Torque Mode Control Method for Networked Motion Control System Based on High-Order Full Drive

Abstract

The present invention discloses a torque mode control method for a networked motion control system based on high-order full drive, comprising the following steps: (1) obtaining the state space model of the system by using the Matlab system identification toolbox, pre-compensating the dead zone, and designing a full drive control law to convert the state space model into a full drive model; (2) constructing an intermediate observer and designing and solving for the intermediate observer gain through matrix inequalities; (3) designing an MPC controller to solve for the optimal control sequence and obtaining the final input of the networked motion control system through inverse transformation. Compared with the prior art, the advantages of the present application are as follows: using a full drive system model to describe the torque mode motion control system with parameter uncertainty, dead drive characteristics, and external disturbances, maintaining the physical meaning of the system state and facilitating controller design; combining the MPC controller and the intermediate estimator to achieve high-precision disturbance rejection control of the torque mode of the networked motion control system.

Description

Technical Field

[0001] This application belongs to the technical field of networked motion control, and particularly relates to a torque mode control method for a networked motion control system based on high-order full drive. Background Art

[0002] With the rapid development of industrial Internet and network communication technologies, networked motion control systems have become a hot topic in both academia and industry, and are widely used in fields such as machine tool manufacturing, driverless vehicles, and microgrids. It overcomes the problems existing in traditional motion control systems, such as complex wiring, poor scalability, and difficult maintenance. However, networking also brings uncertainties to the control system, such as delays, packet losses, etc., and at the same time does not solve the influence of the time-varying parameters, dead zone characteristics, external disturbances, and other uncertain factors of the motion control system itself on the control performance. Therefore, for networked motion control systems with uncertain factors, achieving high-precision disturbance rejection control has become an important research focus and has received extensive attention.

[0003] To solve the disturbance rejection control problem in networked motion control systems, the observer method has been widely studied. The observer method regards uncertainties and external disturbances as integrated disturbances. Then, an observer is designed to obtain an estimate of the integrated disturbance and the disturbance effect is cancelled in a feedforward manner. Among them, the intermediate estimator does not need to satisfy the observer matching condition, and the accuracy and convergence rate of the disturbance estimation can be improved by adjusting the observer parameters, so it is widely used in networked motion control systems.

[0004] After obtaining accurate disturbance estimation information, it is necessary to design a high-performance disturbance rejection controller to achieve high-precision disturbance rejection control of networked motion control systems. For this purpose, researchers have widely studied advanced methods such as sliding mode control, robust control, and model predictive control (MPC).

[0005] It should be noted that most of the above methods still use state space models to describe networked control motion systems, which leads to the loss of the physical meaning of the original system and the emergence of ill-conditioned matrices in the model simplification process. Compared with the state space model, the full drive system is directly established from physical laws, can more naturally represent the real system, and provides great convenience. Summary of the Invention

[0006] The objective of this application is to provide a torque mode control method for a networked motion control system based on high-order full drive. First, for the motion control system in torque mode, a torque excitation signal is given and its rotational speed output signal is collected. Second, based on the collected torque input signal and rotational speed output signal, a first-order state space model with dead zone nonlinearity is obtained using the Matlab system identification toolbox and discretized. Furthermore, in view of the dead zone nonlinearity characteristic of the system model and the uncertainty of the identified parameters, a dead zone pre-compensation method is used for compensation. Subsequently, an intermediate observer is designed to estimate the system disturbance and compensate for the influence caused by the disturbance. Finally, an MPC method is used to design a high-performance disturbance rejection controller to achieve high-precision error rejection control.

[0007] To achieve the above objective, the technical solution of this application is as follows:

[0008] A torque control method for a networked motion control system based on high-order full drive, including:

[0009] For the motion control system in torque mode, a method of giving a torque excitation signal is used to collect its rotational speed output signal;

[0010] Based on the torque input signal and rotational speed output signal, a first-order state space model with dead zone nonlinearity is obtained using the Matlab system identification toolbox and discretized. At the same time, considering the uncertainty of the system identification parameters, the state equation of the system is as follows:

[0011] (1);

[0012] Among them, represents the system state, represents the system input torque signal, represents the system output rotational speed signal, represents the external disturbance signal, represents the dead zone input signal. represents the parameter matrix. and represent the left and right dead zone characteristic slopes, and represent the dead zone characteristic breakpoints on the left and right axes. and represent the uncertain parameters in the dead zone parameters.

