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CN112214038A - Linear Active Disturbance Rejection Control System for Multiple Input Multiple Output Nonlinear System and Its Application - Google Patents

Linear Active Disturbance Rejection Control System for Multiple Input Multiple Output Nonlinear System and Its Application Download PDF

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CN112214038A
CN112214038A CN202011051392.6A CN202011051392A CN112214038A CN 112214038 A CN112214038 A CN 112214038A CN 202011051392 A CN202011051392 A CN 202011051392A CN 112214038 A CN112214038 A CN 112214038A
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高钦和
刘大伟
刘志浩
陈志翔
邓刚锋
管文良
刘秀钰
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Rocket Force University of Engineering of PLA
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Abstract

本发明公开了一种多输入多输出非线性系统的线性自抗扰控制系统及其应用，多输入多输出非线性系统的线性自抗扰控制系统包括伺服驱动器和运动控制卡，伺服驱动器的输出端与非线性系统的电机相连接，伺服驱动器的输入端与运动控制卡相连接；所述运动控制卡包括自抗扰控制器和非线性系统的控制芯片电路，所述自抗扰控制器以软件形式写入所述控制芯片电路中；所述伺服驱动器中设有驱动芯片电路；控制芯片电路的输出端与驱动芯片电路的输入端对应连接，实现对电机的控制；自抗扰控制器采用基于动态逆的方法输出反馈控制率。本发明的线性自抗扰控制系统利用动态逆来求解控制率对总扰动进行补偿，从而解决了系统控制增益的不确定带来的控制器不稳定问题。

Figure 202011051392

The invention discloses a linear active disturbance rejection control system of a multi-input multi-output nonlinear system and its application. The linear active disturbance rejection control system of the multi-input multi-output nonlinear system comprises a servo driver and a motion control card. The output of the servo driver The terminal is connected with the motor of the nonlinear system, and the input terminal of the servo driver is connected with the motion control card; the motion control card includes the ADRC controller and the control chip circuit of the non-linear system, and the ADRC is connected with the control chip circuit of the nonlinear system. The software is written into the control chip circuit; the servo driver is provided with a drive chip circuit; the output end of the control chip circuit is correspondingly connected with the input end of the drive chip circuit to realize the control of the motor; the active disturbance rejection controller adopts The dynamic inverse based method outputs the feedback control rate. The linear active disturbance rejection control system of the present invention utilizes the dynamic inverse to solve the control rate to compensate the total disturbance, thereby solving the controller instability problem caused by the uncertainty of the system control gain.

Figure 202011051392

Description

多输入多输出非线性系统的线性自抗扰控制系统及其应用Linear Active Disturbance Rejection Control System for Multiple Input Multiple Output Nonlinear System and Its Application

技术领域technical field

本发明涉及机电伺服系统的控制器分析与设计技术领域，尤其涉及多输入多输出非线性系统的线性自抗扰控制系统及其应用。The invention relates to the technical field of controller analysis and design of an electromechanical servo system, in particular to a linear active disturbance rejection control system of a multi-input multi-output nonlinear system and its application.

背景技术Background technique

在许多工程应用中，控制目标(机器臂、轮船、车辆等)沿着某一期望路径运行是首要的，其次关心的是运行过程中对速度的要求.这种类型的应用问题被许多学者所描述,称之为输出机动(outputmaneuvering)控制问题。机动控制问题通常由几何任务和动态任务两部分组成.几何任务是受控目标到达并沿着期望路径(路径变量δ的函数)运行。动态任务是沿期望路径运行时还要满足的额外动态指标,如时间、速度、加速度等指标.而一般跟踪控制问题的路径变量δ都是时间t的函数,通常取为δ＝t,因此机动控制问题比一般的跟踪控制问题更加广泛。In many engineering applications, the control object (robot arm, ship, vehicle, etc.) to run along a desired path is the primary concern, and the second concern is the speed requirement during the operation. This type of application problem has been studied by many scholars Description, called the output maneuvering (output maneuvering) control problem. Maneuver control problems usually consist of two parts: a geometrical task and a dynamical task. The geometrical task is the arrival of the controlled target and running along the desired path (a function of the path variable δ). Dynamic tasks are additional dynamic indicators that must be satisfied when running along the desired path, such as time, speed, acceleration and other indicators. The path variable δ of general tracking control problems is a function of time t, usually taken as δ=t, so maneuvering The control problem is broader than the general tracking control problem.

现有的多输入多输出严反馈非线性控制系统的设计中，由于系统的控制增益是不断变化的，使得传统的线性自抗扰控制器中控制增益标称值的参数不易选取，会导致系统控制的不稳定，抗干扰能力较弱。In the design of the existing multi-input multi-output strict feedback nonlinear control system, because the control gain of the system is constantly changing, it is difficult to select the parameters of the nominal value of the control gain in the traditional linear active disturbance rejection controller, which will cause the system to change. The control is unstable and the anti-interference ability is weak.

发明内容SUMMARY OF THE INVENTION

针对上述存在的问题，本发明旨在提供一种多输入多输出非线性系统的线性自抗扰控制系统及其应用，通过广义比例积分观测器来估计系统的状态和总扰动，然后利用动态逆来求解控制率对总扰动进行补偿，从而解决了系统控制增益的不确定带来的控制器不稳定问题。In view of the above existing problems, the present invention aims to provide a linear active disturbance rejection control system of a multi-input multi-output nonlinear system and its application. The generalized proportional-integral observer is used to estimate the state and total disturbance of the system, and then the dynamic inverse is used to estimate the state and total disturbance of the system. To solve the control rate to compensate the total disturbance, so as to solve the controller instability problem caused by the uncertainty of the system control gain.

为了实现上述目的，本发明所采用的技术方案如下：In order to achieve the above object, the technical scheme adopted in the present invention is as follows:

多输入多输出非线性系统的线性自抗扰控制系统，其特征在于：包括伺服驱动器和运动控制卡，所述伺服驱动器的输出端与所述非线性系统的电机相连接，所述伺服驱动器的输入端与所述运动控制卡相连接；The linear active disturbance rejection control system of the multi-input multi-output nonlinear system is characterized in that: it includes a servo driver and a motion control card, the output end of the servo driver is connected with the motor of the nonlinear system, and the The input end is connected with the motion control card;

所述运动控制卡包括自抗扰控制器和非线性系统的控制芯片电路，所述自抗扰控制器以软件形式写入所述控制芯片电路中；所述伺服驱动器中设有驱动芯片电路，所述控制芯片电路的输出端与所述驱动芯片电路的输入端对应连接，以驱动所述驱动芯片电路；所述驱动芯片电路的驱动频率调节信号输出端和驱动半桥电路调节信号输出端分别与所述非线性系统的电机输入端对应连接；The motion control card includes an active disturbance rejection controller and a control chip circuit of a nonlinear system, and the active disturbance rejection controller is written into the control chip circuit in the form of software; the servo driver is provided with a drive chip circuit, The output end of the control chip circuit is correspondingly connected with the input end of the drive chip circuit to drive the drive chip circuit; the drive frequency adjustment signal output end of the drive chip circuit and the drive half bridge circuit adjustment signal output end are respectively correspondingly connected with the motor input end of the nonlinear system;

所述自抗扰控制器采用基于动态逆的方法输出反馈控制率。The active disturbance rejection controller adopts a dynamic inverse-based method to output a feedback control rate.

