CN112214038A - Linear active disturbance rejection control system of multi-input multi-output nonlinear system and application thereof - Google Patents

Linear active disturbance rejection control system of multi-input multi-output nonlinear system and application thereof 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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output
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disturbance rejection
active disturbance
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CN112214038B (en
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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

The invention discloses a linear active-disturbance-rejection control system of a multi-input multi-output nonlinear system and application thereof, wherein 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 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; the output end of the control chip circuit is correspondingly connected with the input end of the driving chip circuit to realize the control of the motor; and the active disturbance rejection controller outputs a feedback control rate by adopting a method based on dynamic inversion. The linear active disturbance rejection control system utilizes dynamic inverse to solve the control rate to compensate the total disturbance, thereby solving the problem of instability of the controller caused by uncertainty of the control gain of the system.

Description

Linear active disturbance rejection control system of multi-input multi-output nonlinear system and application thereof
Technical Field
The invention relates to the technical field of analysis and design of controllers of electromechanical servo systems, in particular to a linear active disturbance rejection control system of a multi-input multi-output nonlinear system and application thereof.
Background
In many engineering applications, it is of primary interest for a control target (robot arm, ship, vehicle, etc.) to follow a certain desired path, and of secondary interest for the speed requirements during operation. The maneuvering control problem is generally composed of two parts, a geometric task and a dynamic task, the geometric task is that a controlled object reaches and runs along a desired path (a function of a path variable δ). The dynamic task is an additional dynamic index, such as time, speed, acceleration and the like, which is also satisfied when the vehicle runs along a desired path.
In the design of the existing multi-input multi-output strict feedback nonlinear control system, because the control gain of the system is constantly changed, the parameters of the control gain nominal value in the traditional linear active disturbance rejection controller are not easy to select, the instability of system control can be caused, and the anti-interference capability is weak.
Disclosure of Invention
Aiming at the existing problems, the invention aims to provide a linear active disturbance rejection control system of a multi-input multi-output nonlinear system and application thereof.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows:
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.
Further, the dynamic equation of the multi-input multi-output nonlinear system is
Figure RE-GDA0002774958930000021
Wherein the content of the first and second substances,
Figure RE-GDA0002774958930000022
is the status of each subsystem;
Figure RE-GDA0002774958930000023
Figure RE-GDA0002774958930000024
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-GDA0002774958930000025
Figure RE-GDA0002774958930000026
Showing the external disturbance to the system;
Figure RE-GDA0002774958930000027
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-GDA0002774958930000028
i ∈ (1, 2, …, m) represents the coupling 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;
order to
Figure RE-GDA00027749589300000210
The dynamic equation of the multi-input multi-output strict feedback nonlinear system can be expressed as
Figure RE-GDA0002774958930000031
Further, assume the function φi，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-GDA0002774958930000032
Can represent
Figure RE-GDA0002774958930000033
Figure RE-GDA0002774958930000034
Wherein the content of the first and second substances,
Figure RE-GDA0002774958930000035
representing the dynamics of the known system in a way that,
Figure RE-GDA0002774958930000036
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-GDA0002774958930000037
then, according to the assumption, there is a differential homomorphic mapping
Figure RE-GDA0002774958930000038
Wherein the content of the first and second substances,
Figure RE-GDA0002774958930000039
ξi(0)＝0，
Figure RE-GDA00027749589300000310
the differential homoembryo mapping is converted into an integral tandem system
Figure RE-GDA00027749589300000311
Wherein the content of the first and second substances,
Figure RE-GDA00027749589300000312
representing the overall system state, including the sub-systems xiiAnd the state of the subsystems being coupled to each other, and
