the control input is updated through an iterative algorithm, the optimal tracking control problem under state inequality constraints is solved, and the optimal tracking control strategy is obtained.

[0012] The optimal trajectory tracking control method for the nonlinear motor servo system of the embodiment of the present application establishes an error dynamic model of the motor system tracking control, and introduces new state variables to transform the time-varying error system into a non-time-varying augmented system, and further obtains the description form of the optimal tracking control problem under the state inequality constraint; based on the augmented system model, the powerful nonlinear mapping ability of the function approximation method is used to establish a parameter identification model of the unknown dynamic system; through a parallel learning method, online data and existing historical data are simultaneously used to estimate the unknown parameters in the identification model; based on the identification model, the control input is updated through an iterative algorithm to obtain the optimal tracking control strategy under the inequality constraint. The present application does not rely on the precise model of the motor system, and realizes minimization of the tracking error and control energy consumption in a limited time domain while ensuring that the state of the motor system meets the existing constraints, which meets the actual engineering needs; the system considered in the present application is a nonlinear system, which has practical significance.

[0013] Optionally, in one embodiment of the present application, establishing an error dynamic model for motor system tracking control includes:

[0014] The nonlinear system of the motor is defined as:

[0015]

[0016] in, is the system status, is the system initial time, is the initial state of the system, is the system control input, is the system status after u is input into the system, is the dynamic function of the system,

[0017] The state constraints of the motor nonlinear system are defined as:

[0018]

[0019] in, for dimensional column vector function, representing the existence Inequality constraints;

[0020] Define the system tracking signal as , the tracking error is , for the optimal tracking control problem, the quadratic performance index is used to represent the cost function, and the cost function is expressed as:

[0021]

[0022] in, represents a predetermined time interval, , is a real symmetric positive definite matrix,

[0023] The dynamic function and inequality constraints of the error dynamic model are expressed as:

[0024]

[0025] New state variables are introduced to transform the error dynamic model into an augmented system model, including:

[0026] Assume that the tracking signal is generated by an unknown dynamic function, which is expressed as:

[0027]

[0028] Defining new state variables , the augmented system is expressed as:

[0029]

[0030] The inequality constraints satisfied by the new state variables are:

[0031]

[0032] The cost function is expressed as:

[0033]

[0034] Among them, the matrix Defined as:

[0035]

[0036] Determine the description form of the optimal tracking control problem under state inequality constraints, including:

[0037] For inequality constraints, the Kelley-Bryson penalty function is constructed as the cost function, and the solution of the optimal tracking control problem is transformed into the solution of the unconstrained problem. The constructed cost function is expressed as:

[0038]

[0039] in, is a monotonically increasing sequence that satisfies , in the penalty function The term is a step function, which is formulated as:

[0040]

[0041] When the augmented system state satisfies the given inequality constraints, , the solution to the unconstrained problem satisfies the following conditions:

[0042]

[0043] The simplified form of the optimality condition is:

[0044]

[0045] in, is the covariance quantity, is the Hamiltonian function, , .

[0046] Optionally, in one embodiment of the present application, based on the augmented system model, an identification model of an unknown dynamic system is established using a function approximation method, including:

[0047] make represents the unknown dynamic function of the augmented system The function approximation method can be used to approximate it as follows:

[0048]

[0049] in, is the weight coefficient, For hidden layer The activation function of a neuron is is the corresponding approximation error;

[0050] The estimated value of the weight coefficient is defined as , let the matrix , , let the activation function vector be , the parameter identification model of the unknown dynamic system is expressed as: .

[0051] Optionally, in one embodiment of the present application, the unknown parameters in the identification model are estimated using online data and historical data through a parallel learning method, including:

[0052] Collect at any time The historical data points of the augmented system are , the historical data points include the state of the augmented system, the control input, and the derivative of the state, defining the matrix , the collected historical data set meets ;

[0053] Using historical data sets and online data to update the unknown parameters in the identification model, the adaptive update law during update is expressed as:

[0054]

[0055] in, and Respectively represent The estimated values ​​of the system state value and coefficient matrix are augmented in the iteration process. , is the learning rate, and They are The estimation error of the augmented system state and coefficient matrix during the iteration process.

