Cooperative control method for multiple permanent magnet synchronous motors based on consistency theory

Abstract

The invention relates to a multi-permanent magnet synchronous motor cooperative control method based on a consistency theory, and belongs to the technical field of motor control. According to the method, the consistency theory is applied to the permanent magnet synchronous motor, the sliding mode theory and the LQR controller are combined, and the rotating speed control law of the motor is improved and designed. Compared with a traditional multi-motor cooperation method, the robustness and the synchronization performance of the multi-motor system can be improved. According to the method, the sliding mode controller is used for designing the speed ring of the motor, compared with a traditional method, the robustness is high, the response is rapid, and the designed reaching law can enable the sliding mode to rapidly approach the sliding mode surface. According to the method, on the basis of using a sliding mode controller, a consistency theory is introduced, an optimal performance cost function is constructed again, a consistency protocol, namely a cooperative control law, based on an LQR regulator is designed by minimizing the cost function, and a feedback gain matrix in the control law is designed on the optimal control level; and the collaboration precision of the system is further improved.

Description

Technical Field

[0001] The invention relates to a multi-permanent magnet synchronous motor cooperative control method based on consistency theory, belonging to the technical field of motor control. Background Art

[0002] Permanent-magnet synchronous motor (PMSM) has emerged in various fields with its high efficiency, high power density and excellent power factor, gradually replacing traditional asynchronous motors and becoming an ideal choice for automation equipment. With the promotion of permanent-magnet synchronous motors in robotics, aerospace, automobiles and other fields, people have put forward more stringent requirements on their system anti-interference, fast response and robustness. This trend has promoted the continuous optimization and innovation of permanent-magnet synchronous motor control systems to meet the needs of diversified and complex application scenarios.

[0003] At present, in some applications, a single permanent magnet synchronous motor can no longer fully meet the needs. For example, in large industrial production lines, high-speed railway systems, and aerospace vehicles, greater power output and more flexible motion coordination or multi-motor speed synchronization are required, and the capacity of a single motor may be insufficient. In order to meet these challenges, multi-motor systems came into being.

[0004] In a multi-motor synchronous control system, each motor has its own closed-loop follow-up control, and the actual operating status of all motors is fed back to the host computer through a unified information interface. On the one hand, the host computer sends user instructions to each motor, and on the other hand, it uses the feedback information to output the corresponding synchronous compensation to each motor through the coordination of the synchronous control structure and algorithm, thereby achieving the purpose of eliminating the speed difference between motors or maintaining an accurate speed ratio.

[0005] At present, the research work on multi-motor synchronous motion control is mainly focused on synchronous controllers and follower controllers. Synchronous controllers can adopt different control structures such as master command, master-slave, cross coupling, adjacent coupling, virtual axis, etc., and use modern control theory to design appropriate control algorithms; follower controllers can adopt different control algorithms such as sliding mode, fuzzy, anti-disturbance, neural network, adaptive, PID, etc., so as to enhance the synchronization capability of the system. Traditional synchronous controller methods have their own limitations. The overall synchronization capability of the master command control system is weak and the anti-interference ability is poor; under master-slave control, the slave cannot affect the host, so there is a delay in signal transmission; cross coupling is based on master-slave control and adds speed error compensation, which improves the performance, but there is coupling between tracking error and synchronization error, and fixed gain will bring about the problem that the transient compensation effect is inconsistent with the steady-state performance; adjacent coupling usually only focuses on the synchronization of the motor and its adjacent motors, while ignoring the influence of other motors. This may lead to poor synchronization performance at the system level.