进一步的，所述多输入多输出非线性系统的动态方程为

Figure RE-GDA0002774958930000021
其中，
Figure RE-GDA0002774958930000022
是各子系统的状态；
Figure RE-GDA0002774958930000023
Figure RE-GDA0002774958930000024
是非线性系统的控制输入，Ωx，Ωu分别为分别为子系统状态x和控制输入u所取范围的集合，且Ωx，Ωu分别包含其原点；Further, the dynamic equation of the multi-input multi-output nonlinear system is
Figure RE-GDA0002774958930000021
in,
Figure RE-GDA0002774958930000022
is the state of each subsystem;
Figure RE-GDA0002774958930000023
Figure RE-GDA0002774958930000024
is the control input of the nonlinear system, Ω x , Ω u are the sets of the ranges taken by the subsystem state x and the control input u, respectively, and Ω x , Ω u respectively contain the origin;

所述非线性系统的可测量输出为

Figure RE-GDA0002774958930000025
Figure RE-GDA0002774958930000026
示系统受到的外部扰动；
Figure RE-GDA0002774958930000027
表示总的系统状态，包含各子系统xi的状态以及各子系统相互耦合的状态， n＝n1+n2+…nm为系统的总阶数，
Figure RE-GDA0002774958930000028
i∈(1，2，…，m)表示系统的耦合状态，包括外部扰动和内部不确定性的总和；
Figure RE-GDA0002774958930000029
i，j∈{1，2，…m}表示系统的控制增益；The measurable output of the nonlinear system is
Figure RE-GDA0002774958930000025
Figure RE-GDA0002774958930000026
Indicates the external disturbance to the system;
Figure RE-GDA0002774958930000027
Represents the total system state, including the state of each subsystem xi and the state of each subsystem coupling, n=n 1 +n 2 +…n m is the total order of the system,
Figure RE-GDA0002774958930000028
i∈(1, 2,…,m) represents the coupled state of the system, including the sum of external disturbances and internal uncertainties;
Figure RE-GDA0002774958930000029
i, j∈{1, 2,...m} represents the control gain of the system;

令

Figure RE-GDA00027749589300000210
则多输入多输出严反馈非线性系统的动态方程可以表示为make
Figure RE-GDA00027749589300000210
Then the dynamic equation of the multi-input multi-output strict feedback nonlinear system can be expressed as

Figure RE-GDA0002774958930000031
Figure RE-GDA0002774958930000031

进一步的，假设函数φi，l(·)，i∈(1，…，m)，l∈(1，…，ni-1)至少ni+p阶连续可微，且φi，l(0)＝0，则函数

Figure RE-GDA0002774958930000032
可表示
Figure RE-GDA0002774958930000033
Figure RE-GDA0002774958930000034
其中，
Figure RE-GDA0002774958930000035
表示已知的系统动态，
Figure RE-GDA0002774958930000036
表示未知的系统动态且对自变量是局部 Lipschitz的，系统的状态x对各子系统的状态xi是局部Lipschitz的，
Figure RE-GDA0002774958930000037
Further, it is assumed that the functions φ i,l (·), i∈(1,...,m), l∈(1,...,n i -1) are at least of order n i +p continuously differentiable, and φ i,l (0)=0, then the function
Figure RE-GDA0002774958930000032
representable
Figure RE-GDA0002774958930000033
Figure RE-GDA0002774958930000034
in,
Figure RE-GDA0002774958930000035
represents the known system dynamics,
Figure RE-GDA0002774958930000036
represents the unknown system dynamics and is local Lipschitz to the independent variable, the state x of the system is local Lipschitz to the state x i of each subsystem,
Figure RE-GDA0002774958930000037

则根据假设，存在一微分同胚映射Then according to the hypothesis, there is a differential homeomorphic mapping

Figure RE-GDA0002774958930000038
其中，
Figure RE-GDA0002774958930000039
ξi(0)＝0，
Figure RE-GDA00027749589300000310
Figure RE-GDA0002774958930000038
in,
Figure RE-GDA0002774958930000039
ξ i (0)=0,
Figure RE-GDA00027749589300000310

将微分同胚映射变换成积分串联型系统，则可得Transforming the differential homeomorphic map into an integral series system, we can get

Figure RE-GDA00027749589300000311
其中，
Figure RE-GDA00027749589300000312
表示总的系统状态，包含各子系统ξi的状态以及各子系统相互耦合的状态，且
Figure RE-GDA00027749589300000311
in,
Figure RE-GDA00027749589300000312
represents the overall system state, including the state of each subsystem ξ i and the state of the mutual coupling of each subsystem, and

Figure RE-GDA0002774958930000041
Figure RE-GDA0002774958930000041

进一步的，所述多输入多输出严反馈非线性系统跟踪的目标系统为

Figure RE-GDA0002774958930000042
其中，
Figure RE-GDA0002774958930000043
属于一紧集
Figure RE-GDA0002774958930000044
Further, the target system of the multi-input multi-output strict feedback nonlinear system tracking is:
Figure RE-GDA0002774958930000042
in,
Figure RE-GDA0002774958930000043
belong to a compact set
Figure RE-GDA0002774958930000044

将目标系统变换为积分串联型系统，可得

Figure RE-GDA0002774958930000045
其中，
Figure RE-GDA0002774958930000046
Transforming the target system into an integral series system, we can get
Figure RE-GDA0002774958930000045
in,
Figure RE-GDA0002774958930000046

设

Figure RE-GDA0002774958930000047
其中，i＝1，…，m，j＝2，…，ni，根据微分同胚映射的积分串联型系统和目标系统的积分串联型系统可得
Figure RE-GDA0002774958930000048
其中，
Figure RE-GDA0002774958930000049
误差增益矩阵
Figure RE-GDA00027749589300000410
满足
Figure RE-GDA00027749589300000411
为Hurwitz矩阵，
Figure RE-GDA00027749589300000412
Assume
Figure RE-GDA0002774958930000047
Among them, i=1,...,m,j=2,...,n i , according to the integral series system of the differential homeomorphic mapping and the integral series system of the target system, we can get
Figure RE-GDA0002774958930000048
in,
Figure RE-GDA0002774958930000049
Error Gain Matrix
Figure RE-GDA00027749589300000410
Satisfy
Figure RE-GDA00027749589300000411
is the Hurwitz matrix,
Figure RE-GDA00027749589300000412

进一步的，采用基于动态逆的方法输出反馈控制率的具体操作包括以下步骤，Further, the specific operation of using the dynamic inverse-based method to output the feedback control rate includes the following steps:

S1：定义

Figure RE-GDA0002774958930000051
为实际测量的输出与期望输出的状态误差的总和；S1: Definition
Figure RE-GDA0002774958930000051
is the sum of the state error of the actual measured output and the expected output;

S2：根据步骤S1中定义的Fi(ξ，ζ，wi，u)，可将动态逆设计为

Figure RE-GDA0002774958930000052
其中，B＝(bij)m×m，参数μi为小正数，μ＝(μ1，…，μm)T，
Figure RE-GDA0002774958930000053
S2: According to F i (ξ, ζ, wi , u) defined in step S1, the dynamic inverse can be designed as
Figure RE-GDA0002774958930000052
Wherein, B=(b ij ) m×m , the parameter μ i is a small positive number, μ=(μ 1 , . . . , μ m ) T ,
Figure RE-GDA0002774958930000053

S3：令

Figure RE-GDA0002774958930000054
在输出反馈的情况下，只有ξi，1可测量且
Figure RE-GDA0002774958930000055
未知，利用广义比例积分观测器来求解ξi和
Figure RE-GDA0002774958930000056
S3: order
Figure RE-GDA0002774958930000054
In the case of output feedback, only ξi ,1 is measurable and
Figure RE-GDA0002774958930000055
unknown, use a generalized proportional-integral observer to solve for ξ i and
Figure RE-GDA0002774958930000056

Figure RE-GDA0002774958930000057
Figure RE-GDA0002774958930000057

其中，参数

Figure RE-GDA0002774958930000058
满足
Figure RE-GDA0002774958930000059
为Hurwitz多项式，εi为一个小正数，且ε＝(ε1，…，εm)T；Among them, the parameter
Figure RE-GDA0002774958930000058
Satisfy
Figure RE-GDA0002774958930000059
is a Hurwitz polynomial, ε i is a small positive number, and ε=(ε 1 , ..., ε m ) T ;

