A Piecewise Linear Motion Control Method Based on Adaptive MRAC and PID

Abstract

The present invention discloses a segmented linear motion control method based on adaptive MRAC and PID, which relates to the technical field of nonlinear control and includes the following steps: Step 1, construct an MRAC controller; Step 2, construct a PID controller; Step 3, segment the entire motion process of the system multiple times. Each actual output path segment is regarded as a straight line segment. According to the error norm between the state output and the estimated state in the PID control stage, switch the motion control mode of the system to obtain the system state feedback control law for the straight line segment; Step 4, calculate the system state feedback control law for the entire motion process of the system according to the obtained system state feedback control law for the straight line segment. The segmented linear motion control method based on adaptive MRAC and PID provided by the present invention can quickly eliminate deviations and reach the desired position during the motion control process, and has good adaptive motion control effects in complex interference environments such as high dynamics and strong confrontation.

Description

Technical Field

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

[0002] Unmanned systems are affected by uncertain factors such as enemy target attacks and environmental disturbances in combat scenarios. When collaborating with other units in an unmanned cluster for positioning, they also need to perform their own attitude control. Generally speaking, attitude control is a nonlinear process. Linearizing the nonlinear motion process of unmanned systems is a common and effective method because after linearization, the characteristics of the system object are relatively clearly described, and the controller design is relatively simple and effective.

[0003] For the controller design of nonlinear systems, especially piecewise linear systems, the PID and model reference adaptive control (MRAC) algorithms each have their own advantages. The PID controller is convenient for parameter design and has a relatively simple structure. It can achieve deviation control of the input and output through a proportional, integral, and differential controller, and reduce the time to reach the minimum deviation through the integral link. However, due to its relatively strong dependence on PID control parameters, the same controller parameters have less than ideal effects for different linear systems. MRAC can adapt to the model according to the controller to achieve relatively ideal "following" of the input and output. However, in the initial stage of control, due to the relatively large deviation between the adaptive parameters and the expected parameters, it is impossible to achieve good control effects in the initial stage.

[0004] When the characteristics of each piecewise linear system are not very different, a single control method can be used for the controller design of the piecewise linear system. When the system motion process is complex and the running trajectory is tortuous, the above control methods 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 deficiencies of the above 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, which solves the problem that a single PID or MRAC algorithm in the prior art is difficult to be applicable when the system motion process is complex and the running trajectory is tortuous.

[0006] To achieve the above purpose, the present invention provides a piecewise linear motion control method based on adaptive MRAC and PID, including the following steps:

[0007] Step 1, construct an MRAC controller;

[0008] Step 2, construct a PID controller;

[0009] Step 3: Segment the entire motion process S of the system multiple times, and regard the actual output path of each segment as a straight line segment. , , and based on the error norm between the state output and the estimated state in the PID control stage, switch the motion control mode of the system to obtain the system state feedback control law. ;

[0010] Step 4: According to the system state feedback control law obtained in Step 3 , obtain the system state feedback control law u for the entire motion process S of the system.

[0011] Preferably, the MRAC controller constructed in Step 1 is specifically:

[0012] The output of the MRAC controller is calculated as follows:

[0013] (1)

[0014] In the formula, is the system input, is the system output, is the gain scalar, is the gain matrix;

[0015] The tracking state error of the MRAC controller output is calculated as follows:

[0016] (2)

[0017] In the formula, represents the desired output;

[0018] Based on the tracking state error , calculate the gain scalar and the gain matrix after the i-th iteration update, and the expressions are as follows:

[0019] (3)

[0020] (4)

[0021] In the formula, represents the first derivative of the gain scalar , represents the first derivative of the gain matrix , represents the coefficient matrix 1 after the i-th iteration update, Denotes the output tracking state error after the $i$-th iteration update, Denotes the transpose matrix of the system output after the $i$-th iteration update, Denotes the coefficient matrix 2 after the $i$-th iteration update, Is the system input.

[0022] Preferably, the PID controller constructed in step 2 is specifically:

[0023] The output of the PID controller The calculation expression is as follows:

[0024] (5)

[0025] In the formula, Denotes the output tracking state error corresponding to the integral link, , , Are respectively the proportional gain, integral time, and derivative time of the linear system, all of which are known parameters (the numerical values are set according to the controlled object);

[0026] The output tracking state error of the PID controller The calculation expression is as follows:

[0027] (6)

[0028] In the formula, Denotes the desired output;

[0029] The control objective is to ensure that the state output of the controlled system Tracks the desired trajectory , and the expression is as follows:

[0030] (7).

[0031] Preferably, 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:

[0032] (8)

[0033] In the formula, Is the desired output in the PID control stage, used to evaluate the estimated state of the MRAC controller; when , the PID controller updates through the tracking error and ; when , since the MRAC controller has better tracking performance and tracking accuracy, it is switched to the MRAC controller to perform motion control on the system 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.

[0034] Preferably, when When, update and The expression is as follows:

[0035] (9)

[0036] In the formula, is the PID controller output, For system input, is the expected output.

[0037] Preferably, when When, update and The expression is as follows:

[0038] (10)

[0039] In the formula, is the MRAC controller output, System input, System output.

[0040] Preferably, the The system state feedback control law The expression is as follows:

[0041] (11).

[0042] 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, ; :

[0043] (12).

[0044] 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:

[0045] (1) The method provided by the present invention enables the system to have faster control: by establishing a PID and MRAC piecewise linear controller, considering the controller design problems of multiple piecewise linear systems, combining the characteristics of fast control of PID parameters and the accuracy of MRAC adaptive control, the deviation is quickly eliminated during the motion control process to reach the desired position;

[0046] (2) The method provided by the present invention enables the system to have smoother switching: through the design of a switch controller, the adaptive control of the controlled object is realized, reducing the challenges brought by changes in its own characteristics such as system switching to the controller, overcoming small disturbances during the switching process, and quickly approaching the ideal value; this method has good adaptive motion control effects in complex interference environments such as high dynamics and strong confrontation.