[0006] Multi-agent consistency control enables multiple agents to reach a unified state or behavior in the network through collaboration and information exchange between agents. Each agent makes adjustments based on its own and neighboring agent's state information to achieve a consistent goal as a whole. This theory is applied to a multi-permanent magnet synchronous motor system, where each motor and its controller are regarded as an agent. The electrical angular velocity of each motor is identified as a target that needs to be consistent. The electrical angular velocity values ​​of adjacent motors are obtained through the communication network. A collaborative controller is designed by combining the sliding mode theory and the LQR controller to achieve the goal of speed coordination of the multi-motor system, which is expected to improve the robustness and synchronization performance of the system. Summary of the invention

[0007] The purpose of the present invention is to solve the technical problem of multi-motor synchronous motion control of permanent magnet synchronous motors, and creatively propose a cooperative control method of permanent magnet synchronous motors based on consistency theory. This method combines the sliding mode theory with the LQR controller to improve the speed control law of the motor, which can enhance the cooperative performance of the multi-permanent magnet synchronous motor system and improve the accuracy and speed of the response.

[0008] The present invention is implemented by adopting the following technical solutions.

[0009] A coordinated control method for a permanent magnet synchronous motor based on consistency theory comprises the following steps:

[0010] Step 1: Determine the electrical angular velocity coordination target of the multi-permanent magnet synchronous motor system, regard each motor and its controller as an intelligent agent, and construct a mathematical model.

[0011] Step 2: Obtain the communication status between the motors in the multi-motor system and construct a multi-motor communication network topology diagram when a virtual leading motor exists.

[0012] Step 3: Collect the output current and mechanical angular velocity information of each permanent magnet synchronous motor and define the electrical angular velocity coordination error between the motors The target electrical angular velocity value of each motor is obtained.

[0013] Step 4: Design a sliding mode controller based on the difference between the actual electrical angular velocity and the target electrical angular velocity, select the nonlinear sliding mode surface and the new reaching law, and calculate the reference value of the q-axis current.

[0014] Step 5: According to the standard form of the multi-agent system consensus protocol, the electrical angular velocity error between the motors is processed again to construct the optimal performance cost function. The cost function is minimized, and the appropriate weighting matrix is ​​selected to obtain the feedback gain matrix required for designing the consensus protocol.

[0015] Step 6: Perform equivalent substitution on the obtained cooperative control law to obtain the q-axis current compensation signal of the follower motor.

[0016] Step 7: Feedback the q-axis current compensation signal of the follower motor to the current loop controller, control the single motor through vector control, and realize the speed coordination of the multi-permanent magnet synchronous motor system.

[0017] Beneficial Effects

[0018] Compared with the prior art, the method of the present invention has the following advantages:

[0019] 1. This method applies consistency theory to permanent magnet synchronous motors, combines sliding mode theory with LQR controller, and improves the speed control law of the motor. Compared with the traditional multi-motor coordination method, it can improve the robustness and synchronization performance of the multi-motor system.

[0020] 2. This method uses a sliding mode controller to design the speed loop of the motor. Compared with the traditional method, it has strong robustness and fast response. The designed convergence law can make the sliding mode approach the sliding mode surface faster.

[0021] 3. Based on the use of sliding mode controller, this method quotes consistency theory and reconstructs the optimal performance cost function. By minimizing the cost function, the consistency protocol based on LQR regulator, namely the collaborative control law, is designed. The feedback gain matrix in the control law is designed at the optimal control level, which further improves the collaborative accuracy of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 Schematic diagram of the process of this method. DETAILED DESCRIPTION

[0023] The method of the present invention is described in detail below with reference to the accompanying drawings and embodiments.

[0024] Example

[0025] like Figure 1 As shown, a cooperative control method of permanent magnet synchronous motor based on consistency theory.

[0026] Step 1: Determine the electrical angular velocity coordination target of the multi-permanent magnet synchronous motor system, regard each motor and its controller as an intelligent agent, and construct a mathematical model.

[0027] Step 2: Obtain the communication status between each motor in the multi-motor system and construct a multi-motor communication network topology diagram when a virtual leading motor exists.

[0028] Step 3: Collect the output current and mechanical angular velocity information of each permanent magnet synchronous motor and define the electrical angular velocity coordination error between the motors The target electrical angular velocity value of each motor is obtained.