[0013] The dead zone characteristic is divided into an intrinsic uncertainty part composed of deterministic parameters and an unknown uncertainty part composed of uncertain parameters. For the intrinsic uncertainty, a dead zone pre-compensation method is used for compensation. Define which has the following form:

[0014] (2);

[0015] Among them, represents the control input calculated by the upper-layer controller.

[0016] According to (1)-(2), the relationship between the control input calculated by the upper-layer controller and the system input torque can be obtained:

[0017] (3);

[0018] Substitute (3) into (1), and abstract the unknown uncertainty part as the internal perturbation of the system, the following system state-space equation can be obtained:

[0019] (4);

[0020] Based on the high-order fully actuated theory, if the coefficient matrix is invertible, the above system is fully actuated. The direct parameter method is used to design the fully actuated control law, and the state-space model is converted into a fully actuated model, and the design has the following form:

[0021] (5);

[0022] Where is a matrix that can be arbitrarily specified, is an external signal.

[0023] Substitute (5) into (4) to convert the original system into a fully actuated form

[0024] (6);

[0025] Based on the idea of equivalent input disturbance, the internal disturbance and the external disturbance are integrated into the input channel disturbance ;

[0026] (7);

[0027] Denote , , for the input channel disturbance, a middle observer is constructed for estimation. Denote the middle variable as , and design the observer as follows:

[0028] (8);

[0029] Where is the control law obtained by the MPC controller, which is used to cancel the equivalent input disturbance of the system, is a suitable scalar variable, is the observer gain matrix to be solved. Construct the error model and , there are:

[0030] (9);

[0031] Denote , , , , there are:

[0032] (10);

[0033] Denote , , , , there are:

[0034] (11);

[0035] Construct a Lyapunov function to analyze the stability of the error system. Let , , be matrix variables of appropriate dimensions. Construct a stability matrix and solve it to obtain the intermediate observer gain:

[0036] (12);

[0037] If the above linear matrix inequality has a solution, the states of the error system are uniformly ultimately bounded, and the observer gain can be obtained.

[0038] For a given reference speed signal, design a model predictive controller for the high-order full-drive torque model of the networked motion control system. Considering the fault-free case, there is , then the state equation of the system is:

[0039] (13);

[0040] Set the prediction horizon , and the recurrence expression is as follows:

[0041] (14);

[0042] Denote the discrete reference signal as , and define the quadratic performance index as:

[0043] (15);

[0044] Among them, represents the operation cost weight matrix of the system, that is, the cost of adjusting the state deviation of the system; It represents the control quantity cost weight matrix of the system, that is, the cost of the control input. MPC control aims to find the balance between two parts, that is, to save costs while meeting the system performance requirements.

[0045] The optimization objective function is solved through the Yalmip toolbox to obtain the optimal control sequence . Take the first element of the sequence as the system control law at the current moment, and according to , the obtained by MPC is inverse-transformed into

[0046] Compared with the prior art, the advantages of this application are as follows:

[0047] 1) Use the fully actuated system model to describe the torque-mode motion control system with parameter uncertainty, dead-actuated characteristics, and external disturbances, maintaining the physical meaning of the system state and facilitating controller design.

[0048] 2) Divide the dead-zone uncertainty into two parts: intrinsic and unknown. The intrinsic uncertainty is pre-compensated, and for the unknown part, an intermediate estimator is designed based on the fully actuated system model to achieve accurate estimation.

[0049] 3) Propose an MPC method based on the high-order fully actuated model, and combine the MPC controller and the intermediate estimator to achieve high-precision disturbance rejection control of the torque mode in the networked motion control system. Brief Description of the Drawings

[0050] Figure 1 is the framework diagram of the torque-mode control method for the networked motion control system based on high-order fully actuated in this application;

[0051] Figure 2 is the flow chart of the torque-mode control method for the networked motion control system based on high-order fully actuated in this application;

[0052] Figure 3 is the tracking curve of the state variable with respect to the reference signal in this application;

[0053] Figure 4 is the comparison curve of the control law before and after dead-zone pre-compensation in this application. Detailed Embodiments

[0054] In order to make the purpose, technical solutions and advantages of this application clearer, the following further elaborates on this application in combination with the drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain this application and are not used to limit this application.