S4：将步骤S3中的广义比例积分观测器和步骤S2中的动态逆结合起来，得到自抗扰控制器的输出反馈控制率，S4: Combine the generalized proportional-integral observer in step S3 and the dynamic inverse in step S2 to obtain the output feedback control rate of the active disturbance rejection controller,

Figure RE-GDA0002774958930000061
Figure RE-GDA0002774958930000061

其中，

Figure RE-GDA0002774958930000062
in,
Figure RE-GDA0002774958930000062

Figure RE-GDA0002774958930000063
Figure RE-GDA0002774958930000063

Figure RE-GDA0002774958930000064
Figure RE-GDA0002774958930000064

进一步的，多输入多输出非线性系统的线性自抗扰控制系统在具有多输入多输出特征的两自由度机械臂机电伺服控制装置中的应用。Further, the application of the linear active disturbance rejection control system of the multiple-input multiple-output nonlinear system in the electromechanical servo control device of a two-degree-of-freedom manipulator with multiple-input multiple-output characteristics.

进一步的，所述两自由度机械臂机电伺服控制装置包括基座和安装在所述基座上的第一减速器，所述第一减速器的输入轴与第一永磁同步电机的输出轴固定连接，所述第一减速器的输出轴与第一机械臂的首端固定连接，所述第一机械臂的末端连接有第二减速器，所述第二减速器的输入轴与第二永磁同步电机的输出轴固定连接，所述第二减速器的输出轴上连接有第二机械臂；Further, the two-degree-of-freedom mechanical arm electromechanical servo control device includes a base and a first reducer mounted on the base, the input shaft of the first reducer and the output shaft of the first permanent magnet synchronous motor. Fixed connection, the output shaft of the first reducer is fixedly connected to the head end of the first mechanical arm, the end of the first mechanical arm is connected with a second reducer, and the input shaft of the second reducer is connected to the second reducer. The output shaft of the permanent magnet synchronous motor is fixedly connected, and the output shaft of the second reducer is connected with a second mechanical arm;

所述第一永磁同步电机和所述第二永磁同步电机的输入端与所述伺服驱动器的输出端对应连接。The input ends of the first permanent magnet synchronous motor and the second permanent magnet synchronous motor are correspondingly connected with the output end of the servo driver.

进一步的，所述两自由度机械臂机电伺服控制装置的动态方程为

Figure RE-GDA0002774958930000065
其中，Further, the dynamic equation of the two-degree-of-freedom mechanical arm electromechanical servo control device is:
Figure RE-GDA0002774958930000065
in,

M11＝a1+a2 cosθ2，M 11 =a 1 +a 2 cosθ 2 ,

Figure RE-GDA0002774958930000071
Figure RE-GDA0002774958930000071

M22＝a3，M 22 =a 3 ,

Figure RE-GDA0002774958930000072
Figure RE-GDA0002774958930000072

Figure RE-GDA0002774958930000073
Figure RE-GDA0002774958930000073

G1(θ)＝a4 sinθ1+a5 sin(θ1+θ2)，G 1 (θ)=a 4 sinθ 1 +a 5 sin(θ 1 +θ 2 ),

G2(θ)＝a5 sin(θ1+θ2)，G 2 (θ)=a 5 sin(θ 1 +θ 2 ),

Figure RE-GDA0002774958930000074
Figure RE-GDA0002774958930000074

a2＝m2l2l1，a 2 =m 2 l 2 l 1 ,

Figure RE-GDA0002774958930000075
Figure RE-GDA0002774958930000075

式中，l1，l2分别表示第一机械臂和第二机械臂的长度，θ1，θ2分别表示第一机械臂和第二机械臂的关节角，m1，m2分别表示第一机械臂和第二机械臂的质量，u1为第一机械臂的控制输入，u2为第二机械臂的控制输入， d1，d2分别表示第一机械臂和第二机械臂受到的外部扰动；In the formula, l 1 and l 2 represent the lengths of the first manipulator and the second manipulator respectively, θ 1 and θ 2 represent the joint angles of the first manipulator and the second manipulator respectively, m 1 and m 2 represent the first manipulator and the second manipulator respectively. The mass of the first manipulator and the second manipulator, u1 is the control input of the first manipulator, u2 is the control input of the second manipulator, d1, d2 represent the first manipulator and the second manipulator respectively. external disturbance;

令NG1＝N1+G1，NG2＝N2+G2，则两自由度机械臂机电伺服控制装置的动态方程可以变换为Let NG 1 =N 1 +G 1 , NG 2 =N 2 +G 2 , then the dynamic equation of the two-degree-of-freedom manipulator electromechanical servo control device can be transformed into

Figure RE-GDA0002774958930000076
Figure RE-GDA0002774958930000076

Figure RE-GDA0002774958930000077
Figure RE-GDA0002774958930000077

由于M11，M22随着θ2的变化而变化，因此两自由度机械臂机电伺服控制装置是控制增益不确定的多入多出的非线性系统，并且子系统之间存在着状态耦合和控制耦合。Since M 11 and M 22 change with the change of θ 2 , the electromechanical servo control device of the two-degree-of-freedom manipulator is a nonlinear system with multiple inputs and multiple outputs with uncertain control gains, and there are state coupling and Control coupling.

进一步的，所述应用的具体操作包括以下步骤，Further, the specific operation of the application includes the following steps:

S5：令

Figure RE-GDA0002774958930000081
S5: order
Figure RE-GDA0002774958930000081

Figure RE-GDA0002774958930000082
Figure RE-GDA0002774958930000082

Figure RE-GDA0002774958930000083
Figure RE-GDA0002774958930000083

Figure RE-GDA0002774958930000084
Figure RE-GDA0002774958930000084

则两自由度机械臂机电伺服控制装置的动态方程可以继续变换成Then the dynamic equation of the electromechanical servo control device of the two-degree-of-freedom manipulator can be transformed into

Figure RE-GDA0002774958930000085
Figure RE-GDA0002774958930000085

S6：令

Figure RE-GDA0002774958930000086
其中
Figure RE-GDA0002774958930000087
用x表示θ，则两自由度机械臂机电伺服控制装置的动态方程进一步变换为
Figure RE-GDA0002774958930000088
其中，
Figure RE-GDA0002774958930000089
表示控制装置的两个状态，w1表示第一机械臂受到d1，d2干扰的总和,w2表示第二机械臂受到d1，d2干扰的总和；S6: order
Figure RE-GDA0002774958930000086
in
Figure RE-GDA0002774958930000087
Using x to represent θ, the dynamic equation of the two-degree-of-freedom manipulator electromechanical servo control device is further transformed into
Figure RE-GDA0002774958930000088
in,
Figure RE-GDA0002774958930000089
Indicates the two states of the control device, w 1 represents the sum of the disturbances of d 1 and d 2 for the first manipulator, and w 2 represents the sum of the disturbances of d 1 and d 2 for the second manipulator;

S7：步骤S6中的两自由度机械臂机电伺服控制装置的动态方程的参考系统为

Figure RE-GDA0002774958930000091
其中，r1＝[r1，1 r1，2]T，r2＝[r2，1 r2，2]T，
Figure RE-GDA0002774958930000092
是利用五次项拟合生成的有界指令信号；S7: The reference system of the dynamic equation of the two-degree-of-freedom manipulator electromechanical servo control device in step S6 is:
Figure RE-GDA0002774958930000091
where, r 1 =[r 1,1 r 1,2 ] T , r 2 =[r 2,1 r 2,2 ] T ,
Figure RE-GDA0002774958930000092
is the bounded command signal generated by quintic fitting;

S8：将步骤S4中的自抗扰控制器设计成

Figure RE-GDA0002774958930000093
根据控制器的输出来控制第一永磁同步电机和第二永磁同步电机的旋转角度；S8: Design the active disturbance rejection controller in step S4 as
Figure RE-GDA0002774958930000093
controlling the rotation angles of the first permanent magnet synchronous motor and the second permanent magnet synchronous motor according to the output of the controller;

其中，

Figure RE-GDA0002774958930000094
分别表示
Figure RE-GDA0002774958930000095
的控制输出结果，
Figure RE-GDA0002774958930000096
分别表示
Figure RE-GDA0002774958930000097
的控制输出结果。in,
Figure RE-GDA0002774958930000094
Respectively
Figure RE-GDA0002774958930000095
The control output result of ,
Figure RE-GDA0002774958930000096
Respectively
Figure RE-GDA0002774958930000097
control output result.

