Position Tracking Control Method for Networked Motion Control System Based on High-Order Full Drive

Abstract

The present invention discloses a position tracking control method for a networked motion control system based on high-order full drive. By using the high-order full drive theory, the system state space model is converted into a second-order full drive model with dead zone nonlinearity, which provides great convenience for the design of the controller. The dead zone pre-compensation method is adopted to compensate the deterministic parameter part of the dead zone during the system identification process, helping the system reduce response hysteresis and improve dynamic performance. The equivalent input disturbance method is used to integrate internal disturbances 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 full drive control law through corresponding relations to achieve high-precision control of the system.

Description

Technical Field

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

[0002] In recent decades, with the rapid development of industrial control technology, networked motion control systems have become a hot topic in academia and industry, and have been widely used in fields such as mechanical manufacturing, autonomous vehicles, and robotic arms. There are three control modes for networked motion control systems, namely position, speed, and torque. Among them, the speed mode can directly achieve speed control or speed-position control, and has received great attention in occasions that require precise control, such as range-extended electric vehicle engines, doubly-fed wind turbines, marine diesel engines, and multi-degree-of-freedom motion motors of spacecraft. However, in the actual speed-position control process, due to the mechanical and physical characteristics of the system, its control process exhibits non-linear characteristics, such as dead zones, saturation, and backlash. In addition, due to inaccurate system identification results, system aging and wear, and environmental noise, networked motion control systems are also affected by system uncertainties and external disturbances. Therefore, high-precision position tracking control for networked motion control systems with dead-zone non-linearity, system uncertainties, and external disturbances has always been an urgent problem to be solved.

[0003] To solve the problem of disturbance rejection control of networked motion control systems in the speed mode, 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 canceled in a feed-forward manner. Among them, the intermediate observer does not need to satisfy the observer matching condition, and the accuracy and convergence rate of 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 position tracking 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 appearance 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 purpose of this application is to provide a position tracking control method for a networked motion control system based on high-order full drive. First, for the networked motion control system in the speed mode, a speed excitation signal is given to collect its position output signal. Second, according to the collected speed input signal and position output signal, a second-order state space model with dead-zone nonlinearity is obtained using the Matlab system identification toolbox, and further discretized and converted into a high-order full drive model. Furthermore, for the deterministic parameter part in the dead-zone nonlinearity characteristic of the system model, a dead-zone pre-compensation method is used for compensation. Subsequently, for the dead zone and the uncertain parameter part in the system, they are abstracted as internal disturbances and combined with external disturbances into equivalent input disturbances, and an intermediate observer is designed to estimate and compensate for the influence caused by the disturbances. Finally, the MPC method is used to design a high-precision tracking controller.

[0007] Using the high-order full drive theory to convert the system state space model into a second-order full drive model with dead-zone nonlinearity provides great convenience for the design of the controller. The dead-zone pre-compensation method is used to compensate for the deterministic parameter part 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 disturbances 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 the disturbance estimation are improved by adjusting the observer parameters. The MPC controller is designed to solve the control law and inversely transform it into a full drive control law through the corresponding relationship to achieve high-precision control of the system.

[0008] To achieve the above purpose, the technical solution of this application is as follows:

[0009] A position tracking control method for a networked motion control system based on high-order full drive, including:

[0010] For the networked motion control system in the speed mode, a method of giving a speed excitation signal is used to collect its position output signal;

[0011] According to the speed input signal and the position output signal, a second-order state space model with dead-zone nonlinearity is obtained using the Matlab system identification toolbox. Considering the uncertainty of the identified parameters, the state equation of the system is as follows:

[0012] (1);

[0013] Where, , represents the system state, represents the system input speed signal, represents the system output position signal, represents the external disturbance signal, Represents the dead zone input signal. Represents the system parameters, , Represents the slopes of the left and right dead zone characteristics, , Represents the breakpoints of the dead zone characteristics on the left and right axes. Represents the system parameter uncertainty, Represents the dead zone parameter uncertainty.

[0014] For Take the derivative and substitute Substitute and discretize according to the sampling time The following state - space equations can be obtained:

[0015] (2);

[0016] Among them, , , , . It can be seen from (1) and (2) that the dead zone of the system consists of a deterministic parameter part and an uncertain parameter part. For the deterministic parameter part, the method of dead zone pre - compensation is used for compensation. Define It has the following form:

[0017] (3);

[0018] Among them, Represents the control input calculated by the upper - layer controller.

[0019] According to (2) - (3), the relationship between the control input calculated by the upper - layer controller and the input rotational speed of the system can be obtained:

[0020] (4);

[0021] Substitute (4) into (2), and abstract the dead zone and the system uncertainty parameter part as the internal perturbation of the system. The following system state - space equations can be obtained:

[0022] (5);

[0023] (6);

[0024] Based on the high - order fully actuated theory, if the coefficient matrix is invertible, the above - mentioned system is fully actuated. The direct parameter method is used to design the fully actuated control law, convert the state - space model into a fully actuated model, and design It has the following form:

[0025] (7);

[0026] where is a matrix that can be arbitrarily specified, is an external signal.