[0055] An embodiment of the present application proposes a torque control method for a networked motion control system based on high-order full drive, including the following steps:

[0056] Step 1: Use the Matlab system identification toolbox to obtain the state-space model of the system, pre-compensate the dead zone, and design a full drive control law to convert the state-space model into a full drive model:

[0057] 1.1) For the networked motion control system in torque mode, collect its rotational speed output signal by a given torque excitation signal method; according to the torque input signal and the rotational speed output signal, use the Matlab system identification toolbox to obtain a first-order state-space model with dead zone nonlinearity and discretize it. Considering the uncertainty of the system identification parameters, the state equation of the system is as follows:

[0058] (1);

[0059] Where, represents the system state, represents the system input torque signal, represents the system output rotational speed signal, represents the external disturbance signal, represents the dead zone input signal, represents the parameter matrix. and represent the left and right dead zone characteristic slopes, and represent the dead zone characteristic breakpoints on the left and right axes. All parameter uncertainties are in the following form:

[0060] ;

[0061] Divide the dead zone characteristics into an intrinsic uncertainty part composed of deterministic parameters and an unknown uncertainty part composed of uncertain parameters. For the intrinsic uncertainty, use the method of dead zone pre-compensation for compensation, and define in the following form:

[0062] (2);

[0063] Where, represents the control input calculated by the upper-layer controller.

[0064] 1.2) According to (1)-(2), the relationship between the control input calculated by the upper-layer controller and the system input torque can be obtained:

[0065] (3);

[0066] Substitute (3) into (1), and abstract the unknown uncertainty part as the internal perturbation of the system, then the following system state space can be obtained:

[0067] (4);

[0068] Based on the high-order fully actuated theory, here is invertible, and the above system is fully actuated. The direct parameter method is used to design the fully actuated control law, and the state space model is converted into a fully actuated model. Design to have the following form:

[0069] (5);

[0070] where , is an external signal.

[0071] Substitute (5) into (4) to convert the original system into a fully actuated form

[0072] (6);

[0073] Step 2: Construct an intermediate observer, design and solve the intermediate observer gain through matrix inequalities to estimate the equivalent input disturbance, including the following steps;

[0074] 2.1) Based on the idea of equivalent input disturbance, integrate the internal perturbation and the external perturbation into the input channel disturbance ;

[0075] (7);

[0076] where , , for the input channel disturbance, construct an intermediate observer for estimation. Denote the intermediate variable as , and design the observer as follows:

[0077] (8);

[0078] where, is the control law obtained by the MPC controller, which is used to cancel the equivalent input disturbance of the system. Select as the intermediate observer parameter, is the observer gain matrix to be solved.

[0079] 2.2) Construct the error model and , there is:

[0080] (9);

[0081] Denote , , , , there is:

[0082] (10);

[0083] Denote , , , , there is:

[0084] (11);

[0085] 2.3) Construct a Lyapunov function to analyze the stability of the error system. Let , construct a stability matrix and solve it to obtain the intermediate observer gain:

[0086] (12);

[0087] Solve the above linear matrix inequality, and we can get , , , and the state of the error system is uniformly ultimately bounded.

[0088] Step 3: Design an MPC controller to solve the optimal control sequence, and obtain the final input of the networked motion control system through inverse transformation, including the following steps:

[0089] 3.1) For a given reference speed signal, design a model predictive controller for the high-order system. Considering the fault-free case, there is , then the state equation of the system is:

[0090] (13);

[0091] Set the prediction interval , and the recurrence expression is as follows:

[0092] (14);

[0093] where represents the matrix transpose symbol,

[0094] ;

[0095] Denote the discrete reference signal as , and define the quadratic performance index as:

[0096] (15);

[0097] where, It represents the operation cost weight matrix of the system, that is, the cost of regulating the state deviation of the system; It represents the control variable cost weight matrix of the system, that is, the cost of control input. MPC control aims to find the balance point between the two parts, that is, to save costs while meeting the system performance requirements.

[0098] The optimization objective function is solved through the Yalmip toolbox to obtain the optimal control sequence . Take the first element of the sequence as the system control law at the current moment, and according to , the obtained by MPC is inverse-transformed into , and after dead zone pre-compensation, it is used as the input of the networked motion control system, so as to complete the high-precision disturbance rejection control of the torque mode.