本发明的有益效果是：The beneficial effects of the present invention are:

本发明的线性自抗扰控制系统采用基于动态逆的方法输出反馈控制率的控制器，通过广义比例积分观测器来估计系统的状态和总扰动，然后利用动态逆来求解控制率对总扰动进行补偿，从而解决了系统控制增益的不确定带来的控制器不稳定问题，使得非线性系统在轨迹跟踪运动效果上有着显著的改善，参数的变动、系统模型不确定性等因素几乎无法对系统运动效果造成影响，并且系统在运动过程中具有很强的抗干扰能力。The linear active disturbance rejection control system of the present invention adopts a dynamic inverse-based method to output a controller of the feedback control rate, estimates the state and total disturbance of the system through a generalized proportional-integral observer, and then uses the dynamic inverse to solve the control rate for the total disturbance. Therefore, the instability of the controller caused by the uncertainty of the control gain of the system is solved, and the nonlinear system has a significant improvement in the trajectory tracking motion effect. The movement effect has an impact, and the system has a strong anti-interference ability during the movement.

附图说明Description of drawings

图1为本发明中两自由度机械臂机电伺服控制装置结构示意图。FIG. 1 is a schematic structural diagram of an electromechanical servo control device for a two-degree-of-freedom manipulator according to the present invention.

图2为本发明仿真实验中两自由度机械臂实验平台结构示意图。FIG. 2 is a schematic structural diagram of an experimental platform of a two-degree-of-freedom manipulator in a simulation experiment of the present invention.

图3为本发明仿真实验中不同系统抗干扰能力的实验结果。FIG. 3 is the experimental result of the anti-interference ability of different systems in the simulation experiment of the present invention.

其中：1-第一永磁同步电机，2-第一减速器，3-基座，4-第一机械臂， 5-第二机械臂，6-第二减速器，7-第二永磁同步电机。Among them: 1-first permanent magnet synchronous motor, 2-first reducer, 3-base, 4-first manipulator, 5-second manipulator, 6-second reducer, 7-second permanent magnet Synchronous motor.

具体实施方式Detailed ways

为了使本领域的普通技术人员能更好的理解本发明的技术方案，下面结合附图和实施例对本发明的技术方案做进一步的描述。In order to enable those skilled in the art to better understand the technical solutions of the present invention, the technical solutions of the present invention are further described below with reference to the accompanying drawings and embodiments.

多输入多输出非线性系统的线性自抗扰控制系统，包括伺服驱动器和运动控制卡，所述伺服驱动器的输出端与所述非线性系统的电机相连接，所述伺服驱动器的输入端与所述运动控制卡相连接；A linear active disturbance rejection control system for a multi-input multi-output nonlinear system, including a servo driver and a motion control card, the output end of the servo driver is connected to the motor of the nonlinear system, and the input end of the servo driver is connected to the connected to the motion control card;

所述运动控制卡包括自抗扰控制器和非线性系统的控制芯片电路，所述自抗扰控制器以软件形式写入所述控制芯片电路中；所述伺服驱动器中设有驱动芯片电路，所述控制芯片电路的输出端与所述驱动芯片电路的输入端对应连接，以驱动所述驱动芯片电路；所述驱动芯片电路的驱动频率调节信号输出端和驱动半桥电路调节信号输出端分别与所述非线性系统的电机输入端对应连接；The motion control card includes an active disturbance rejection controller and a control chip circuit of a nonlinear system, and the active disturbance rejection controller is written into the control chip circuit in the form of software; the servo driver is provided with a drive chip circuit, The output end of the control chip circuit is correspondingly connected with the input end of the drive chip circuit to drive the drive chip circuit; the drive frequency adjustment signal output end of the drive chip circuit and the drive half bridge circuit adjustment signal output end are respectively correspondingly connected with the motor input end of the nonlinear system;

所述自抗扰控制器采用基于动态逆的方法输出反馈控制率。The active disturbance rejection controller adopts a dynamic inverse-based method to output a feedback control rate.

具体的，所述多输入多输出非线性系统的动态方程为

Figure RE-GDA0002774958930000111
其中，
Figure RE-GDA0002774958930000112
是各子系统的状态；
Figure RE-GDA0002774958930000113
Figure RE-GDA0002774958930000114
是非线性系统的控制输入，Ωx，Ωu分别为分别为子系统状态x和控制输入u所取范围的集合，且Ωx，Ωu分别包含其原点；Specifically, the dynamic equation of the multi-input multi-output nonlinear system is:
Figure RE-GDA0002774958930000111
in,
Figure RE-GDA0002774958930000112
is the state of each subsystem;
Figure RE-GDA0002774958930000113
Figure RE-GDA0002774958930000114
is the control input of the nonlinear system, Ω x , Ω u are the sets of the ranges taken by the subsystem state x and the control input u, respectively, and Ω x , Ω u respectively contain the origin;

所述非线性系统的可测量输出为

Figure RE-GDA0002774958930000115
Figure RE-GDA0002774958930000116
示系统受到的外部扰动；
Figure RE-GDA0002774958930000117
表示总的系统状态，包含各子系统xi的状态以及各子系统相互耦合的状态， n＝n1+n2+…nm为系统的总阶数，
Figure RE-GDA0002774958930000118
i∈(1，2，…，m)表示系统的耦合状态，包括外部扰动和内部不确定性的总和；
Figure RE-GDA0002774958930000119
i，j∈{1，2，…m}表示系统的控制增益；The measurable output of the nonlinear system is
Figure RE-GDA0002774958930000115
Figure RE-GDA0002774958930000116
Indicates the external disturbance to the system;
Figure RE-GDA0002774958930000117
Represents the total system state, including the state of each subsystem xi and the state of each subsystem coupling, n=n 1 +n 2 +…n m is the total order of the system,
Figure RE-GDA0002774958930000118
i∈(1, 2,…,m) represents the coupled state of the system, including the sum of external disturbances and internal uncertainties;
Figure RE-GDA0002774958930000119
i, j∈{1, 2,...m} represents the control gain of the system;

令

Figure RE-GDA00027749589300001110
则多输入多输出严反馈非线性系统的动态方程可以表示为make
Figure RE-GDA00027749589300001110
Then the dynamic equation of the multi-input multi-output strict feedback nonlinear system can be expressed as