[0029] Step 4: Design a sliding mode controller based on the difference between the actual electrical angular velocity and the target electrical angular velocity, select the nonlinear sliding mode surface and the new reaching law, and calculate the reference value of the q-axis current.

[0030] Step 5: According to the standard form of the multi-agent system consensus protocol, the electrical angular velocity error between the motors is again calculated. Process and construct the optimal performance cost function J C . For the cost function J C Minimize and select appropriate weight matrices Q and R to obtain the feedback gain matrix K required to design the consistency protocol.

[0031] Step 6: Perform equivalent substitution on the obtained cooperative control law to obtain the q-axis current compensation signal of the follower motor.

[0032] Step 7: Feedback the q-axis current compensation signal of the follower motor to the current loop controller, control the single motor through vector control, and realize the speed coordination of the multi-permanent magnet synchronous motor system.

[0033] The stator voltage equation of the permanent magnet synchronous motor in the synchronous rotating coordinate system is expressed as:

[0034]

[0035] Among them, u d Represents the d-axis component of the stator voltage. q Represents the q-axis component of the stator voltage. s Indicates stator resistance, L s represents the stator inductance. d represents the d-axis component of the stator current, i q Indicates the q-axis component of the stator current. d / dt indicates differential calculation. ωe Represents the rotor electrical angular velocity. f Represents the flux linkage of a permanent magnet.

[0036] For permanent magnet synchronous motors, the stator inductance satisfies L d =L q =L s , where L d ,L q Respectively represent the d-axis and q-axis inductance, L s The motor in the present invention is considered to have been decomposed into a speed subsystem and a current subsystem that are independent of each other through feedback linearization.

[0037] The motor motion equation is:

[0038]

[0039] Where J represents the moment of inertia of the PMSM (permanent magnet synchronous motor), ω m Represents the mechanical angular velocity of the PMSM rotor. T e Represents electromagnetic torque. T L represents the load torque. B represents the damping coefficient.

[0040] The electromagnetic torque equation is expressed as:

[0041]

[0042] Among them, T e is the electromagnetic torque, P n stands for pole pair.

[0043] Combining the motor motion equation with the torque equation, we get:

[0044]

[0045] And ω e =P n ω m , where P n Represents the number of pole pairs.

[0046] Assume that there are i motors in the multi-permanent magnet synchronous motor system, and the electrical angular velocity value of the i-th motor is recorded as The coordination goal of the multi-motor system is determined as:

[0047]

[0048] The multi-agent theory is used to construct the multi-motor communication network topology diagram, as follows:

[0049] The communication network contains n motors in total. A set ε is called an edge. If there is a connection (i, j) between motor i and motor j, the two motors are said to be adjacent and can transmit information. The number of edges increases by 1. Then the topological graph is called an undirected or bidirectional graph, otherwise it is a directed graph. Then, construct an adjacency matrix A, and the elements of A are defined as: if motor i and motor j are adjacent, then a ij =1, otherwise a ij =0,a ij Represents the element in the i-th row and j-th column of the adjacency matrix. The degree matrix D is a diagonal matrix. The elements on the diagonal are the degrees of each node, that is, the motor. The degree represents the number of edges associated with the motor. If a node is reachable from any other node, then this point is called globally reachable, and this motor is connected to any motor in the system. If there is a directed path between any two points, that is, any motors can communicate, then the topological graph is called strongly connected; when it is not fully satisfied, it is weakly connected. The Laplace matrix L is defined as L=D–A. For a connected graph, L has exactly one eigenvalue of zero, and these eigenvalues ​​are listed in descending order, that is: 0=λ1<λ2≤...≤λ N ,λ N represents the Nth eigenvalue of the Laplacian matrix.

[0050] Assume the system dynamics equation is: represents the first-order derivative of the state variable, x i represents the state variable of the system, u i Denotes the control input. Assuming that the system matrix A and matrix C are both stable, controllable and observable, the standard form of the consensus protocol of the multi-agent system is:

[0051]

[0052] Among them, k is the matrix to be designed; N i represents the neighbor set of the ith agent, that is, the index set of other agents that communicate or interact with it directly.