[0047] The technical solution of the present invention will be further described in detail below through the accompanying drawings and embodiments. Description of the Drawings

[0048] Figure 1 is the overall flowchart of a piecewise linear motion control method based on adaptive MRAC and PID of the present invention;

[0049] Figure 2 is the structural diagram of the MRAC controller of the embodiment of the present invention;

[0050] Figure 3 is the structural diagram of the PID controller of the embodiment of the present invention;

[0051] Figure 4 is the schematic diagram of the curve segmentation process of the embodiment of the present invention;

[0052] Figure 5 is the structural diagram of the piecewise linear system controller of the embodiment of the present invention. Specific Embodiments

[0053] 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 claimed invention, but merely represents selected embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts fall within the scope of protection of the present invention.

[0054] Please refer to Figures 1 - 5 , a piecewise linear motion control method based on adaptive MRAC and PID, comprising the following steps:

[0055] Step 1, construct an MRAC controller, as Figure 2As shown in the figure; for the stability of the motion control and state tracking of a piecewise linear system, an adaptive controller for state feedback, namely the model reference adaptive controller (MRAC), is proposed; the specific MRAC controller constructed is as follows:

[0056] The output of the MRAC controller The calculation expression is as follows:

[0057] (1)

[0058] In the formula, is the system input, is the system output, is the gain scalar, is the gain matrix;

[0059] The MRAC controller output tracking state error The calculation expression is as follows:

[0060] (2)

[0061] In the formula, represents the desired output;

[0062] Based on the tracking state error , the gain scalar and the gain matrix after the i-th iteration update are calculated, and the expressions are as follows:

[0063] (3)

[0064] (4)

[0065] In the formula, represents the first derivative of the gain scalar , represents the first derivative of the gain matrix , 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 transpose matrix of the system output after the i-th iteration update, represents the coefficient matrix 2 after the i-th iteration update, is the system input.

[0066] Step 2: Construct a PID controller, as Figure 3 shown; in order to enable the system state output to asymptotically track the desired trajectory faster, a PID controller is used; the specific PID controller constructed is as follows:

[0067] Output of the PID controller The calculation expression is as follows:

[0068] (5)

[0069] In the formula, represents the output tracking state error corresponding to the integral link, , , are respectively the proportional gain, integral time, and derivative time of the linear system, all of which are known parameters (the numerical values are set according to the controlled object);

[0070] PID controller output tracking state error The calculation expression is as follows:

[0071] (6)

[0072] In the formula, represents the desired output;

[0073] The control objective is to ensure that the state output of the controlled system tracks the desired trajectory , and the expression is as follows:

[0074] (7).

[0075] Step 3: Segment the entire motion process S of the system multiple times, and regard the actual output path of each segment as a straight line segment , and the specific curve segmentation process is as Figure 4 shown, , according to the error norm between the state output and the estimated state in the PID control stage, switch the motion control mode of the system. To achieve fast asymptotic tracking of the system state output to the desired trajectory, corresponding switching devices are designed for both the PID and MRAC parts, as Figure 5 shown, to obtain the system state feedback control law ; among them, 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:

[0076] (8)

[0077] In the formula, is the desired output in the PID control stage, which is used to evaluate the estimated state of the MRAC controller; when , the PID controller updates through the tracking error and , the use of a PID controller can ensure error convergence to a certain extent; when , since the MRAC controller has better tracking performance and tracking accuracy, it is switched to the MRAC controller for motion control of the system and and are updated; where and represent the gain scalar and gain matrix in the PID control stage respectively, and represent the gain scalar and gain matrix in the MRAC control stage respectively.

[0078] When , the expressions of and are updated as follows:

[0079] (9)

[0080] In the formula, is the output of the PID controller, is the system input, is the desired output.

[0081] When , the expressions of and are updated as follows:

[0082] (10)

[0083] In the formula, is the output of the MRAC controller, system input, system output.

[0084] The obtained system state feedback control law is expressed as follows:

[0085] (11).

[0086] Step 4. According to the system state feedback control law obtained in step 3, the system state feedback control law u of the entire motion process S of the system is obtained. Each can adaptively select the regulation ratio corresponding to the motion state through the piecewise control law , giving full play to the control advantages of the two algorithms in the piecewise linear system, and finally realizing the closed-loop control of the entire curve motion process S; where ; ; The specific expression of the system state feedback control law u is as follows:

[0087] (12).

[0088] Therefore, the present invention adopts the above-mentioned piecewise linear motion control method based on adaptive MRAC and PID. In the initial stage, the PID controller is used to control the motion of the piecewise linear system. When the tracking state error is greater than the threshold, it switches to the MRAC adaptive control state, thereby realizing the fast asymptotic tracking of the system state output to the desired trajectory.

[0089] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions of the present invention or make equivalent replacements, and these modifications or equivalent replacements do not make the modified technical solutions deviate from the spirit and scope of the technical solutions 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; 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 state 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 matrix and gain scalar of the PID control stage, and They represent the gain matrix and gain scalar of the MRAC control stage respectively.

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 system output Tracking expected output , 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: 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.

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: (10) In the formula, is the MRAC controller output, System input, System output.

6. The piecewise linear motion control method based on adaptive MRAC and PID according to claim 5, characterized in that: Obtained in step 3 The system state feedback control law The expression is as follows: (11)。 7. The piecewise linear motion control method based on adaptive MRAC and PID according to claim 6, 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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