Figure RE-GDA00027749589300001111
Figure RE-GDA00027749589300001111

假设函数φi，l(·)，i∈(1，…，m)，l∈(1，…，ni-1)至少ni+p阶连续可微，且φi，l(0)＝0，则函数

Figure RE-GDA00027749589300001112
可表示
Figure RE-GDA00027749589300001113
Figure RE-GDA0002774958930000121
其中，
Figure RE-GDA0002774958930000122
表示已知的系统动态，
Figure RE-GDA0002774958930000123
表示未知的系统动态且对自变量是局部 Lipschitz的，系统的状态x对各子系统的状态xi是局部Lipschitz的，
Figure RE-GDA0002774958930000124
Assume that the functions φ i,l (·),i∈(1,…,m),l∈(1,…,n i -1) are continuously differentiable at least of order n i +p, and φ i,l (0) =0, then the function
Figure RE-GDA00027749589300001112
representable
Figure RE-GDA00027749589300001113
Figure RE-GDA0002774958930000121
in,
Figure RE-GDA0002774958930000122
represents the known system dynamics,
Figure RE-GDA0002774958930000123
represents the unknown system dynamics and is local Lipschitz to the independent variable, the state x of the system is local Lipschitz to the state x i of each subsystem,
Figure RE-GDA0002774958930000124

该假设保证了原点是开环系统的平衡点，若

Figure RE-GDA0002774958930000125
完全未知，那么
Figure RE-GDA0002774958930000126
This assumption guarantees that the origin is the equilibrium point of the open-loop system, if
Figure RE-GDA0002774958930000125
completely unknown, then
Figure RE-GDA0002774958930000126

根据该假设，存在一微分同胚映射

Figure RE-GDA0002774958930000127
其中，
Figure RE-GDA0002774958930000128
ξi(0)＝0，
Figure RE-GDA0002774958930000129
According to this assumption, there is a differential homeomorphic map
Figure RE-GDA0002774958930000127
in,
Figure RE-GDA0002774958930000128
ξ i (0)=0,
Figure RE-GDA0002774958930000129

将微分同胚映射变换成积分串联型系统，则可得

Figure RE-GDA00027749589300001210
其中，
Figure RE-GDA00027749589300001211
表示总的系统状态，包含各子系统ξi的状态以及各子系统相互耦合的状态，且
Figure RE-GDA00027749589300001212
Transforming the differential homeomorphic map into an integral series system, we can get
Figure RE-GDA00027749589300001210
in,
Figure RE-GDA00027749589300001211
represents the overall system state, including the state of each subsystem ξ i and the state of the mutual coupling of each subsystem, and
Figure RE-GDA00027749589300001212

本发明中的自抗扰控制器的设计目标是使得多输入多输出严反馈非线性系统的状态x跟踪一个目标系统的状态r。The design goal of the active disturbance rejection controller in the present invention is to make the state x of the multi-input multi-output strict feedback nonlinear system track the state r of a target system.

所述多输入多输出严反馈非线性系统跟踪的目标系统为

Figure RE-GDA0002774958930000131
其中，
Figure RE-GDA0002774958930000132
Figure RE-GDA0002774958930000133
属于一紧集
Figure RE-GDA0002774958930000134
The target system of the multi-input multi-output strict feedback nonlinear system tracking is:
Figure RE-GDA0002774958930000131
in,
Figure RE-GDA0002774958930000132
Figure RE-GDA0002774958930000133
belong to a compact set
Figure RE-GDA0002774958930000134

将目标系统变换为积分串联型系统，可得

Figure RE-GDA0002774958930000135
其中，
Figure RE-GDA0002774958930000136
Transforming the target system into an integral series system, we can get
Figure RE-GDA0002774958930000135
in,
Figure RE-GDA0002774958930000136

设

Figure RE-GDA0002774958930000137
其中，i＝1，…，m，j＝2，…，ni，根据微分同胚映射的积分串联型系统和目标系统的积分串联型系统可得
Figure RE-GDA0002774958930000138
其中，
Figure RE-GDA0002774958930000139
误差增益矩阵
Figure RE-GDA00027749589300001310
满足
Figure RE-GDA00027749589300001311
为Hurwitz矩阵，
Figure RE-GDA00027749589300001312
Assume
Figure RE-GDA0002774958930000137
Among them, i=1,...,m,j=2,...,n i , according to the integral series system of the differential homeomorphic mapping and the integral series system of the target system, we can get
Figure RE-GDA0002774958930000138
in,
Figure RE-GDA0002774958930000139
Error Gain Matrix
Figure RE-GDA00027749589300001310
Satisfy
Figure RE-GDA00027749589300001311
is the Hurwitz matrix,
Figure RE-GDA00027749589300001312

由多输入多输出非线性系统的动态方程可知，该非线性系统的控制增益bij(t)是时变的，因此对该系统设计传统的LADRC时，bij(t)的标称值b0不易选取，所以本发明的目标是为多输入多输出非线性不确定严反馈系统设计一个引入动态逆的线性自抗扰控制器，不仅能对系统的外扰，内部不确定性组成的总扰动进行估计补偿，并且不涉及b0值的选取问题，避免了 bij(t)的不确定性对闭环系统的稳定性带来影响。From the dynamic equation of the multi-input multi-output nonlinear system, it can be known that the control gain b ij (t) of the nonlinear system is time-varying, so when designing the traditional LADRC for this system, the nominal value of b ij (t) b 0 is not easy to choose, so the goal of the present invention is to design a linear active disturbance rejection controller with dynamic inverse for the multi-input multi-output nonlinear uncertain strict feedback system, which can not only control the external disturbance of the system, but also the total amount composed of internal uncertainties. The disturbance is estimated and compensated, and the selection of the b 0 value is not involved, which avoids the influence of the uncertainty of b ij (t) on the stability of the closed-loop system.

采用基于动态逆的方法输出反馈控制率的具体操作包括以下步骤，The specific operation of using the dynamic inverse-based method to output the feedback control rate includes the following steps:

S1：定义

Figure RE-GDA0002774958930000141
为实际测量的输出与期望输出的状态误差的总和……；S1: Definition
Figure RE-GDA0002774958930000141
is the sum of the state error of the actual measured output and the expected output...;

S2：根据步骤S1中定义的Fi(ξ，ζ，wi，u)，可将动态逆设计为

Figure RE-GDA0002774958930000142
其中，B＝(bij)m×m，参数μi为小正数，
Figure RE-GDA0002774958930000143
S2: According to F i (ξ, ζ, wi , u) defined in step S1, the dynamic inverse can be designed as
Figure RE-GDA0002774958930000142
Among them, B=(b ij ) m×m , the parameter μ i is a small positive number,
Figure RE-GDA0002774958930000143

S3：令

Figure RE-GDA0002774958930000144
在输出反馈的情况下，只有ξi，1可测量且
Figure RE-GDA0002774958930000145
未知，利用广义比例积分观测器来求解ξi和
Figure RE-GDA0002774958930000146
S3: order
Figure RE-GDA0002774958930000144
In the case of output feedback, only ξi ,1 is measurable and
Figure RE-GDA0002774958930000145
unknown, use a generalized proportional-integral observer to solve for ξ i and
Figure RE-GDA0002774958930000146

Figure RE-GDA0002774958930000147
Figure RE-GDA0002774958930000147

其中，参数

Figure RE-GDA0002774958930000148
满足
Figure RE-GDA0002774958930000149
为Hurwitz多项式，εi为一个小正数，且ε＝(ε1，…，εm)T；Among them, the parameter
Figure RE-GDA0002774958930000148
Satisfy
Figure RE-GDA0002774958930000149
is a Hurwitz polynomial, ε i is a small positive number, and ε=(ε 1 , ..., ε m ) T ;

S4：将步骤S3中的广义比例积分观测器和步骤S2中的动态逆结合起来，得到自抗扰控制器的输出反馈控制率，S4: Combine the generalized proportional-integral observer in step S3 and the dynamic inverse in step S2 to obtain the output feedback control rate of the active disturbance rejection controller,

Figure RE-GDA0002774958930000151
Figure RE-GDA0002774958930000151

其中，

Figure RE-GDA0002774958930000152
in,
Figure RE-GDA0002774958930000152

Figure RE-GDA0002774958930000153
Figure RE-GDA0002774958930000153

Figure RE-GDA0002774958930000154
Figure RE-GDA0002774958930000154

进一步的，将本发明中的多输入多输出非线性系统的线性自抗扰控制系统应用在具有多输入多输出特征的两自由度机械臂机电伺服控制装置中。Further, the linear active disturbance rejection control system of the multi-input multi-output nonlinear system in the present invention is applied to a two-degree-of-freedom mechanical arm electromechanical servo control device with multi-input and multi-output characteristics.