Figure RE-GDA0002774958930000041
further, the target system tracked by the multi-input multi-output strict feedback nonlinear system is
Figure RE-GDA0002774958930000042
Wherein the content of the first and second substances,
Figure RE-GDA0002774958930000043
belongs to a tight set
Figure RE-GDA0002774958930000044
The target system is converted into an integral cascade system to obtain
Figure RE-GDA0002774958930000045
Wherein the content of the first and second substances,
Figure RE-GDA0002774958930000046
is provided with
Figure RE-GDA0002774958930000047
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-GDA0002774958930000048
Wherein the content of the first and second substances,
Figure RE-GDA0002774958930000049
error gain matrix
Figure RE-GDA00027749589300000410
Satisfy the requirement of
Figure RE-GDA00027749589300000411
Is a Hurwitz matrix and is a Hurwitz matrix,
Figure RE-GDA00027749589300000412
further, the specific operation of outputting the feedback control rate using the dynamic inverse-based method includes the steps of,
s1: definition of
Figure RE-GDA0002774958930000051
For actual measurementThe sum of the state errors of the output and the desired output;
s2: according to F defined in step S1i(ξ，ζ，wiU), the dynamic inverse can be designed as
Figure RE-GDA0002774958930000052
Wherein B ═ Bij)m×mParameter μiIs small positive number, mu ═ mu (mu)1，…，μm)T，
Figure RE-GDA0002774958930000053
S3: order to
Figure RE-GDA0002774958930000054
In the case of output feedback, only xii，1Can measure and
Figure RE-GDA0002774958930000055
unknown, solving xi using a generalized proportional integral observeriAnd
Figure RE-GDA0002774958930000056
Figure RE-GDA0002774958930000057
wherein the parameters
Figure RE-GDA0002774958930000058
Satisfy the requirement of
Figure RE-GDA0002774958930000059
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-GDA0002774958930000061
wherein the content of the first and second substances,
Figure RE-GDA0002774958930000062
Figure RE-GDA0002774958930000063
Figure RE-GDA0002774958930000064
further, the linear active disturbance rejection control system of the multi-input multi-output nonlinear system is applied to the two-degree-of-freedom mechanical arm electromechanical servo control device with the multi-input multi-output characteristic.
Further, the two-degree-of-freedom mechanical arm electromechanical servo control device comprises a base and a first speed reducer installed on the base, wherein an input shaft of the first speed reducer is fixedly connected with an output shaft of a first permanent magnet synchronous motor, an output shaft of the first speed reducer is fixedly connected with the head end of a first mechanical arm, the tail end of the first mechanical arm is connected with a second speed reducer, an input shaft of the second speed reducer is fixedly connected with an output shaft of a second permanent magnet synchronous motor, and an output shaft of the second speed reducer is connected with a second mechanical arm;
and 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.
Further, the dynamic equation of the electromechanical servo control device of the two-degree-of-freedom mechanical arm is
Figure RE-GDA0002774958930000065
Wherein the content of the first and second substances,
M11＝a1+a2 cosθ2，
Figure RE-GDA0002774958930000071
M22＝a3，
Figure RE-GDA0002774958930000072
Figure RE-GDA0002774958930000073
G1(θ)＝a4 sinθ1+a5 sin(θ1+θ2)，
G2(θ)＝a5 sin(θ1+θ2)，
Figure RE-GDA0002774958930000074
a2＝m2l2l1，
Figure RE-GDA0002774958930000075
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-GDA0002774958930000076
Figure RE-GDA0002774958930000077
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.
Further, the specific operation of the application includes the steps of,
s5: order to
Figure RE-GDA0002774958930000081
Figure RE-GDA0002774958930000082
Figure RE-GDA0002774958930000083
Figure RE-GDA0002774958930000084
The dynamic equation of the electromechanical servo control device of the two-degree-of-freedom mechanical arm can be continuously transformed into
Figure RE-GDA0002774958930000085
S6: order to
Figure RE-GDA0002774958930000086
Wherein
Figure RE-GDA0002774958930000087
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-GDA0002774958930000088
Wherein the content of the first and second substances,
Figure RE-GDA0002774958930000089
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-GDA0002774958930000091
Wherein r is1＝[r1，1 r1，2]T，r2＝[r2，1 r2，2]T，
Figure RE-GDA0002774958930000092
Is a bounded command signal generated using a quintic fit;
s8: the active disturbance rejection controller in step S4 is designed to
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;
wherein the content of the first and second substances,
Figure RE-GDA0002774958930000094
respectively represent
Figure RE-GDA0002774958930000095
The result is outputted by the control of (1),
Figure RE-GDA0002774958930000096
respectively represent
Figure RE-GDA0002774958930000097
And (4) outputting the result.