[0053] In order to achieve the speed coordination of multiple permanent magnet synchronous motors, the electrical angular velocity of the motor is considered to be the goal that needs to be consistent, and the consistency theory is:

[0054]

[0055] Based on this idea, the coordination error is first determined: the electrical angular velocity error between the i-th motor and the motor connected to it is determined If there is a leader motor, set the consistency error as well Taking the two errors into consideration, we get the coordinated error of the electrical angular velocity: for:

[0056]

[0057] Among them, m i Indicates the connection between the follower motor and the leader motor. If connected, m i =1, otherwise m i =0; represents the electrical angular velocity of the i-th motor, represents the electrical angular velocity of the jth motor.

[0058] Let the coordinated error of electrical angular velocity be is 0:

[0059]

[0060] The target control quantity of the cooperative controller of the i-th motor in the multi-motor system is obtained, that is, the target electrical angular velocity value ω sy for:

[0061]

[0062] Assuming the sliding mode of the sliding surface is the difference between the actual electrical angular velocity and the target electrical angular velocity, we have:

[0063]

[0064] in, represents the first-order derivative of x1, represents the first-order derivative of the electrical angular velocity of the i-th motor, Represents the first derivative of the target electrical angular velocity value.

[0065] Select the nonlinear sliding surface: s = x1 + α |x1| γ sign(x1)+β|x2| λ sign(x2), where s represents the sliding surface function, α, β, γ, and λ are all unknown parameters; and γ = g / h; λ = p / q; g, h, p, and q are all positive odd numbers, 1<λ<2, γ>λ, α, β>0.

[0066] After taking the derivative of the sliding surface, we get:

[0067]

[0068] in, represents the first-order derivative of the sliding surface.

[0069] The new reaching law is designed as:

[0070]

[0071] Among them, ε, k, μ are unknown parameters, and ε, k>0, 0<μ<1, s represents the sliding surface function.

[0072] sign(s) represents the sign function, defined as:

[0073]

[0074] have The electrical angular velocity and current i q The relationship is introduced into the sliding surface differential equation, and we get:

[0075]

[0076] in, Represents the second derivative of the target electrical angular velocity value. Represents the first derivative of the load torque. Represents the first derivative of the q-axis current. Represents the first-order derivative of the electrical angular velocity of the i-th motor.

[0077] Setting the above formula equal to the reaching law, we get:

[0078]

[0079] The q-axis current is:

[0080]

[0081] After controlling the current, obtain the electrical angular velocity of the motor again. Assume that the error limit value is σ. When the LQR controller (linear quadratic regulator) is used again for optimal control.

[0082] For motor i, the consistency agreement of the electrical angular velocity is:

[0083]

[0084] Among them, k is the matrix to be designed.

[0085] If the permanent magnet synchronous motor takes electrical angular velocity and angle as input, the dynamic equation is:

[0086]

[0087] in, Represents the first derivative of the electrical angle.

[0088] The electrical angular velocity error of motor i is

[0089]

[0090] The cost function J based on the LQR controller C Defined as:

[0091]

[0092] Where Q and R are symmetric positive definite matrices. e represents the error. T Represents the transpose of the error matrix. N represents the n-th order identity matrix. T Represents the transpose of the input. Ru represents the product of R and u.

[0093] To minimize the cost function, if the system matrices A and B are stable, controllable, and observable and the communication graph is connected, then there exists a symmetric positive definite matrix P and a feedback gain matrix k, corresponding to the following algebraic Riccati equation:

[0094] PA+A T P+Q-PBR -1 B T P=0

[0095] So k = -R -1 B T P. Among them, A T Represents the transpose of the A matrix.

[0096] Proof of stability:

[0097] Let the Lyapunov function Then we have:

[0098]

[0099] in, represents the first-order derivative of Lyapunov, and ξ represents the feedback correction part of the controller.

