Piecewise linear motion control method based on adaptive MRAC and PID

Abstract

The invention discloses a piecewise linear motion control method based on adaptive MRAC and PID, and relates to the technical field of non-linear control, and the method comprises the following steps: 1, constructing an MRAC controller; step 2, constructing a PID controller; step 3, segmenting the whole motion process of the system for multiple times, taking each segment of actual output path as a straight line segment, and switching motion control modes of the system according to an error norm between state output and PID control stage estimation states to obtain a system state feedback control law of the straight line segment; 4, calculating a system state feedback control law of the whole motion process of the system according to the obtained system state feedback control law of the straight line segment; according to the piecewise linear motion control method based on the adaptive MRAC and the PID, deviation can be rapidly eliminated in the motion control process to reach the expected position, and the good adaptive motion control effect is achieved in the high-dynamic, strong-countermeasure and other complex interference environments.

Description

Technical Field

[0001] The invention relates to the technical field of nonlinear control, and in particular to a piecewise linear motion control method based on adaptive MRAC and PID. Background Art

[0002] Unmanned systems face uncertain factors such as enemy target attacks and environmental interference in combat scenarios. When coordinating positioning with other units in the unmanned cluster, they also need to control their own attitude. In general, attitude control is a nonlinear process. Linearizing the nonlinear motion process of unmanned systems is a common and effective method, because after linearization, the system object characteristics are relatively clear, and the controller design is relatively simple and effective.

[0003] For controller design of nonlinear systems, especially piecewise linear systems, PID and model reference adaptive control (MRAC) algorithms each have their own advantages. Due to its convenient parameter design and relatively simple structure, the PID controller can achieve input and output deviation control through proportional, integral, and differential controllers, and reduce the time for control to reach the minimum deviation through the integral link; but due to its relative dependence on PID control parameters, the same controller parameters for different linear systems are not ideal. MRAC can adapt the model according to the controller to achieve relatively ideal "following" of input and output, but in the early stage of control, due to the large deviation of the adaptive parameters compared with the expected parameters, it cannot achieve a good control effect in the initial stage.

[0004] When the characteristics of each linear system are not much different, a single control method can be used to design the controller of the piecewise linear system; when the system motion process is complex and the running trajectory is tortuous, the above control method will no longer be applicable. Therefore, the present invention proposes a piecewise linear motion control method based on adaptive MRAC and PID to solve the shortcomings of the above-mentioned prior art. Summary of the invention

[0005] The purpose of the present invention is to provide a piecewise linear motion control method based on adaptive MRAC and PID, so as to solve the problem that a single PID or MRAC algorithm in the prior art is difficult to be applied when the system motion process is complex and the running trajectory is tortuous.

[0006] To achieve the above object, the present invention provides a piecewise linear motion control method based on adaptive MRAC and PID, comprising the following steps: Step 1: Build the MRAC controller; Step 2: Build a PID controller; Step 3: Divide the entire motion process S of the system into multiple segments, and regard each actual output path as a straight line segment. , , according to the error norm between the state output and the estimated state in the PID control stage, the motion control mode of the system is switched to obtain The system state feedback control law ; Step 4: According to step 3 The system state feedback control law , obtain the system state feedback control law u of the entire motion process S of the system.

[0007] Preferably, the MRAC controller constructed in step 1 is specifically: Output of MRAC controller The calculation expression is as follows: (1) In the formula, For system input, is the system output, is the gain scalar, is the gain matrix; MRAC controller output tracking state error The calculation expression is as follows: (2) In the formula, Indicates the expected output; Based on the tracking state error , calculate the gain scalar after the i-th iteration update , gain matrix , the expression is as follows: (3) (4) In the formula, Represents the gain scalar The first derivative of Represents the gain matrix The first derivative of represents the coefficient matrix 1 after the i-th iteration update, represents the output tracking state error after the i-th iteration update, represents the system output transposed matrix after the i-th iteration update, represents the coefficient matrix 2 after the i-th iteration update, Input to the system.

[0008] Preferably, the PID controller constructed in step 2 is specifically: Output of PID controller The calculation expression is as follows: (5) In the formula, represents the output tracking state error corresponding to the integral link, , , They are the proportional gain, integral time and differential time of the linear system, which are all known parameters (the values ​​are set according to the controlled object); PID controller output tracking state error The calculation expression is as follows: (6) In the formula, Indicates the expected output; The control goal is to ensure the state output of the controlled system Tracking the expected trajectory , the expression is as follows: (7).

