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CN119668091A - A piecewise linear motion control method based on adaptive MRAC and PID - Google Patents

A piecewise linear motion control method based on adaptive MRAC and PID Download PDF

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CN119668091A
CN119668091A CN202510186456.XA CN202510186456A CN119668091A CN 119668091 A CN119668091 A CN 119668091A CN 202510186456 A CN202510186456 A CN 202510186456A CN 119668091 A CN119668091 A CN 119668091A
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CN119668091B (en
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徐山峰
王成才
潘琦
王肖
刘春旭
王兆伟
王茹斐
张容静
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Electronic Science Research Institute Of China Electronics Technology Group Co ltd
Beihang University
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Beihang University
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Abstract

The invention discloses a piecewise linear motion control method based on self-adaptive MRAC and PID, which relates to the technical field of nonlinear control and comprises the following steps of 1, constructing an MRAC controller, 2, constructing a PID controller, 3, segmenting the whole motion process of a system for a plurality of times, regarding each section of actual output path as a linear line segment, switching the motion control mode of the system according to the error norm between state output and the estimation state of the PID control stage to obtain a system state feedback control law of the linear line segment, and 4, calculating the system state feedback control law of the whole motion process of the system according to the obtained system state feedback control law of the linear line segment.

Description

Piecewise linear motion control method based on self-adaptive MRAC and PID
Technical Field
The invention relates to the technical field of nonlinear control, in particular to a piecewise linear motion control method based on self-adaptive MRAC and PID.
Background
The unmanned system faces the influence of uncertain factors such as enemy target attack, environmental interference and the like in a combat scene, and when the unmanned system is co-located with other units in the unmanned cluster, the unmanned system also performs self-attitude control. In summary, attitude control is a nonlinear process, and linearizing the nonlinear motion process of an unmanned system is a common and efficient method, because the system object characteristics after linearization are relatively clear, and the controller design is relatively simple and efficient.
The PID and Model Reference Adaptive Control (MRAC) algorithms each have advantages for controller design of nonlinear systems, especially piecewise linear systems. The PID controller has the advantages of convenient parameter design and relatively simple structure, can realize the deviation control of input and output through a proportional, integral and derivative controller, and reduces the time for controlling to reach the minimum deviation through an integral link, but has less ideal parameter effect for the same controller of different linear systems because the PID controller relatively depends on PID control parameters. The MRAC can adapt to the model according to the controller to realize the relatively ideal follow-up of input and output, but in the initial control stage, the adaptive parameters have larger deviation compared with the expected parameters, so that a better control effect cannot be achieved in the initial stage.
When the characteristics of each section of linear system are not different, a single control method can be adopted to design the piecewise linear system controller, and when the motion process of the system is complex and the motion track is tortuous, the control method is not applicable any more. Therefore, the present invention proposes a piecewise linear motion control method based on adaptive MRAC and PID to solve the above-mentioned shortcomings of the prior art.
Disclosure of Invention
The invention aims to provide a piecewise linear motion control method based on self-adaptive MRAC and PID, which solves the problem that a single PID or MRAC algorithm in the prior art is difficult to be applied under the conditions of complex system motion process and tortuous motion track.
In order to achieve the above object, the present invention provides a piecewise linear motion control method based on adaptive MRAC and PID, comprising the steps of:
step 1, constructing an MRAC controller;
step 2, constructing a PID controller;
Step3, segmenting the whole motion process S of the system for a plurality of times, wherein each segment of actual output path is regarded as a straight line segment ,Switching the motion control mode of the system according to the error norm between the state output and the PID control stage estimation state to obtainSystem state feedback control law of (2);
Step 4, obtained according to step 3System state feedback control law of (2)And obtaining a system state feedback control law u of the whole motion process S of the system.
Preferably, the MRAC controller constructed in step 1 specifically includes:
output of MRAC controller The calculated expression of (2) is as follows:
(1)