[0056] Optionally, in one embodiment of the present application, the process of generating the optimal tracking control strategy includes:

[0057] Step S1: Initialize coefficients , , , set the accuracy error , , , select the initial control input and the initial coefficient matrix estimates , measure the state of the original system under the initial control input, and calculate the trajectory of the corresponding augmented system And the cost function ,make , ,in, ;

[0058] Step S2: Update the control input by solving the first set of equations, where the first set of equations is expressed as:

[0059]

[0060] in, , Represents the first n columns of the coefficient matrix;

[0061] Step S3: Update the coefficient matrix by solving the second set of equations, where the second set of equations is expressed as:

[0062]

[0063] Step S4: Calculate the trajectory of the augmented system using the updated control input And the corresponding cost function ;

[0064] Step S5: Repeat steps S2-S4. After each repetition, , , , is the iteration step length until ,

[0065] Step S6: Repeat steps S2-S5. After each repetition, , , , until the control input and the identification model converge to a given accuracy error, where the control input converges to a given accuracy error, expressed as: , the identification model converges to a given accuracy error, expressed as: ;

[0066] Step S7: Repeat steps S2-S6, and after each repetition, let , , , , , is the iteration step length until the state of the augmented system satisfies the inequality constraint under the given accuracy error, and the identification model parameters are obtained. And the optimal tracking control strategy , where the state of the augmented system satisfies the inequality constraint under a given precision error, expressed as: .

[0067] To achieve the above-mentioned purpose, the second embodiment of the present application proposes an optimal trajectory tracking control device for a nonlinear motor servo system, comprising:

[0068] The system building module is used to establish the error dynamic model of the motor system tracking control, introduce new state variables to transform the error dynamic model into an augmented system model, and determine the description form of the optimal tracking control problem under the state inequality constraints;

[0069] The system building module is also used to build an identification model of an unknown dynamic system based on the augmented system model using a function approximation method;

[0070] The system identification module is used to estimate the unknown parameters in the identification model using online data and historical data through a parallel learning method;

[0071] The calculation and solution module is used to update the control input through an iterative algorithm based on the identification model, solve the optimal tracking control problem under the state inequality constraints, and obtain the optimal tracking control strategy.

[0072] Additional aspects and advantages of the present application will be given in part in the description below, and in part will become apparent from the description below, or will be learned through the practice of the present application. BRIEF DESCRIPTION OF THE DRAWINGS

[0073] The above and / or additional aspects and advantages of the present application will become apparent and easily understood from the following description of the embodiments in conjunction with the accompanying drawings, in which:

[0074] Figure 1 A schematic flow chart of an optimal trajectory tracking control method for a nonlinear motor servo system provided in Embodiment 1 of the present application;

[0075] Figure 2 A schematic diagram of the structure of a nonlinear dual-motor servo system according to an embodiment of the present application;

[0076] Figure 3 It is a schematic diagram of the iteration of the cost function of the augmented system according to an embodiment of the present application;

[0077] Figure 4 It is a schematic diagram of the iterative change of the system identification error of the embodiment of the present application;

[0078] Figure 5 It is a schematic diagram of system constraint change iteration in an embodiment of the present application;

[0079] Figure 6 A schematic structural diagram of an optimal trajectory tracking control device for a nonlinear motor servo system provided in an embodiment of the present application. DETAILED DESCRIPTION

[0080] Embodiments of the present application are described in detail below, and examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are intended to be used to explain the present application, and should not be construed as limiting the present application.

[0081] The optimal trajectory tracking control method and device for a nonlinear motor servo system according to an embodiment of the present application will be described below with reference to the accompanying drawings.