[0100] Set k = -R -1 B T Substituting P into the equation, we get:

[0101]

[0102] Transformed into inequalities, we have:

[0103]

[0104] Substituting the Riccati equation into the equation, we get:

[0105]

[0106] For all e≠0, we have Therefore, the proposed scheme is stable.

[0107] The q-axis current compensation signal of the follower motor is:

[0108]

[0109] Among them, b i Indicates the motor parameter items,

Claims

1. A cooperative control method of a permanent magnet synchronous motor based on consistency theory, characterized in that: The following steps are involved: Step 1: Determine the electrical angular velocity coordination target of the multi-permanent magnet synchronous motor system, regard each motor and its controller as an intelligent agent, and construct a mathematical model; Step 2: Obtain the communication status between the motors in the multi-motor system and construct a multi-motor communication network topology diagram when a virtual leading motor exists; Step 3: Collect the output current and mechanical angular velocity information of each permanent magnet synchronous motor, define the electrical angular velocity coordination error between the motors, and obtain the target electrical angular velocity value of each motor; Step 4: Design a sliding mode controller according to the difference between the actual electrical angular velocity and the target electrical angular velocity, select the nonlinear sliding mode surface and the new reaching law, and calculate the reference value of the q-axis current; Step 5: According to the standard form of the multi-agent system consensus protocol, the electrical angular velocity error between the motors is processed again to construct the optimal performance cost function; the function is minimized, and a suitable weighting matrix is ​​selected to obtain the feedback gain matrix required for designing the consensus protocol; Step 6: Perform equivalent substitution on the obtained cooperative control law to obtain the q-axis current compensation signal of the follower motor; Step 7: Feedback the q-axis current compensation signal of the follower motor to the current loop controller, control the single motor through vector control, and realize the speed coordination of the multi-permanent magnet synchronous motor system.