In the formula, For the input to the system,For the output of the system,As a scalar of the gain,Is a gain matrix;
MRAC controller outputs tracking state error The calculated expression of (2) is as follows:
(2)
In the formula, Representing a desired output;
Based on tracking state errors Calculating the gain scalar updated by the ith iterationGain matrixThe expression is as follows:
(3)
(4)
In the formula, Representing gain scalarIs used as a first derivative of (a),Representing gain matrixIs used as a first derivative of (a),Representing the coefficient matrix 1 after the i-th iteration update,Representing the output tracking state error after the i-th iteration update,Representing the system output transpose after the i-th iteration update,Representing the coefficient matrix 2 after the i-th iteration update,Is a system input.
Preferably, the PID controller constructed in step 2 specifically comprises:
output of PID controller The calculated expression of (2) is as follows:
(5)
In the formula, Representing the output tracking state error corresponding to the integration segment,、、Proportional gain, integral time and differential time of the linear system are known parameters (the numerical value is set according to the controlled object);
PID controller outputs tracking state error The calculated expression of (2) is as follows:
(6)
In the formula, Representing a desired output;
the control target is to ensure the state output of the controlled system Tracking a desired trajectoryThe expression is as follows:
(7)。
preferably, the expression for switching the motion control mode of the system according to the error norm between the state output and the PID control phase estimation state is as follows:
(8)
In the formula, Is the desired output during the PID control phase for evaluating the estimated state of the MRAC controller whenThe PID controller passes the tracking errorUpdatingAndWhen (1)When the system is in operation, the MRAC controller has better tracking performance and tracking precision, so that the MRAC controller is switched to perform motion control and update on the systemAndWherein, the method comprises the steps of,AndRespectively represent the gain scalar and gain matrix of the PID control stage,AndRespectively representing the gain scalar, gain matrix of the MRAC control stage.
Preferably, whenWhen updatingAndThe expression of (2) is as follows:
(9)
In the formula, Is output by the PID controller and is used for controlling the output,For the input to the system,Is the desired output.
Preferably, whenWhen updatingAndThe expression of (2) is as follows:
(10)
In the formula, For the output of the MRAC controller,The input of the system is provided by,And outputting a system.
Preferably, obtained in step 3System state feedback control law of (2)The expression of (2) is as follows:
(11)。
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)。
Therefore, the invention adopts the piecewise linear motion control method based on the self-adaptive MRAC and PID, and has the following beneficial effects:
(1) The method provided by the invention enables the system to have faster control, considers the design problem of controllers of a plurality of piecewise linear systems by establishing PID and MRAC piecewise linear controllers, combines the characteristics of PID parameter fast control and MRAC self-adaptive control accuracy, and rapidly eliminates deviation to reach the expected position in the motion control process;
(2) The method provided by the invention enables the system to be switched more stably, realizes the self-adaptive control of the controlled object through the design of the switch controller, reduces the challenges brought to the controller by the characteristic change of the system switching and the like, overcomes the small disturbance in the switching process, and quickly approaches to an ideal value, and has good self-adaptive motion control effect under complex interference environments of high dynamic, strong countermeasure and the like.
The technical scheme of the invention is further described in detail through the drawings and the embodiments.
Drawings
FIG. 1 is an overall flow chart of a piecewise linear motion control method based on adaptive MRAC and PID of the present invention;
FIG. 2 is a block diagram of an MRAC controller according to an embodiment of the present invention;
FIG. 3 is a block diagram of a PID controller according to an embodiment of the invention;
FIG. 4 is a schematic diagram of a graph segmentation process according to an embodiment of the present invention;
Fig. 5 is a block diagram of a piecewise linear system controller in accordance with an embodiment of the present invention.
Detailed Description
The following detailed description of the embodiments of the invention, provided in the accompanying drawings, is not intended to limit the scope of the invention, as claimed, but is merely representative of selected embodiments of the invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
Referring to fig. 1-5, a piecewise linear motion control method based on adaptive MRAC and PID includes the steps of:
Step 1, constructing an MRAC controller, as shown in fig. 2, and providing an adaptive controller for state feedback, namely a Model Reference Adaptive Controller (MRAC), aiming at the stability of motion control and state tracking of a piecewise linear system, wherein the constructed MRAC controller specifically comprises:
output of MRAC controller The calculated expression of (2) is as follows:
(1)
In the formula, For the input to the system,For the output of the system,As a scalar of the gain,Is a gain matrix;
MRAC controller outputs tracking state error The calculated expression of (2) is as follows:
(2)
In the formula, Representing a desired output;
Based on tracking state errors Calculating the gain scalar updated by the ith iterationGain matrixThe expression is as follows:
(3)
(4)
In the formula, Representing gain scalarIs used as a first derivative of (a),Representing gain matrixIs used as a first derivative of (a),Representing the coefficient matrix 1 after the i-th iteration update,Representing the output tracking state error after the i-th iteration update,Representing the system output transpose after the i-th iteration update,Representing the coefficient matrix 2 after the i-th iteration update,Is a system input.
Step 2, constructing a PID controller as shown in fig. 3, wherein in order to enable the system state output to gradually track the expected track more quickly, the PID controller is used, and the constructed PID controller specifically comprises:
output of PID controller The calculated expression of (2) is as follows:
(5)
In the formula, Representing the output tracking state error corresponding to the integration segment,、、Proportional gain, integral time and differential time of the linear system are known parameters (the numerical value is set according to the controlled object);
PID controller outputs tracking state error The calculated expression of (2) is as follows:
(6)
In the formula, Representing a desired output;
the control target is to ensure the state output of the controlled system Tracking a desired trajectoryThe expression is as follows:
(7)。
Step3, segmenting the whole motion process S of the system for a plurality of times, wherein each segment of actual output path is regarded as a straight line segment The specific curve segmentation procedure is shown in figure 4,Switching the motion control mode of the system according to the error norm between the state output and the PID control stage estimation state, designing corresponding switching devices for the PID and MRAC parts to obtain the fast asymptotic tracking of the system state output to the expected track, as shown in figure 5System state feedback control law of (2)Wherein the expression for switching the motion control mode of the system according to the error norm between the state output and the PID control stage estimation state is as follows:
(8)
In the formula, Is the desired output during the PID control phase for evaluating the estimated state of the MRAC controller whenThe PID controller passes the tracking errorUpdatingAndThe PID controller can ensure error convergence to a certain extent whenWhen the system is in operation, the MRAC controller has better tracking performance and tracking precision, so that the MRAC controller is switched to perform motion control and update on the systemAndWherein, the method comprises the steps of,AndRespectively represent the gain scalar and gain matrix of the PID control stage,AndRespectively representing the gain scalar, gain matrix of the MRAC control stage.
When (when)When updatingAndThe expression of (2) is as follows:
(9)
In the formula, Is output by the PID controller and is used for controlling the output,For the input to the system,Is the desired output.
When (when)When updatingAndThe expression of (2) is as follows:
(10)
In the formula, For the output of the MRAC controller,The input of the system is provided by,And outputting a system.
Obtained bySystem state feedback control law of (2)The expression of (2) is as follows:
(11)。
Step 4, obtained according to step 3 System state feedback control law of (2)Obtaining a system state feedback control law u of the whole motion process S of the system, wherein each sectionCan control law by segmentationThe control proportion of the corresponding motion state is selected in a self-adaptive way, the control advantages of the two algorithms on the piecewise linear system are fully exerted, and the closed-loop control of the whole curve motion process S is finally realized, wherein,;The specific expression of the system state feedback control law u is as follows:
(12)。
therefore, the invention adopts the piecewise linear motion control method based on the self-adaptive MRAC and the PID, the piecewise linear system is controlled by the PID controller in the initial stage, and when the tracking state error is greater than the threshold value, the method is switched into the MRAC self-adaptive control state, thereby realizing the rapid asymptotic tracking of the system state output to the expected track.
It should be noted that the above-mentioned embodiments are merely for illustrating the technical solution of the present invention and not for limiting the same, and although the present invention has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that the technical solution of the present invention may be modified or substituted by the same, and the modified or substituted technical solution may not deviate from the spirit and scope of the technical solution of the present invention.