[0082] Figure 1 A flowchart of an optimal trajectory tracking control method for a nonlinear motor servo system provided in Example 1 of the present application.

[0083] like Figure 1 As shown, the optimal trajectory tracking control method of the nonlinear motor servo system includes the following steps:

[0084] Step 101, establishing an error dynamic model of motor system tracking control, introducing new state variables to transform the error dynamic model into an augmented system model, and determining a description form of the optimal tracking control problem under state inequality constraints;

[0085] In the embodiment of the present application, the following nonlinear system is considered:

[0086]

[0087] in, is the system state and the initial state is , is the system control input, is the dynamic function of the system;

[0088] System state constraints are expressed as inequality vectors of the following form:

[0089]

[0090] in, for dimensional column vector function, representing the existence of the system Inequality constraints;

[0091] Define the system tracking signal as , then the tracking error is expressed as: , for the optimal tracking control problem, the following quadratic performance index is adopted:

[0092]

[0093] in, represents a predetermined time interval, , is a real symmetric positive definite matrix.

[0094] At the same time, the dynamic function of the tracking error system and the inequality constraints can be expressed as:

[0095]

[0096] Assume that the trace signal is generated by the following unknown dynamic function:

[0097]

[0098] Defining new state variables , then the error system can be transformed into the following time-invariant augmented system:

[0099]

[0100] The inequality constraints satisfied by the new state variables can be expressed as:

[0101]

[0102] At the same time, the original cost function can be further expressed as:

[0103]

[0104] Among them, the matrix Defined as:

[0105]

[0106] For inequality constraints, the following Kelley-Bryson penalty function is constructed as the cost function, and the original problem is transformed into solving a series of unconstrained problems:

[0107]

[0108] Among them, the penalty function The term is a step function and can be formulated as:

[0109]

[0110] is a monotonically increasing sequence that satisfies , when the augmented system state satisfies the given inequality constraints, we have According to the Pontryagin minimum principle, the solutions to the above series of unconstrained problems satisfy the following conditions:

[0111]

[0112] in, is the covariance quantity, is the Hamiltonian function, defined as:

[0113]

[0114] definition , the optimality condition in the Pontryagin minimum principle can be further written as:

[0115]

[0116] Due to the inequality constraints as well as This term is related to the control input Therefore, the optimality condition can be simplified to:

[0117]

[0118] As Figure 2 Taking the nonlinear dual-motor servo system shown in the figure as an example, the construction process of its augmented system includes:

[0119] The dynamic equation of the dual-motor servo system can be described as:

[0120]

[0121]

[0122] in, and Represent the angles of the two motors and the load respectively, and Represent the rotational inertia of the two motors and the load respectively, and Represent the resistance coefficients of the two motors and the load respectively, The transmission torque, due to the existence of backlash, is described as a dead zone function in the following form:

[0123]

[0124] in, is the angular error between the motor and the load, is the transmission ratio, is the tooth gap, is the torsion coefficient. Due to the non-differentiability of the dead zone function, it is usually approximated by the following smooth continuous differentiable function: ,in, Formulated as:

[0125]

[0126] in, is a constant, let , the state space expression of the above dual-motor system can be described as:

[0127]

[0128] The parameter values ​​of the nonlinear dual-motor servo system are shown in Table 1.

[0129] Table 1

[0130]

[0131] Select the motor system tracking signal as , , define the tracking error , since the two motors and the load have the same tracking target, the augmented system state can be simplified as: , by introducing new state variables, the time-varying error system can be transformed into the following time-invariant augmented system:

[0132]

[0133] The inequality constraints required by the motor system are: the angular velocity of the motor and the load is less than or equal to 1.2 , which is formulated as: , , , then the inequality constraints of the augmented system can be expressed as:

[0134]

[0135] Select the finite time domain as , select the optimal tracking control cost function as , the cost function caused by the state inequality constraint is selected as: ,make is the Kelley-Bryson penalty function. It should be noted that the precise system model in this embodiment is not necessarily known, and based on the unknown augmented system and the Kelley-Bryson cost function, the original tracking control problem can be transformed into solving a series of optimal control problems without constraints.