[0009] Preferably, the expression for switching the motion control mode of the system according to the error norm between the state output and the estimated state in the PID control stage is as follows: (8) In the formula, is the expected output in the PID control stage and is used to evaluate the estimated state of the MRAC controller; When the PID controller tracks the error renew and ;when When the MRAC controller has better tracking performance and tracking accuracy, the MRAC controller is switched to control the system motion and update and ;in, and Respectively represent the gain scalar and gain matrix of the PID control stage, and They represent the gain scalar and gain matrix of the MRAC control stage respectively.

[0010] Preferably, when When, update and The expression is as follows: (9) In the formula, is the PID controller output, For system input, is the expected output.

[0011] Preferably, when When, update and The expression is as follows: (10) In the formula, is the MRAC controller output, System input, System output.

[0012] Preferably, the The system state feedback control law The expression is as follows: (11).

[0013] Preferably, the expression of the system state feedback control law u of the entire motion process S of the system obtained in step 4 is as follows, wherein, ; : (12).

[0014] Therefore, the present invention adopts the above-mentioned piecewise linear motion control method based on adaptive MRAC and PID, which has the following beneficial effects: (1) The method provided by the present invention enables the system to have faster control: by establishing PID and MRAC piecewise linear controllers, the controller design problems of multiple piecewise linear systems are considered, and the characteristics of PID parameter fast control and MRAC adaptive control accuracy are combined to quickly eliminate deviations during motion control to achieve the desired position; (2) The method provided by the present invention enables the system to have smoother switching: through the design of the switch controller, adaptive control of the controlled object is achieved, the challenges brought to the controller by changes in the system's own characteristics such as switching are reduced, small disturbances during the switching process are overcome, and the ideal value is quickly approached; this method has good adaptive motion control effects in complex interference environments such as high dynamics and strong confrontation.

[0015] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 The overall flow chart of a piecewise linear motion control method based on adaptive MRAC and PID of the present invention; Figure 2 is a structural diagram of an MRAC controller according to an embodiment of the present invention; Figure 3 It is a structural diagram of a PID controller according to an embodiment of the present invention; Figure 4A schematic diagram of a curve segmentation process according to an embodiment of the present invention; Figure 5 4 is a structural diagram of a piecewise linear system controller according to an embodiment of the present invention. DETAILED DESCRIPTION

[0017] The following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention claimed for protection, but merely represents selected embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0018] See also Figure 1-Figure 5 , a piecewise linear motion control method based on adaptive MRAC and PID, comprising the following steps: Step 1: Build the MRAC controller, such as Figure 2 As shown in the figure, an adaptive controller for state feedback, namely the model reference adaptive controller (MRAC), is proposed to improve the stability of motion control and state tracking of piecewise linear systems. The MRAC controller constructed is as follows: Output of MRAC controller The calculation expression is as follows: (1) In the formula, For system input, is the system output, is the gain scalar, is the gain matrix; MRAC controller output tracking state error The calculation expression is as follows: (2) In the formula, Indicates the expected output; Based on the tracking state error , calculate the gain scalar after the i-th iteration update , gain matrix , the expression is as follows: (3) (4) In the formula, Represents the gain scalar The first derivative of Represents the gain matrix The first derivative of represents the coefficient matrix 1 after the i-th iteration update, represents the output tracking state error after the i-th iteration update, represents the system output transposed matrix after the i-th iteration update, represents the coefficient matrix 2 after the i-th iteration update, Input to the system.

[0019] Step 2: Build a PID controller, such as Figure 3 As shown; in order to make the system state output asymptotically track the desired trajectory faster, a PID controller is used; the constructed PID controller is specifically: Output of PID controller The calculation expression is as follows: (5) In the formula, represents the output tracking state error corresponding to the integral link, , , They are the proportional gain, integral time and differential time of the linear system, which are all known parameters (the values ​​are set according to the controlled object); PID controller output tracking state error The calculation expression is as follows: (6) In the formula, Indicates the expected output; The control goal is to ensure the state output of the controlled system Tracking the expected trajectory , the expression is as follows: (7).

[0020] Step 3: Divide the entire motion process S of the system into multiple segments, and regard each actual output path as a straight line segment. The specific curve segmentation process is as follows: Figure 4 As shown, According to the error norm between the state output and the estimated state in the PID control stage, the motion control mode of the system is switched. In order to achieve fast asymptotic tracking of the system state output to the desired trajectory, corresponding switching devices are designed for the PID and MRAC parts, such as Figure 5 As shown, obtain The system state feedback control law ; The expression for switching the motion control mode of the system according to the error norm between the state output and the estimated state in the PID control stage is as follows: (8) In the formula, is the expected output in the PID control stage and is used to evaluate the estimated state of the MRAC controller; When the PID controller tracks the error renew and , the use of PID controller can ensure error convergence to a certain extent; when When the MRAC controller has better tracking performance and tracking accuracy, the MRAC controller is switched to control the system motion and update and ;in, and Respectively represent the gain scalar and gain matrix of the PID control stage, and They represent the gain scalar and gain matrix of the MRAC control stage respectively.