具体的，所述两自由度机械臂机电伺服控制装置包括基座3和安装在所述基座3上的第一减速器2，所述第一减速器2通过螺栓与所述基座3 连接，所述第一减速器2的输入轴与第一永磁同步电机1的输出轴也通过螺栓固定连接，所述第一减速器2的输出轴与第一机械臂4的首端通过轴销固定连接，所述第一机械臂4的末端通过螺栓连接有第二减速器6，所述第二减速器6的输入轴与第二永磁同步电机7的输出轴通过螺栓固定连接，所述第二减速器6的输出轴上通过轴销连接有第二机械臂5；Specifically, the two-degree-of-freedom mechanical arm electromechanical servo control device includes a base 3 and a first reducer 2 mounted on the base 3, and the first reducer 2 is connected to the base 3 through bolts , the input shaft of the first reducer 2 and the output shaft of the first permanent magnet synchronous motor 1 are also fixedly connected by bolts, and the output shaft of the first reducer 2 and the head end of the first mechanical arm 4 are connected by shaft pins Fixed connection, the end of the first mechanical arm 4 is connected with a second reducer 6 through bolts, and the input shaft of the second reducer 6 and the output shaft of the second permanent magnet synchronous motor 7 are fixedly connected through bolts. A second mechanical arm 5 is connected to the output shaft of the second reducer 6 through a shaft pin;

所述第一永磁同步电机1和所述第二永磁同步电机7的输入端与所述伺服驱动器的输出端对应连接。The input ends of the first permanent magnet synchronous motor 1 and the second permanent magnet synchronous motor 7 are correspondingly connected to the output end of the servo driver.

进一步的，所述两自由度机械臂机电伺服控制装置的动态方程为Further, the dynamic equation of the two-degree-of-freedom mechanical arm electromechanical servo control device is:

Figure RE-GDA0002774958930000161
其中，
Figure RE-GDA0002774958930000161
in,

M11＝a1+a2 cosθ2，M 11 =a 1 +a 2 cosθ 2 ,

Figure RE-GDA0002774958930000162
Figure RE-GDA0002774958930000162

M22＝a3，M 22 =a 3 ,

Figure RE-GDA0002774958930000163
Figure RE-GDA0002774958930000163

Figure RE-GDA0002774958930000164
Figure RE-GDA0002774958930000164

G1(θ)＝a4 sinθ1+a5 sin(θ1+θ2)，G 1 (θ)=a 4 sinθ 1 +a 5 sin(θ 1 +θ 2 ),

G2(θ)＝a5 sin(θ1+θ2)，G 2 (θ)=a 5 sin(θ 1 +θ 2 ),

Figure RE-GDA0002774958930000165
Figure RE-GDA0002774958930000165

a2＝m2l2l1，a 2 =m 2 l 2 l 1 ,

Figure RE-GDA0002774958930000166
Figure RE-GDA0002774958930000166

式中，l1，l2分别表示第一机械臂和第二机械臂的长度，θ1，θ2分别表示第一机械臂和第二机械臂的关节角，m1，m2分别表示第一机械臂和第二机械臂的质量，u1为第一机械臂的控制输入，u2为第二机械臂的控制输入， d1，d2分别表示第一机械臂和第二机械臂受到的外部扰动；In the formula, l 1 and l 2 represent the lengths of the first manipulator and the second manipulator respectively, θ 1 and θ 2 represent the joint angles of the first manipulator and the second manipulator respectively, m 1 and m 2 represent the first manipulator and the second manipulator respectively. The mass of the first manipulator and the second manipulator, u1 is the control input of the first manipulator, u2 is the control input of the second manipulator, d1, d2 represent the first manipulator and the second manipulator respectively. external disturbance;

令NG1＝N1+G1，NG2＝N2+G2，则两自由度机械臂机电伺服控制装置的动态方程可以变换为Let NG 1 =N 1 +G 1 , NG 2 =N 2 +G 2 , then the dynamic equation of the two-degree-of-freedom manipulator electromechanical servo control device can be transformed into

Figure RE-GDA0002774958930000167
Figure RE-GDA0002774958930000167

Figure RE-GDA0002774958930000171
Figure RE-GDA0002774958930000171

由于M11，M22随着θ2的变化而变化，因此两自由度机械臂机电伺服控制装置是控制增益不确定的多入多出的非线性系统，并且子系统之间存在着状态耦合和控制耦合。Since M 11 and M 22 change with the change of θ 2 , the electromechanical servo control device of the two-degree-of-freedom manipulator is a nonlinear system with multiple inputs and multiple outputs with uncertain control gains, and there are state coupling and Control coupling.

进一步，将本发明中的多输入多输出非线性系统的线性自抗扰控制系统应用到两自由度机械臂机电伺服控制装置中的具体操作包括以下步骤，Further, the specific operation of applying the linear active disturbance rejection control system of the multi-input multi-output nonlinear system in the present invention to the electromechanical servo control device of a two-degree-of-freedom manipulator includes the following steps:

S5：令

Figure RE-GDA0002774958930000172
S5: order
Figure RE-GDA0002774958930000172

Figure RE-GDA0002774958930000173
Figure RE-GDA0002774958930000173

Figure RE-GDA0002774958930000174
Figure RE-GDA0002774958930000174

Figure RE-GDA0002774958930000175
Figure RE-GDA0002774958930000175

则两自由度机械臂机电伺服控制装置的动态方程可以继续变换成Then the dynamic equation of the electromechanical servo control device of the two-degree-of-freedom manipulator can be transformed into

Figure RE-GDA0002774958930000176
Figure RE-GDA0002774958930000176

S6：令

Figure RE-GDA0002774958930000177
其中
Figure RE-GDA0002774958930000178
用x表示θ，则两自由度机械臂机电伺服控制装置的动态方程进一步变换为
Figure RE-GDA0002774958930000181
其中，
Figure RE-GDA0002774958930000182
表示控制装置的两个状态，w1表示第一机械臂受到d1，d2干扰的总和,w2表示第二机械臂受到d1，d2干扰的总和；S6: order
Figure RE-GDA0002774958930000177
in
Figure RE-GDA0002774958930000178
Using x to represent θ, the dynamic equation of the two-degree-of-freedom manipulator electromechanical servo control device is further transformed into
Figure RE-GDA0002774958930000181
in,
Figure RE-GDA0002774958930000182
Indicates the two states of the control device, w 1 represents the sum of the disturbances of d 1 and d 2 for the first manipulator, and w 2 represents the sum of the disturbances of d 1 and d 2 for the second manipulator;

S7：步骤S6中的两自由度机械臂机电伺服控制装置的动态方程的参考系统为

Figure RE-GDA0002774958930000183
其中，r1＝[r1，1 r1，2]T，r2＝[r2，1 r2，2]T，
Figure RE-GDA0002774958930000184
是利用五次项拟合生成的有界指令信号；S7: The reference system of the dynamic equation of the two-degree-of-freedom manipulator electromechanical servo control device in step S6 is:
Figure RE-GDA0002774958930000183
where, r 1 =[r 1,1 r 1,2 ] T , r 2 =[r 2,1 r 2,2 ] T ,
Figure RE-GDA0002774958930000184
is the bounded command signal generated by quintic fitting;

S8：将步骤S4中的自抗扰控制器设计成

Figure RE-GDA0002774958930000191
根据控制器的输出来控制第一永磁同步电机和第二永磁同步电机的旋转角度；S8: Design the active disturbance rejection controller in step S4 as
Figure RE-GDA0002774958930000191
controlling the rotation angles of the first permanent magnet synchronous motor and the second permanent magnet synchronous motor according to the output of the controller;

其中，

Figure RE-GDA0002774958930000192
分别表示
Figure RE-GDA0002774958930000193
的控制输出结果，
Figure RE-GDA0002774958930000194
分别表示
Figure RE-GDA0002774958930000195
的控制输出结果。in,
Figure RE-GDA0002774958930000192
Respectively
Figure RE-GDA0002774958930000193
The control output result of ,
Figure RE-GDA0002774958930000194
Respectively
Figure RE-GDA0002774958930000195
control output result.