[0136] Step 102, based on the augmented system model, using a function approximation method to establish an identification model of the unknown dynamic system;

[0137] In this application example, represents the unknown dynamic function of the augmented system term, and use neural network to approximate it as:

[0138]

[0139] in, is the weight coefficient, For hidden layer The activation function of a neuron is is the corresponding approximate error. When the number of neurons in the hidden layer is large enough, the approximate error can approach 0 infinitely;

[0140] Since the true value of the weight coefficient is unknown, the estimated value of the weight coefficient is defined as , let the matrix ,in , and let the activation function vector be: , we get the following parameter identification model of the unknown dynamic system: .

[0141] Taking the nonlinear dual-motor servo system as an example, a single hidden layer neural network is selected. .

[0142] Step 103, using a parallel learning method to estimate unknown parameters in the identification model using online data and historical data;

[0143] In this application example, the collection is performed at any time The historical data points of the unknown augmented system are recorded as , including the state of the augmented system, the control input, and the derivative of the state. is predefined, so the state of the augmented system can be directly calculated. At the same time, the system state derivative usually has physical meanings such as velocity or acceleration, so it can be accurately measured. Define the matrix The historical data set collected is required to meet ,The parallel learning method simultaneously utilizes the historical data set and the online data to update the unknown parameters in the identification model and avoids the online verification of PE conditions;

[0144] definition and Respectively represent In the iteration process, the estimated values ​​of the system state value and coefficient matrix are augmented, and the following form of adaptive update law is designed:

[0145]

[0146] in, , is the learning rate, and They are The estimation error of the augmented system state and coefficient matrix during the iteration process.

[0147] Taking the nonlinear dual-motor servo system as an example, the historical offline data sets of 12 sample points were collected as shown in Tables 2 and 3, and 6 groups of data are listed in each table.

[0148] Table 2

[0149]

[0150] Table 3

[0151]

[0152] Step 104 , based on the identification model, the control input is updated through an iterative algorithm, the optimal tracking control problem under the state inequality constraint is solved, and the optimal tracking control strategy is obtained.

[0153] In the embodiment of the present application, an adaptive policy iteration algorithm is proposed to solve the optimal tracking control problem under the state inequality constraint. The specific steps of the algorithm are:

[0154] S1: Initialization coefficients , , , and the convergence accuracy , , , select the initial control input And the initial coefficient matrix estimate , measure the state of the original system under the initial control input, and calculate the trajectory of the corresponding augmented system And the cost function ,make , ,in, ;

[0155] S2: Update the control input by solving the following system of equations:

[0156]

[0157] in, , Represents the first n columns of the coefficient matrix;

[0158] S3: Update the coefficient matrix by solving the following system of equations:

[0159]

[0160] S4: Calculate the trajectory of the augmented system using the updated control input And the corresponding cost function , and determine whether the updated control input reduces the augmented system cost function: If , then let , , , is the iteration step length, and returns to S2, otherwise, enters S5;

[0161] S5: Determine whether the control input and identification model converge to a given accuracy error: If or , then let , , , and return to S2, otherwise, enter S6;

[0162] S6: Determine whether the state of the augmented system satisfies the inequality constraint under a given precision error: If , then let , , , , , is the iteration step length, and returns to S2, otherwise, the iteration process is stopped to obtain the augmented system identification model parameters And the optimal tracking control strategy .