Claims (8)

1.一种基于自适应MRAC和PID的分段线性运动控制方法，其特征在于，包括以下步骤：1. A piecewise linear motion control method based on adaptive MRAC and PID, characterized by comprising the following steps: 步骤1、构建MRAC控制器；Step 1: Build the MRAC controller; 步骤2、构建PID控制器；Step 2: Build a PID controller; 步骤3、对系统整个运动过程S进行多次分段，每段实际输出路径看做直线线段，，根据状态输出和PID控制阶段估计状态之间的误差范数，对系统的运动控制模式进行切换，获得的系统状态反馈控制律；Step 3: Divide the entire motion process S of the system into multiple segments, and treat 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 ; 步骤4、根据步骤3获得的的系统状态反馈控制律，获得系统整个运动过程S的系统状态反馈控制律u。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.根据权利要求1所述的一种基于自适应MRAC和PID的分段线性运动控制方法，其特征在于，步骤1中构建的MRAC控制器具体为：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 specifically: MRAC控制器的输出的计算表达式如下：Output of MRAC controller The calculation expression is as follows: (1) (1) 式中，为系统输入，为系统输出，为增益标量，为增益矩阵；In the formula, For system input, is the system output, is the gain scalar, is the gain matrix; MRAC控制器输出跟踪状态误差的计算表达式如下：MRAC controller output tracking state error The calculation expression is as follows: (2) (2) 式中，表示期望输出；In the formula, Indicates the expected output; 基于跟踪状态误差，计算得出第i次迭代更新后的增益标量、增益矩阵，表达式如下：Based on the tracking state error , calculate the gain scalar after the i-th iteration update , gain matrix , the expression is as follows: (3) (3) (4) (4) 式中，表示增益标量的一阶导数，表示增益矩阵的一阶导数，表示第i次迭代更新后的系数矩阵1，表示第i次迭代更新后的输出跟踪状态误差，表示第i次迭代更新后的系统输出转置矩阵，表示第i次迭代更新后的系数矩阵2，为系统输入。In the formula, Represents the gain scalar The first-order derivative of Represents the gain matrix The first-order 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.根据权利要求2所述的一种基于自适应MRAC和PID的分段线性运动控制方法，其特征在于，步骤2中构建的PID控制器具体为：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: PID控制器的输出的计算表达式如下：Output of PID controller The calculation expression is as follows: (5) (5) 式中，表示积分环节对应的输出跟踪状态误差，、、分别为线性系统的比例增益、积分时间、微分时间，均为已知参数；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控制器输出跟踪状态误差的计算表达式如下：PID controller output tracking state error The calculation expression is as follows: (6) (6) 式中，表示期望输出；In the formula, Indicates the expected output; 控制目标是保障被控系统状态输出跟踪期望轨迹，表达式如下：The control goal is to ensure the state output of the controlled system Tracking the expected trajectory , the expression is as follows: (7)。 (7). 4.根据权利要求3所述的一种基于自适应MRAC和PID的分段线性运动控制方法，其特征在于：根据状态输出和PID控制阶段估计状态之间的误差范数，对系统的运动控制模式进行切换的表达式如下：4. A 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) (8) 式中，是在PID控制阶段的期望输出，用于评估MRAC控制器的估计状态；当时，PID控制器通过跟踪误差更新和；当时，切换为MRAC控制器对系统进行运动控制并更新和；其中，和分别表示PID控制阶段的增益标量、增益矩阵，和分别表示MRAC控制阶段的增益标量、增益矩阵。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.根据权利要求4所述的一种基于自适应MRAC和PID的分段线性运动控制方法，其特征在于：当时，更新和的表达式如下：5. The piecewise linear motion control method based on adaptive MRAC and PID according to claim 4 is characterized in that: When, update and The expression is as follows: (9) (9) 式中，为PID控制器输出，为系统输入，为期望输出。In the formula, is the PID controller output, For system input, is the expected output. 6.根据权利要求5所述的一种基于自适应MRAC和PID的分段线性运动控制方法，其特征在于：当时，更新和的表达式如下：6. The piecewise linear motion control method based on adaptive MRAC and PID according to claim 5 is characterized in that: When, update and The expression is as follows: (10) (10) 式中，为MRAC控制器输出，系统输入，系统输出。In the formula, is the MRAC controller output, System input, System output. 7.根据权利要求6所述的一种基于自适应MRAC和PID的分段线性运动控制方法，其特征在于，步骤3中获得的的系统状态反馈控制律的表达式如下：7. The piecewise linear motion control method based on adaptive MRAC and PID according to claim 6, characterized in that the The system state feedback control law The expression is as follows: (11)。 (11). 8.根据权利要求7所述的一种基于自适应MRAC和PID的分段线性运动控制方法，其特征在于，步骤4中获得的系统整个运动过程S的系统状态反馈控制律u的表达式如下，其中，；：8. A 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 of the entire motion process S of the system obtained in step 4 is as follows, wherein, ; : (12)。 (12).
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