通过上述过程，即可获得引入动态逆方法的多输入多输出严反馈非线性系统的线性自抗扰控制器来控制两自由度机械臂系统两个永磁同步电机的旋转角度。Through the above process, the linear active disturbance rejection controller of the multi-input multi-output strict feedback nonlinear system incorporating the dynamic inverse method can be obtained to control the rotation angles of the two permanent magnet synchronous motors of the two-degree-of-freedom manipulator system.

仿真实验：Simulation:

利用两自由度机械臂实验平台验证本发明中的线性自抗扰控制系统在轨迹跟踪控制中的应用效果，实验平台如附图2所示，由旋转电机、减速器、机械臂、GTHD伺服驱动器以及GT-800-SV运动控制卡组成。The application effect of the linear active disturbance rejection control system in the present invention in trajectory tracking control is verified by using a two-degree-of-freedom manipulator experimental platform. The experimental platform is shown in Figure 2. And GT-800-SV motion control card.

让第二机械臂末端跟踪一个字母R的轨迹，在第二机械臂末端增加 1kg负载，分别在3s和13s给θ1,θ2同时增加幅值为10V的阶跃信号，对比本发明中的控制系统(DILADRC)与传统LADRC在带有负载情况下的抗干扰能力，结果如附图3所示，其中，(a)为x方向跟踪轨迹对比结果， (b)为x方向跟踪误差对比结果，(c)为y方向跟踪轨迹对比结果，(d) 为y方向跟踪误差对比结果，(e)为R的轨迹跟踪情况对比结果。Let the end of the second manipulator track the trajectory of a letter R, add a load of 1kg to the end of the second manipulator, and add a step signal with an amplitude of 10V to θ 1 and θ 2 at 3s and 13s respectively. The anti-interference ability of the control system (DILADRC) and traditional LADRC under load, the results are shown in Figure 3, where (a) is the comparison result of the x-direction tracking trajectory, (b) is the x-direction tracking error comparison result , (c) is the comparison result of the y-direction tracking trajectory, (d) is the comparison result of the y-direction tracking error, and (e) is the comparison result of the trajectory tracking of R.

根据附图3中(a)(c)可知，在3s和13s时，无论是在x方向还是 y方向，传统LADRC控制下的系统受到干扰的影响导致跟踪位移偏离期望位移的值大于DILADRC，反应在R轨迹上的效果如图(e)所示，在受到干扰之后，DILADRC受到干扰的影响导致R轨迹的变形小于LADRC。根据附图3中(b)(d)可知，无论是在x还是y方向，由于受到干扰的作用，导致LADRC控制下系统在3s和13s的跟踪偏差明显大于 DILADRC。According to (a) and (c) in Figure 3, at 3s and 13s, no matter in the x-direction or the y-direction, the system under the traditional LADRC control is affected by the disturbance, causing the tracking displacement to deviate from the expected displacement value greater than DILADRC, and the response The effect on the R trajectory is shown in Fig. (e), after being disturbed, DILADRC is affected by the disturbance resulting in the deformation of the R trajectory smaller than that of LADRC. According to (b) and (d) in Fig. 3, whether in the x or y direction, the tracking deviation of the system under the control of LADRC at 3s and 13s is significantly larger than that of DILADRC due to the interference.

仿真实验结果验证了本发明设计的DILADRC的抗干扰性能比传统 LADRC好。The simulation experiment results verify that the anti-interference performance of the DILADRC designed by the present invention is better than that of the traditional LADRC.

以上显示和描述了本发明的基本原理、主要特征和本发明的优点。本行业的技术人员应该了解，本发明不受上述实施例的限制，上述实施例和说明书中描述的只是说明本发明的原理，在不脱离本发明精神和范围的前提下，本发明还会有各种变化和改进，这些变化和改进都落入要求保护的本发明范围内。本发明要求保护范围由所附的权利要求书及其等效物界定。The foregoing has shown and described the basic principles, main features and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited by the above-mentioned embodiments, and the descriptions in the above-mentioned embodiments and the description are only to illustrate the principle of the present invention. Without departing from the spirit and scope of the present invention, the present invention will have Various changes and modifications fall within the scope of the claimed invention. The claimed scope of the present invention is defined by the appended claims and their equivalents.

Claims (9)