[0021] when When, update and The expression is as follows: (9) In the formula, is the PID controller output, For system input, is the expected output.

[0022] when When, update and The expression is as follows: (10) In the formula, is the MRAC controller output, System input, System output.

[0023] Obtained The system state feedback control law The expression is as follows: (11).

[0024] Step 4: According to step 3 The system state feedback control law , obtain the system state feedback control law u for the entire motion process S of the system, each segment Through the segmented control law Adaptively select the control ratio corresponding to the motion state, give full play to the control advantages of the two algorithms on the piecewise linear system, and finally realize the closed-loop control of the entire curve motion process S; ; ; The specific expression of the system state feedback control law u is as follows: (12).

[0025] Therefore, the present invention adopts the above-mentioned piecewise linear motion control method based on adaptive MRAC and PID. In the initial stage, the piecewise linear system is motion controlled by a PID controller. When the tracking state error is greater than the threshold, it switches to the MRAC adaptive control state, thereby achieving rapid asymptotic tracking of the system state output to the desired trajectory.

[0026] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solution of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solution to deviate from the spirit and scope of the technical solution of the present invention.

Claims

1. A piecewise linear motion control method based on adaptive MRAC and PID, characterized in that: The following steps are involved: Step 1: Build the MRAC controller; Step 2: Build a PID controller; Step 3: Divide the entire motion process S of the system into multiple segments, and regard each actual output path as a straight line segment. , , according to the error norm between the state output and the estimated state in the PID control stage, the motion control mode of the system is switched to obtain The system state feedback control law ; Step 4: According to step 3 The system state feedback control law , obtain the system state feedback control law u of the entire motion process S of the system.

2. The piecewise linear motion control method based on adaptive MRAC and PID according to claim 1, characterized in that: The MRAC controller constructed in step 1 is as follows: Output of MRAC controller The calculation expression is as follows: (1) In the formula, For system input, is the system output, is the gain scalar, is the gain matrix; MRAC controller output tracking state error The calculation expression is as follows: (2) In the formula, Indicates the expected output; Based on the tracking state error , calculate the gain scalar after the i-th iteration update , gain matrix , the expression is as follows: (3) (4) In the formula, Represents the gain scalar The first derivative of Represents the gain matrix The first derivative of represents the coefficient matrix 1 after the i-th iteration update, represents the output tracking state error after the i-th iteration update, represents the system output transposed matrix after the i-th iteration update, represents the coefficient matrix 2 after the i-th iteration update, Input to the system.

3. The piecewise linear motion control method based on adaptive MRAC and PID according to claim 2, characterized in that: The PID controller constructed in step 2 is specifically: Output of PID controller The calculation expression is as follows: (5) In the formula, represents the output tracking state error corresponding to the integral link, , , They are the proportional gain, integral time, and differential time of the linear system, which are all known parameters; PID controller output tracking state error The calculation expression is as follows: (6) In the formula, Indicates the expected output; The control goal is to ensure the state output of the controlled system Tracking the expected trajectory , the expression is as follows: (7)。 4. The piecewise linear motion control method based on adaptive MRAC and PID according to claim 3, characterized in that: According to the error norm between the state output and the estimated state in the PID control stage, the expression for switching the motion control mode of the system is as follows: (8) In the formula, is the expected output in the PID control stage and is used to evaluate the estimated state of the MRAC controller; When the PID controller tracks the error renew and ;when When the system is switched to the MRAC controller, it will perform motion control and update and ;in, and Respectively represent the gain scalar and gain matrix of the PID control stage, and They represent the gain scalar and gain matrix of the MRAC control stage respectively.

5. The piecewise linear motion control method based on adaptive MRAC and PID according to claim 4, characterized in that: when When, update and The expression is as follows: (9) In the formula, is the PID controller output, For system input, is the expected output.

6. The piecewise linear motion control method based on adaptive MRAC and PID according to claim 5, characterized in that: when When, update and The expression is as follows: (10) In the formula, is the MRAC controller output, System input, System output.

7. The piecewise linear motion control method based on adaptive MRAC and PID according to claim 6, characterized in that: Obtained in step 3 The system state feedback control law The expression is as follows: (11)。 8. The piecewise linear motion control method based on adaptive MRAC and PID according to claim 7, characterized in that: The expression of the system state feedback control law u for the entire motion process S of the system obtained in step 4 is as follows, where: ; : (12)。

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