[0163] Taking the nonlinear dual-motor servo system as an example, the initial state value of the system is selected as: The initial control input is selected as: , the initial parameters of the adaptive iterative algorithm are set as: , , , the initial coefficient matrix is ​​randomly selected as , as shown below:

[0164]

[0165] After calculation, we know that the initial augmented system trajectory cost function is: ,definition To measure the identification error of the augmented system, Represents the trace of the matrix, and the initial identification error can be calculated as: According to the iterative algorithm process, it converges after 86 iterations, and the augmented system cost function is as follows: Figure 3 As shown, we can see that It is significantly reduced to 5.6261. At the same time, the cost caused by the system state inequality constraint It converges to 0, which means that the augmented system satisfies the given inequality constraints within the given error range.

[0166] Figure 4 The curve of identification error changing with iteration is shown. It can be seen that the identification error decreases to 10 as the number of iterations increases. -7 Below. Definition The first Constraints in The maximum value within Figure 5 Reflects As the number of iterations changes, we can see that as the number of iterations increases, the augmented state gradually satisfies each given inequality constraint.

[0167] The optimal trajectory tracking control method for the nonlinear motor servo system of the embodiment of the present application establishes an error dynamic model of the motor system tracking control, and introduces new state variables to transform the time-varying error system into a non-time-varying augmented system, and further obtains the description form of the optimal tracking control problem under the state inequality constraint; based on the augmented system model, the powerful nonlinear mapping ability of the function approximation method is used to establish a parameter identification model of the unknown dynamic system; through a parallel learning method, online data and existing historical data are simultaneously used to estimate the unknown parameters in the identification model; based on the identification model, the control input is updated through an iterative algorithm to obtain the optimal tracking control strategy under the inequality constraint. The present application does not rely on the precise model of the motor system, and realizes minimization of the tracking error and control energy consumption in a limited time domain while ensuring that the state of the motor system meets the existing constraints, which meets the actual engineering needs; the system considered in the present application is a nonlinear system, which has practical significance.

[0168] In order to implement the above embodiment, the present application also proposes an optimal trajectory tracking control device for a nonlinear motor servo system.

[0169] Figure 6 A schematic structural diagram of an optimal trajectory tracking control device for a nonlinear motor servo system provided in an embodiment of the present application.

[0170] like Figure 6 As shown, the optimal trajectory tracking control device of the nonlinear motor servo system includes:

[0171] The system building module is used to establish the error dynamic model of the motor system tracking control, introduce new state variables to transform the error dynamic model into an augmented system model, and determine the description form of the optimal tracking control problem under the state inequality constraints;

[0172] The system building module is also used to build an identification model of an unknown dynamic system based on the augmented system model using a function approximation method;

[0173] The system identification module is used to estimate the unknown parameters in the identification model using online data and historical data through a parallel learning method;

[0174] The calculation and solution module is used to update the control input through an iterative algorithm based on the identification model, solve the optimal tracking control problem under the state inequality constraints, and obtain the optimal tracking control strategy.

[0175] It should be noted that the above explanation of the optimal trajectory tracking control method embodiment of the nonlinear motor servo system is also applicable to the optimal trajectory tracking control device of the nonlinear motor servo system of this embodiment, which will not be repeated here.

[0176] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example" or "some examples" etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present application. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art may combine and combine the different embodiments or examples described in this specification and the features of the different embodiments or examples, unless they are contradictory.

[0177] In addition, the terms "first" and "second" are used for descriptive purposes only and should not be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Therefore, the features defined as "first" and "second" may explicitly or implicitly include at least one of the features. In the description of this application, the meaning of "plurality" is at least two, such as two, three, etc., unless otherwise clearly and specifically defined.

[0178] Any process or method description in a flowchart or otherwise described herein may be understood to represent a module, fragment or portion of code comprising one or more executable instructions for implementing the steps of a custom logical function or process, and the scope of the preferred embodiments of the present application includes alternative implementations in which functions may not be performed in the order shown or discussed, including performing functions in a substantially simultaneous manner or in the reverse order depending on the functions involved, which should be understood by technicians in the technical field to which the embodiments of the present application belong.