1. The linear active disturbance rejection control system of the multi-input multi-output nonlinear system is characterized in that: the servo control system comprises a servo driver and a motion control card, wherein the output end of the servo driver is connected with a motor of the nonlinear system, and the input end of the servo driver is connected with the motion control card;
the motion control card comprises an active disturbance rejection controller and a control chip circuit of a nonlinear system, wherein the active disturbance rejection controller is written into the control chip circuit in a software form; a driving chip circuit is arranged in the servo driver, and the output end of the control chip circuit is correspondingly connected with the input end of the driving chip circuit so as to drive the driving chip circuit; the driving frequency adjusting signal output end and the driving half-bridge circuit adjusting signal output end of the driving chip circuit are respectively and correspondingly connected with the motor input end of the nonlinear system;
and the active disturbance rejection controller outputs a feedback control rate by adopting a method based on dynamic inversion.
2. The linear active disturbance rejection control system for a multiple-input multiple-output nonlinear system as claimed in claim 1, wherein: the dynamic equation of the multi-input multi-output nonlinear system is
Figure RE-FDA0002774958920000011
Wherein,
Figure RE-FDA0002774958920000012
is the status of each subsystem;
Figure RE-FDA0002774958920000013
control input of a non-linear system, omegax，ΩuAre respectively the set of ranges taken for the subsystem state x and the control input u, and Ωx，ΩuRespectively containing the origin thereof;
the measurable output of the nonlinear system is
Figure RE-FDA0002774958920000014
Figure RE-FDA0002774958920000021
Showing the external disturbance to the system;
Figure RE-FDA0002774958920000022
representing the overall system state, including each subsystem xiAnd the state in which the subsystems are coupled to each other, n ═ n1+n2+…nmFor the total order of the system,
Figure RE-FDA0002774958920000023
i ∈ (1, 2, …, m) represents the coupling state of the system, including the sum of external disturbances and internal uncertainties;
Figure RE-FDA0002774958920000024
i, j ∈ {1, 2, … m } represents the control gain of the system;
order to
Figure RE-FDA0002774958920000025
The dynamic equation of the multi-input multi-output strict feedback nonlinear system can be expressed as
Figure RE-FDA0002774958920000026
3. The linear active disturbance rejection control system for a multiple-input multiple-output nonlinear system in accordance with claim 2, wherein: let us assume a function phii，l(·)，i∈(1，…，m)，l∈(1，…，ni-1) at least niThe + p order is continuously differentiable, and phii，l(0) 0, then function
Figure RE-FDA0002774958920000027
Can represent
Figure RE-FDA0002774958920000028
Figure RE-FDA0002774958920000029
Wherein,
Figure RE-FDA00027749589200000210
Figure RE-FDA00027749589200000211
representing the dynamics of the known system in a way that,
Figure RE-FDA00027749589200000212
Figure RE-FDA00027749589200000213
representing unknown system dynamics and being local to arguments, state x of the system versus state x of each subsystemiIs locally applied to the body of the Lipschitz,
Figure RE-FDA00027749589200000214
then, according to the assumption, there is a differential homomorphic mapping
Figure RE-FDA0002774958920000031
Wherein,
Figure RE-FDA0002774958920000032
ξi(0)＝0，
Figure RE-FDA0002774958920000033
the differential homoembryo mapping is converted into an integral tandem system
Figure RE-FDA0002774958920000034
Wherein,
Figure RE-FDA0002774958920000035
showing the overall system state, including subsystems ζiAnd the state of the subsystems being coupled to each other, and
Figure RE-FDA0002774958920000036
4. the linear active disturbance rejection control system for a multiple-input multiple-output nonlinear system in accordance with claim 3, wherein: the target system tracked by the multi-input multi-output strict feedback nonlinear system is
Figure RE-FDA0002774958920000037
Wherein,
Figure RE-FDA0002774958920000038
Figure RE-FDA0002774958920000039
belongs to a tight set
Figure RE-FDA00027749589200000310
The target system is converted into an integral cascade system to obtain
Figure RE-FDA00027749589200000311
Wherein,
Figure RE-FDA00027749589200000312
i∈(1，…，m)，j∈(1，…，ni-1)；
is provided with
Figure RE-FDA0002774958920000041
Wherein i is 1, …, m, j is 2, …, niThe integral tandem system based on differential homoembryo mapping and the integral tandem system of the target system can be obtained
Figure RE-FDA0002774958920000042
Wherein,
Figure RE-FDA0002774958920000043
error gain matrix
Figure RE-FDA0002774958920000044
Satisfy the requirement of
Figure RE-FDA0002774958920000045
Is a Hurwitz matrix and is a Hurwitz matrix,
Figure RE-FDA0002774958920000046
5. the linear active disturbance rejection control system for a multiple-input multiple-output nonlinear system in accordance with claim 4, wherein: the specific operation of outputting the feedback control rate using the dynamic inversion-based method includes the following steps,
s1: definition of
Figure RE-FDA0002774958920000047
The sum of the state errors of the actual measured output and the expected output;
s2: according to F defined in step S1i(ξ，ζ，wiU), the dynamic inverse can be designed as
Figure RE-FDA0002774958920000048
Wherein B ═ Bij)m×mParameter μiIs small positive number, mu ═ mu (mu)1，…，μm)T，
Figure RE-FDA0002774958920000049
S3: order to
Figure RE-FDA00027749589200000410
In the case of output feedback, only xii，1Can measure and
Figure RE-FDA00027749589200000411
unknown, solving xi using a generalized proportional integral observeriAnd
Figure RE-FDA00027749589200000412
Figure RE-FDA0002774958920000051
wherein the parameters
Figure RE-FDA0002774958920000052
Satisfy the requirement of
Figure RE-FDA0002774958920000053
Is a Hurwitz polynomial, epsiloniIs a small positive number, and e ═ e1，…，εm)T；
S4: combining the generalized proportional-integral observer in step S3 and the dynamic inverse observer in step S2 to obtain the output feedback control rate of the active disturbance rejection controller,
Figure RE-FDA0002774958920000054
wherein,
Figure RE-FDA0002774958920000055
Figure RE-FDA0002774958920000056
Figure RE-FDA0002774958920000057
6. use of the linear active disturbance rejection control system of a multiple-input multiple-output nonlinear system as claimed in claim 5 in a two-degree-of-freedom robot electromechanical servo control device with multiple-input multiple-output characteristics.
7. The application of the linear active disturbance rejection control system of the multiple-input multiple-output nonlinear system according to claim 6, wherein the two-degree-of-freedom mechanical arm electromechanical servo control device comprises a base (3) and a first speed reducer (2) installed on the base (3), an input shaft of the first speed reducer (2) is fixedly connected with an output shaft of a first permanent magnet synchronous motor (1), an output shaft of the first speed reducer (2) is fixedly connected with a head end of a first mechanical arm (4), a tail end of the first mechanical arm (4) is connected with a second speed reducer (6), an input shaft of the second speed reducer (6) is fixedly connected with an output shaft of a second permanent magnet synchronous motor (7), and an output shaft of the second speed reducer (6) is connected with a second mechanical arm (5);
the input ends of the first permanent magnet synchronous motor (1) and the second permanent magnet synchronous motor (7) are correspondingly connected with the output end of the servo driver.
8. The use of the linear active disturbance rejection control system of a multiple-input multiple-output nonlinear system as claimed in claim 7, wherein the dynamic equation of said two-degree-of-freedom robot electromechanical servo control device is
Figure RE-FDA0002774958920000061
Wherein,
M11＝a1+a2cosθ2，
Figure RE-FDA0002774958920000062
M22＝a3，
Figure RE-FDA0002774958920000063
Figure RE-FDA0002774958920000064
G1(θ)＝a4sinθ1+a5sin(θ1+θ2)，
G2(θ)＝a5sin(θ1+θ2)，
Figure RE-FDA0002774958920000065
a2＝m2l2l1，
Figure RE-FDA0002774958920000066
in the formula I1，l2Respectively representing the lengths of the first and second arms, theta1，θ2Respectively representing joint angles, m, of the first and second robot arms1，m2Respectively representing the mass of the first and second arm, u1Is a control input of the first robot arm, u2For control input of the second robot arm, d1，d2Respectively representing the external disturbance to the first mechanical arm and the second mechanical arm;
let NG1＝N1+G1，NG2＝N2+G2The dynamic equation of the electromechanical servo control device of the two-degree-of-freedom mechanical arm can be transformed into
Figure RE-FDA0002774958920000071
Figure RE-FDA0002774958920000072
Due to M11，M22With theta2The two-degree-of-freedom mechanical arm electromechanical servo control device is a multi-input multi-output nonlinear system with uncertain control gain, and state coupling and control coupling exist between subsystems.
9. The use of a linear active disturbance rejection control system for a multiple input multiple output nonlinear system as claimed in claim 8, wherein the specific operation of said use comprises the steps of,
s5: order to
Figure RE-FDA0002774958920000073
Figure RE-FDA0002774958920000074
Figure RE-FDA0002774958920000075
Figure RE-FDA0002774958920000081
The dynamic equation of the electromechanical servo control device of the two-degree-of-freedom mechanical arm can be continuously transformed into
Figure RE-FDA0002774958920000082
S6: order to
Figure RE-FDA0002774958920000083
Wherein
Figure RE-FDA0002774958920000084
The x represents theta, and the dynamic equation of the electromechanical servo control device of the two-freedom mechanical arm is further transformed into
Figure RE-FDA0002774958920000085
Wherein,
Figure RE-FDA0002774958920000086
representing two states of the control device, w1Indicating that the first robot arm is subjected to d1，d2Sum of interference, w2Indicating that the second robot arm is subjected to d1，d2The sum of the interferences;
s7: the reference system of the dynamic equation of the two-DOF mechanical arm electromechanical servo control device in the step S6 is
Figure RE-FDA0002774958920000087
Wherein r is1＝[r1，1 r1，2]T，r2＝[r2，1 r2，2]T，
Figure RE-FDA0002774958920000088
Is a bounded command signal generated using a quintic fit;
s8: the active disturbance rejection controller in step S4 is designed to
Figure RE-FDA0002774958920000091
Controlling the rotation angles of the first permanent magnet synchronous motor and the second permanent magnet synchronous motor according to the output of the controller;
wherein,
Figure RE-FDA0002774958920000092
respectively represent x1，
Figure RE-FDA0002774958920000093
The result is outputted by the control of (1),
Figure RE-FDA0002774958920000094
respectively represent x2，
Figure RE-FDA0002774958920000095
And (4) outputting the result.
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