[0099] The high-order fully actuated theory is used to convert the system state space model into a first-order fully actuated model with dead zone nonlinearity, which provides great convenience for the design of the controller; the dead zone pre-compensation method is used to compensate for the intrinsic uncertainty of the dead zone in the system identification process, helping the system reduce response hysteresis and improve dynamic performance; the equivalent input disturbance method is used to integrate internal and external disturbances into input channel disturbances, reducing the complexity of the control system design; an intermediate observer is introduced to estimate the input channel disturbances, and the accuracy and convergence speed of disturbance estimation are improved by adjusting the observer parameters; an MPC controller is designed to solve the control law and inverse-transform it into a fully actuated control law through the corresponding relational expression to achieve high-precision control of the system.

[0100] As mentioned above, it is only the preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art within the technical scope disclosed by the present invention, according to the technical solution and inventive concept of the present invention, makes equivalent substitutions or changes, and all should be covered by the protection scope of the present invention.

Claims

1. A torque mode control method for a networked motion control system based on high-order full drive, characterized in that, The steps are as follows: (1) Use the Matlab system identification toolbox to obtain the state-space model of the system, pre-compensate the dead zone, and design a full-drive control law to convert the state-space model into a full-drive model; use the high-order full-drive theory to convert the system state-space model into a first-order full-drive model with dead-zone nonlinearity, which is expressed by the formula as follows: x(k + 1) = Ax(k) + Bu(k) + Ef(k) y(k) = Cx(k) where x(k) represents the system state, u(k) represents the system input torque signal, y(k) represents the system output rotational speed signal, f(k) represents the external disturbance signal, and u1(k) represents the dead-zone input signal; A, B, C, and E represent parameter matrices; m1 and m2 represent the left and right dead-zone characteristic slopes, d1 and d2 represent the left and right dead-zone characteristic breakpoints on the axis; Δm1, Δm2, Δd1, and Δd2 represent the uncertain parameters in the dead-zone parameters; First, for the motion control system in torque mode, given a torque excitation signal, collect its rotational speed output signal; Second, according to the collected torque input signal and rotational speed output signal, use the Matlab system identification toolbox to obtain a first-order state-space model with dead-zone nonlinearity and discretize it; Furthermore, for the dead-zone nonlinear characteristics of the system model and the uncertainty of the identified parameters, use the dead-zone pre-compensation method for compensation, which is expressed by the formula as follows: where u2(k) represents the control input obtained by the upper-layer controller, and u1(k) represents the control input after dead-zone pre-compensation; (2) Construct an intermediate observer, design and solve the intermediate observer gain through matrix inequalities to estimate the equivalent input disturbance: Design an intermediate observer to estimate the system disturbance and compensate for the influence caused by the disturbance; (3) Design an MPC controller to solve the optimal control sequence and obtain the final input of the networked motion control system through inverse transformation: Use the MPC method to design a high-performance disturbance rejection controller to achieve high-precision error rejection control.

2. The torque mode control method of the networked motion control system based on high-order full drive according to claim 1, wherein In step (2), the equivalent input disturbance method is expressed by the formula as follows: f e (k) = Ef(k) + d(k) Among them, f e (k) is the input channel interference integrated by the external disturbance f(k) and the internal disturbance d(k).

3. The torque mode control method of the networked motion control system based on high-order full drive according to claim 1, characterized in that, In step (2), an intermediate observer is introduced to estimate the input channel disturbance, which is expressed by the formula as follows: where, v f is the control law obtained by the MPC controller for canceling the equivalent input disturbance of the system, w is a suitable scalar variable, and H and L are the observer gain matrices to be determined; where u2(k) represents the control input obtained by the upper-layer controller, and u1(k) represents the control input after dead-zone pre-compensation.

4. The torque mode control method of the networked motion control system based on high-order full drive according to claim 1, characterized in that, In step (3), design an MPC controller to solve the control law and inverse-transform it into a full-drive control law through the corresponding relational expression, \(x(k + 1)=A_0x(k)+B_0v\) f (k) It is expressed by the formula as follows: A0 and B0 represent the parameter matrices of the system, jointly constituting a recurrence equation with a prediction interval of 5; denote the discrete reference signal as X r , and define the quadratic performance index as: J=(X - X r ) T Q(X - X r ) + V f T RV f where Q represents the system operation cost weight matrix, that is, the cost of the system to adjust the state deviation; R represents the system control quantity cost weight matrix, that is, the cost of the control input. The MPC control aims to find the balance point between the two parts; According to u2(k) = B -1 (K0x(k) + v(k)), the v obtained by MPC is inversely transformed into u2(k), and after dead zone pre-compensation, it is brought into the motion control system to complete high-precision control of the torque mode.

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