[0179] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as an ordered list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by an instruction execution system, device or apparatus (such as a computer-based system, a system including a processor, or other system that can fetch instructions from an instruction execution system, device or apparatus and execute instructions), or in combination with these instruction execution systems, devices or apparatuses. For the purposes of this specification, "computer-readable medium" can be any device that can contain, store, communicate, propagate or transmit a program for use by an instruction execution system, device or apparatus, or in combination with these instruction execution systems, devices or apparatuses. More specific examples (non-exhaustive list) of computer-readable media include the following: an electrical connection with one or more wires (electronic device), a portable computer disk box (magnetic device), a random access memory (RAM), a read-only memory (ROM), an erasable and programmable read-only memory (EPROM or flash memory), an optical fiber device, and a portable compact disk read-only memory (CDROM). In addition, the computer-readable medium may even be paper or other suitable medium on which the program is printed, since the program may be obtained electronically, for example, by optically scanning the paper or other medium and then editing, interpreting or processing in other suitable ways if necessary, and then stored in a computer memory.

[0180] It should be understood that the various parts of the present application can be implemented by hardware, software, firmware or a combination thereof. In the above-mentioned embodiments, multiple steps or methods can be implemented by software or firmware stored in a memory and executed by a suitable instruction execution system. For example, if implemented by hardware, as in another embodiment, it can be implemented by any one of the following technologies known in the art or their combination: a discrete logic circuit having a logic gate circuit for implementing a logic function for a data signal, a dedicated integrated circuit having a suitable combination of logic gate circuits, a programmable gate array (PGA), a field programmable gate array (FPGA), etc.

[0181] A person skilled in the art may understand that all or part of the steps in the method for implementing the above-mentioned embodiment may be completed by instructing related hardware through a program, and the program may be stored in a computer-readable storage medium, which, when executed, includes one or a combination of the steps of the method embodiment.

[0182] In addition, each functional unit in each embodiment of the present application may be integrated into a processing module, or each unit may exist physically separately, or two or more units may be integrated into one module. The above-mentioned integrated module may be implemented in the form of hardware or in the form of a software functional module. If the integrated module is implemented in the form of a software functional module and sold or used as an independent product, it may also be stored in a computer-readable storage medium.

[0183] The storage medium mentioned above may be a read-only memory, a magnetic disk or an optical disk, etc. Although the embodiments of the present application have been shown and described above, it can be understood that the above embodiments are exemplary and cannot be understood as limiting the present application. A person of ordinary skill in the art may change, modify, replace and modify the above embodiments within the scope of the present application.

Claims

1. An optimal trajectory tracking control method for a nonlinear motor servo system, characterized in that: include: Establish an error dynamic model of motor system tracking control, introduce new state variables to transform the error dynamic model into an augmented system model, and determine the description form of the optimal tracking control problem under state inequality constraints; Based on the augmented system model, an identification model of the unknown dynamic system is established using a function approximation method; Through parallel learning methods, online data and historical data are used to estimate unknown parameters in the identification model; Based on the identification model, the control input is updated through an iterative algorithm, the optimal tracking control problem under the state inequality constraint is solved, and the optimal tracking control strategy is obtained; Wherein, the error dynamic model of the motor system tracking control is established, including: The nonlinear system of the motor is defined as: in, is the system status, is the system initial time, is the initial state of the system, is the system control input, is the system status after u is input into the system, is the dynamic function of the system, The state constraints of the motor nonlinear system are defined as: in, for dimensional column vector function, representing the existence Inequality constraints; Define the system tracking signal as , the tracking error is For the optimal tracking control problem, a quadratic performance index is used to represent the cost function, which is expressed as: in, represents a predetermined time interval, , is a real symmetric positive definite matrix, The dynamic function and inequality constraints of the error dynamic model are expressed as: The introducing of new state variables to transform the error dynamic model into an augmented system model includes: Assume that the tracking signal is generated by an unknown dynamic function, which is expressed as: Defining new state variables , the augmented system is expressed as: The inequality constraints satisfied by the new state variables are: The cost function is expressed as: Among them, the matrix Defined as: The description form of the optimal tracking control problem under the determined state inequality constraint includes: For inequality constraints, the Kelley-Bryson penalty function is constructed as the cost function, and the solution of the optimal tracking control problem is transformed into the solution of the unconstrained problem. The constructed cost function is expressed as: in, is a monotonically increasing sequence that satisfies , in the penalty function The term is a step function, which is formulated as: When the augmented system state satisfies the given inequality constraints, , the solution to the unconstrained problem satisfies the following conditions: The simplified form of the optimality condition is: in, is the covariance quantity, is the Hamiltonian function, , .