[0027] Substitute (7) into (5) to convert the original system into a fully actuated form

[0028] (8);

[0029] Based on the idea of equivalent input disturbance, integrate the internal and external disturbances into the input channel disturbance Then, we can obtain:

[0030] (9);

[0031] Denote For the input channel disturbance, construct an intermediate observer for estimation. Denote the intermediate variable as Design the observer as follows:

[0032] (10);

[0033] where is the control law obtained by the MPC controller, 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 models and Then, we have:

[0034] (11);

[0035] Denote Then, we have:

[0036] (12);

[0037] Denote Then, we have:

[0038] (13);

[0039] Construct the Lyapunov function to analyze the stability of the error system. Let be matrix variables of appropriate dimensions. Construct the stability matrix and solve it to obtain the intermediate observer gain:

[0040] (14);

[0041] If the above linear matrix inequality has a solution, the state of the error system is uniformly ultimately bounded, and the observer gain can be obtained .

[0042] For a given reference speed signal, a model predictive controller for the high-order all-drive speed model of a networked motion control system is designed. Considering the fault-free case, there is , then the state equation of the system is:

[0043] (15);

[0044] Set the prediction horizon , and the recurrence expression is as follows:

[0045] (16);

[0046] Denote the discrete reference signal as , and define the quadratic performance index as:

[0047] (17);

[0048] Among them, represents the weight matrix of the system operation cost, that is, the cost of adjusting the state deviation of the system; represents the weight matrix of the system control quantity cost, that is, the cost of the control input. The optimization objective function is solved by 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 position tracking control;

[0049] Compared with the prior art, the advantages of this application are as follows:

[0050] 1) Use the all-drive system model to describe the networked motion control system with parameter uncertainty, dead zone characteristics and external disturbances, maintain the physical meaning of the system state, and facilitate the design of the controller.

[0051] 2) Divide the dead zone uncertainty into two parts: the deterministic parameter part and the uncertain parameter part. For the deterministic parameter part, dead zone pre-compensation is performed, and for the uncertain parameter part, an intermediate observer is designed based on the all-drive system model to achieve accurate estimation.

[0052] 3) A MPC method based on a high-order fully actuated model is proposed, and the MPC controller is combined with an intermediate observer to achieve high-precision position tracking control of a networked motion control system. Description of the Drawings

[0053] Figure 1 It is a flowchart of the position tracking control method for the networked motion control system based on high-order full actuation of this application;

[0054] Figure 2 It is the tracking curve of the state variable with respect to the reference signal in this application;

[0055] Figure 3 It is the comparison curve of the control laws before and after dead zone pre-compensation in this application. Detailed Embodiment

[0056] In order to make the objectives, technical solutions and advantages of this application clearer, the following further details this application in conjunction 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.

[0057] An embodiment of this application has steps as Figure 1 shown, and a rotational speed control method for a networked motion control system based on high-order full actuation is proposed, including the following steps:

[0058] Step S1: Use the Matlab system identification toolbox to obtain the state space model of the system, pre-compensate the dead zone, and design a full actuation control law to convert the state space model into a full actuation model:

[0059] S1.1) For the networked motion control system in the rotational speed mode, collect its position output signal by giving a rotational speed excitation signal; according to the rotational speed input signal and the position output signal, use the Matlab system identification toolbox to obtain a second-order state space model with dead zone non-linearity, and at the same time consider the uncertainty of the system identification parameters. The state equation of the system is as follows: (1);

[0060] Where, , represents the system state, represents the system input rotational speed signal, represents the system output position signal, represents the external disturbance signal, represents the dead zone input signal. represents the system parameter, , represents the slopes of the dead zone characteristics on the left and right, , represents the breakpoints of the dead zone characteristics on the left and right axes. Denote the system parameter uncertainty, Denote the dead zone parameter uncertainty. All forms of parameter uncertainty are as follows:

[0061] ;

[0062] For Take the derivative and substitute Substitute it and discretize according to the sampling time to obtain the following state - space equation:

[0063] (2);

[0064] where , denotes the parameter matrix, denotes the sampling time,

[0065] It can be seen from (1) and (2) that the dead zone of the system consists of a deterministic parameter part and an uncertain parameter part. For the deterministic parameter part, the method of dead zone pre - compensation is used for compensation. Define which has the following form:

[0066] (3);

[0067] where, denotes the control input calculated by the upper - layer controller.

[0068] S1.2) According to (1)-(2), the relationship between the control input calculated by the upper - layer controller and the input rotational speed of the system can be obtained:

[0069] (4);

[0070] Substitute (4) into (2), and abstract the uncertain parameter part as the internal perturbation of the system, then the following system state - space can be obtained:

[0071] (5);

[0072] (6);

[0073] Based on the high - order fully - actuated theory, here is invertible, the above - mentioned system is fully - actuated. The direct parameter method is used to design the fully - actuated control law, convert the state - space model into a fully - actuated model, and design which has the following form:

[0074] (7);

[0075] where , is an external signal.