2. A cooperative control method for a permanent magnet synchronous motor based on consistency theory as claimed in claim 1, characterized in that: In step 1, the motor motion equation is constructed as: Where, J represents the moment of inertia of the permanent magnet synchronous motor, ω m represents the rotor mechanical angular velocity of the permanent magnet synchronous motor; T e Represents electromagnetic torque; T L represents load torque; B represents damping coefficient; d / dt represents differential calculation; The electromagnetic torque equation is expressed as: Among them, T e is the electromagnetic torque, P n represents the number of pole pairs; i d represents the d-axis component of the stator current, i q represents the q-axis component of the stator current; ψ f Represents the permanent magnet flux; for permanent magnet synchronous motors, the stator inductance satisfies L d =L q =L s , where L d , L q Respectively represent the d-axis and q-axis inductance, L s It is represented as the stator inductance of the motor; Combining the motor motion equation with the torque equation, we get: And ω e =P n ω m , where P n represents the number of pole pairs; In step 2, the communication network contains n motors in total. A set ε is set as an edge. If there is a connection (i, j) between motor i and motor j, the two motors are said to be adjacent and can transmit information. The number of edges increases by 1. Then the topological graph is called an undirected or bidirectional graph, otherwise it is a directed graph; then, construct an adjacency matrix A, the elements of A are defined as: if motor i and motor j are adjacent, then a ij =1, otherwise a ij =0,a ij represents the element in the i-th row and j-th column of the adjacency matrix; the degree matrix D is a diagonal matrix, and the elements on the diagonal are the degrees of each node, that is, the motor, and the degree represents the number of edges associated with the motor; if a node is reachable from any other node, then this point is called globally reachable, and this motor is connected to any motor in the system; if there is a directed path between any two points, that is, any motor can communicate with each other, then the topological graph is called strongly connected; when it is not fully satisfied, it is weakly connected; the Laplace matrix L is defined as L = D-A; for a connected graph, L has exactly one eigenvalue of zero, and these eigenvalues ​​are listed in descending order, that is: 0 = λ1<λ2≤...≤λ N ,λ N represents the Nth eigenvalue of the Laplacian matrix; In step 3, the system dynamics equation is assumed to be: represents the first-order derivative of the state variable, x i represents the state variable of the system, u i Denotes the control input. Assuming that the system matrix A and matrix C are both stable, controllable and observable, the standard form of the consensus protocol of the multi-agent system is: Among them, k is the matrix to be designed, N i represents the neighbor set of the ith agent; In order to achieve the speed coordination of multiple permanent magnet synchronous motors, the electrical angular velocity of the motor is considered to be the goal that needs to be consistent, and the consistency theory is: Assume that there are i motors in the multi-permanent magnet synchronous motor system, and the electrical angular velocity value of the i-th motor is recorded as The coordination goal of the multi-motor system is determined as: Determine the electrical angular velocity error between the i-th motor and the motor connected to it If there is a leader motor, set the consistency error as well Taking the two errors into consideration, we get the coordinated error of the electrical angular velocity: for: Among them, m i Indicates the connection status of the follower motor and the leader motor. If connected, m i =1, otherwise m i =0, represents the electrical angular velocity of the i-th motor, represents the electrical angular velocity of the jth motor; Let the coordinated error of electrical angular velocity be is 0: The target control quantity of the cooperative controller of the i-th motor in the multi-motor system is obtained, that is, the target electrical angular velocity value ω sy for: In step 4, the sliding mode of the sliding surface is assumed to be the difference between the actual electrical angular velocity and the target electrical angular velocity, which is: in, represents the first-order derivative of x1, represents the first-order derivative of the electrical angular velocity of the i-th motor, Represents the first-order derivative of the target electrical angular velocity value; Select the nonlinear sliding surface: s = x1 + α |x1| γ sign(x1)+β|x2| λ sign(x2), where s represents the sliding surface function, α, β, γ and λ are all unknown parameters; and γ = g / h; λ = p / q; g, h, p, q are all positive odd numbers, 1<λ<2, γ>λ, α, β>0; After taking the derivative of the sliding surface, we get: in, represents the first-order derivative of the sliding surface; The new reaching law is designed as: Among them, ε, k, and μ are all unknown parameters, and ε, k>0, 0<μ<1, ω>1; s represents the sliding surface function; sign(s) represents the sign function, which is defined as: have The electrical angular velocity and current i q The relationship is introduced into the sliding surface differential equation, and we get: in, Represents the second-order derivative of the target electrical angular velocity value; Represents the first derivative of the load torque; represents the first derivative of the q-axis current; represents the first-order derivative of the electrical angular velocity of the i-th motor; Setting the above formula equal to the reaching law, we get: The q-axis current is: In step 5, after controlling the current, the electrical angular velocity of the motor is obtained again; the error limit value is set to σ, when When , the LQR controller is used again for optimal control; For motor i, the consistency agreement of the electrical angular velocity is: Among them, k is the matrix to be designed; If the permanent magnet synchronous motor takes electrical angular velocity and angle as input, the dynamic equation is: in, Represents the first derivative of the electrical angle; The electrical angular velocity error of motor i is The cost function J based on the LQR controller C Defined as: Where Q and R are symmetric positive definite matrices; e represents the error; e T represents the transpose of the error matrix; I N represents the n-order identity matrix; u T represents the transpose of the input; Ru represents the product of R and u; To minimize the cost function, if the system matrices A and B are stable, controllable, and observable and the communication graph is connected, then there exists a symmetric positive definite matrix P and a feedback gain matrix k, corresponding to the following algebraic Riccati equation: PA+A T P+Q-PBR -1 B T P=0 So k = -r -1 B T P; among them, A T represents the transpose of matrix A; Proof of stability: Assume that the Lyapunov function Then we have: in, represents the first-order derivative of Lyapunov, ξ represents the feedback correction part of the controller; Set k = -R -1 B T Substituting P into the equation, we get: Transformed into inequalities, we have: Substituting the Riccati equation into the equation, we get: For all e≠0, we have In step 6, the q-axis current compensation signal of the follower motor is: Among them, b i Indicates the motor parameter items,

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