2. The optimal trajectory tracking control method for a nonlinear motor servo system according to claim 1, characterized in that: The method of establishing an identification model of an unknown dynamic system based on the augmented system model by using a function approximation method includes: make represents the unknown dynamic function of the augmented system The function approximation method can be used to approximate it as follows: in, is the weight coefficient, For hidden layer The activation function of a neuron is is the corresponding approximation error; The estimated value of the weight coefficient is defined as , let the matrix , , let the activation function vector be , the parameter identification model of the unknown dynamic system is expressed as: .

3. The optimal trajectory tracking control method for a nonlinear motor servo system according to claim 2, characterized in that: The method of estimating unknown parameters in the identification model using online data and historical data through a parallel learning method includes: Collect at any time The historical data points of the augmented system are , the historical data points include the state of the augmented system, the control input and the derivative of the state, and the definition matrix , the collected historical data set meets ; Using historical data sets and online data to update the unknown parameters in the identification model, the adaptive update law during update is expressed as: in, and Respectively represent The estimated values ​​of the system state value and coefficient matrix are augmented in the iteration process. , is the learning rate, and They are The estimation error of the augmented system state and coefficient matrix during the iteration process.

4. The optimal trajectory tracking control method for a nonlinear motor servo system according to claim 3, characterized in that: The generation process of the optimal tracking control strategy includes: Step S1: Initialize coefficients , , , set the accuracy error , , , select the initial control input and the initial coefficient matrix estimates , measure the state of the original system under the initial control input, and calculate the trajectory of the corresponding augmented system And the cost function ,make , ,in, ; Step S2: Update the control input by solving a first set of equations, wherein the first set of equations is expressed as: in, , Represents the first n columns of the coefficient matrix; Step S3: Update the coefficient matrix by solving the second set of equations, wherein the second set of equations is expressed as: Step S4: Calculate the trajectory of the augmented system using the updated control input And the corresponding cost function ; Step S5: Repeat steps S2-S4. After each repetition, , , , is the iteration step length until , Step S6: Repeat steps S2-S5. After each repetition, , , , until the control input and the identification model converge to a given accuracy error, where the control input converges to a given accuracy error, expressed as: , the identification model converges to a given accuracy error, expressed as: ; Step S7: Repeat steps S2-S6, and after each repetition, let , , , , , is the iteration step length until the state of the augmented system satisfies the inequality constraint under the given accuracy error, and the identification model parameters are obtained. And the optimal tracking control strategy , where the state of the augmented system satisfies the inequality constraint under a given precision error, expressed as: .

5. An optimal trajectory tracking control device for a nonlinear motor servo system, characterized in that: The device implements the optimal trajectory tracking control method according to claim 1, and the device comprises: A system building module is used to establish an error dynamic model of the motor system tracking control, introduce new state variables to transform the error dynamic model into an augmented system model, and determine the description form of the optimal tracking control problem under the state inequality constraint; The system establishment module is further used to establish an identification model of the unknown dynamic system using a function approximation method based on the augmented system model; The system identification module is used to estimate the unknown parameters in the identification model using online data and historical data through a parallel learning method; The calculation and solution module is used to update the control input through an iterative algorithm based on the identification model, solve the optimal tracking control problem under the state inequality constraint, and obtain the optimal tracking control strategy.

Images