[0076] Substitute (7) into (5) to convert the original system into a fully actuated form

[0077] (8);

[0078] Step S2: Construct an intermediate observer, design and solve for the intermediate observer gain through matrix inequalities to estimate the equivalent input disturbance, including the following steps;

[0079] S2.1) Based on the idea of equivalent input disturbance, integrate the internal and external disturbances into the input channel disturbance , then we can obtain;

[0080] (9);

[0081] Denote , , for the input channel disturbance, construct an intermediate observer for estimation. Denote the intermediate variable as , and design the observer as follows:

[0082] (10);

[0083] where is the control law obtained by the MPC controller, used to cancel the equivalent input disturbance of the system. Select as the intermediate observer parameter, is the observer gain matrix to be solved.

[0084] S2.2) Construct the error model and , we have:

[0085] (11);

[0086] Denote , , , , we have:

[0087] (12);

[0088] Denote , , , , we have:

[0089] (13);

[0090] S2.3) Construct the Lyapunov function to analyze the stability of the error system. Let , construct the stability matrix and solve it to obtain the intermediate observer gain:

[0091] (14);

[0092] Solve the above linear matrix inequality, and we can get , , , and the states of the error system are uniformly ultimately bounded.

[0093] Step S3: Design the 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:

[0094] S3.1) For the given reference speed signal, design a model predictive controller for the high-order system. Considering the fault-free case, we have , then the state equation of the system is:

[0095] (15);

[0096] Set the prediction horizon , and the recurrence expression is as follows:

[0097] (16);

[0098] where represents the matrix transpose symbol,

[0099]

[0100]

[0101] Denote the discrete reference signal as , and define the quadratic performance index as:

[0102] (17);

[0103] where, represents the operation cost weight matrix of the system, that is, the cost of adjusting the state deviation of the system; represents the control quantity cost weight matrix of the system, that is, the cost of the control input. Solve the optimization objective function 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 , inverse transform the obtained by MPC into , and the obtained by solvingIt will first undergo dead zone pre-compensation processing and then be input into the networked motion control system to compensate for the influence of the system dead zone. The comparison curves of the control laws before and after dead zone pre-compensation are as Figure 3 shown. Under this control law, the system state can track the reference signal well, and the tracking curves of its state variables with respect to the reference signal are as Figure 2 shown, thus realizing the high-precision position tracking control of the networked motion control system.

[0104] As mentioned above, the above is only a preferred specific embodiment 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 replacements or changes, and should be covered within the protection scope of the present invention.

Claims

1. A position tracking control method for a networked motion control system based on high-order full drive, characterized in that It includes the following steps: (1) For the motion control system in the speed mode, use the Matlab system identification toolbox to obtain the state space model of the system, pre-compensate the dead zone, and design the full drive control law to convert the state space model into a full drive model. It is expressed by the formula as follows: ； Among them, represents the system state, represents the system input speed signal, represents the system output position signal, represents the external disturbance signal, represents the dead zone input signal, represents the sampling time; represents the parameter matrix; denote represents the deterministic part of the system identification parameters, represents the uncertainty part; , represents the slopes of the left and right dead zone characteristics, , represents the breakpoints of the dead zone characteristics on the left and right axes, represents the dead zone uncertainty parameter; First, for the networked motion control system in the speed mode, given the speed excitation signal, collect its position output signal. Second, according to the collected speed input signal and position output signal, use the Matlab system identification toolbox to obtain the second-order state space model with dead zone nonlinearity, discretize it and convert it into a high-order full drive model. Furthermore, for the deterministic parameter part in the dead zone nonlinearity characteristic of the system model, use the dead zone pre-compensation method for compensation. It is expressed by the formula as follows: ； Among them, represents the control input obtained by the upper-layer controller, 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 realize the estimation of the equivalent input disturbance. Specifically, for the dead zone and the uncertain parameter part in the system, abstract them as internal disturbances and combine them with external disturbances into equivalent input disturbances, design an intermediate observer for estimation and compensate for the influence caused by the disturbances; (3) Use the MPC method to design a high-precision tracking controller, design the MPC controller to solve the optimal control sequence, and obtain the final input of the networked motion control system through inverse transformation.

2. The position tracking control method of the networked motion control system based on high-order full drive according to claim 1, wherein The equivalent input disturbance described in step (2) is expressed by the formula as follows: ； Among them, is the external disturbance and the internal disturbance integrated into the input channel interference.

3. The position tracking 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: ； wherein, is the control law obtained by the MPC controller, is a suitable scalar variable, is the observer gain matrix to be determined.

4. The position tracking control method of the networked motion control system based on high-order full drive according to claim 1, characterized in that, In step (3), the MPC controller is designed to solve the control law and inverse-transform it into the full drive control law through the corresponding relationship, which is expressed by the formula as follows: ； The parameter matrix of the system, which together constitute a recurrence equation with a prediction interval of 5; Denote the discrete reference signal as , and define the quadratic performance index as: ； Among them, represents the operation cost weight matrix of the system, that is, the cost of adjusting the state deviation of the system; 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 of the two parts, that is, to save costs while meeting the system performance requirements; According to , the obtained by MPC is inverse-transformed into . After dead zone pre-compensation, it is introduced into the networked motion control system to complete high-precision position tracking control.

Images