The invention has the beneficial effects that:
the linear active disturbance rejection control system adopts a controller which outputs a feedback control rate based on a dynamic inverse method, estimates the state and the total disturbance of the system through a generalized proportional-integral observer, and then solves the control rate by utilizing the dynamic inverse to compensate the total disturbance, thereby solving the problem of instability of the controller caused by uncertainty of system control gain, obviously improving the track tracking motion effect of a nonlinear system, hardly causing influence on the motion effect of the system due to factors such as parameter change, system model uncertainty and the like, and having strong disturbance rejection capability in the motion process of the system.
Drawings
FIG. 1 is a schematic structural diagram of an electromechanical servo control device of a two-degree-of-freedom robot arm according to the present invention.
FIG. 2 is a schematic structural diagram of a two-degree-of-freedom mechanical arm experimental platform in a simulation experiment of the present invention.
Fig. 3 is an experimental result of the anti-interference capability of different systems in the simulation experiment of the present invention.
Wherein: 1-a first permanent magnet synchronous motor, 2-a first speed reducer, 3-a base, 4-a first mechanical arm, 5-a second mechanical arm, 6-a second speed reducer and 7-a second permanent magnet synchronous motor.
Detailed Description
In order to make those skilled in the art better understand the technical solution of the present invention, the following further describes the technical solution of the present invention with reference to the drawings and the embodiments.
The linear active disturbance rejection control system of the multi-input multi-output nonlinear 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.
Specifically, the dynamic equation of the multi-input multi-output nonlinear system is
Figure RE-GDA0002774958930000111
Wherein the content of the first and second substances,
Figure RE-GDA0002774958930000112
is the status of each subsystem;
Figure RE-GDA0002774958930000113
Figure RE-GDA0002774958930000114
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-GDA0002774958930000115
Figure RE-GDA0002774958930000116
Showing the external disturbance to the system;
Figure RE-GDA0002774958930000117
representing the overall system state, including each subsystem xiState of (1)And the state of the subsystems coupled with each other, n ═ n1+n2+…nmFor the total order of the system,
Figure RE-GDA0002774958930000118
i ∈ (1, 2, …, m) represents the coupling 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;
order to
Figure RE-GDA00027749589300001110
The dynamic equation of the multi-input multi-output strict feedback nonlinear system can be expressed as
Figure RE-GDA00027749589300001111
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-GDA00027749589300001112
Can represent
Figure RE-GDA00027749589300001113
Figure RE-GDA0002774958930000121
Wherein the content of the first and second substances,
Figure RE-GDA0002774958930000122
representing the dynamics of the known system in a way that,
Figure RE-GDA0002774958930000123
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-GDA0002774958930000124
this assumption ensures that the origin is the equilibrium point of the open loop system if
Figure RE-GDA0002774958930000125
Is completely unknown, then
Figure RE-GDA0002774958930000126
According to this assumption, there is a differential homomorphic mapping
Figure RE-GDA0002774958930000127
Wherein the content of the first and second substances,
Figure RE-GDA0002774958930000128
ξi(0)＝0，
Figure RE-GDA0002774958930000129
the differential homoembryo mapping is converted into an integral tandem system
Figure RE-GDA00027749589300001210
Wherein the content of the first and second substances,
Figure RE-GDA00027749589300001211
representing the overall system state, including the sub-systems xiiAnd the state of the subsystems being coupled to each other, and
Figure RE-GDA00027749589300001212
the design goal of the active disturbance rejection controller in the 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.
The target system tracked by the multi-input multi-output strict feedback nonlinear system is
Figure RE-GDA0002774958930000131
Wherein the content of the first and second substances,
Figure RE-GDA0002774958930000132
Figure RE-GDA0002774958930000133
belongs to a tight set
Figure RE-GDA0002774958930000134
The target system is converted into an integral cascade system to obtain
Figure RE-GDA0002774958930000135
Wherein the content of the first and second substances,
Figure RE-GDA0002774958930000136
is provided with
Figure RE-GDA0002774958930000137
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-GDA0002774958930000138
Wherein the content of the first and second substances,
Figure RE-GDA0002774958930000139
error gain matrix
Figure RE-GDA00027749589300001310
Satisfy the requirement of
Figure RE-GDA00027749589300001311
Is a Hurwitz matrix and is a Hurwitz matrix,
Figure RE-GDA00027749589300001312
the control gain b of the nonlinear system can be known from the dynamic equation of the MIMO nonlinear systemij(t) is time-varying and,thus when designing a conventional LADRC for this system, bijNominal value b of (t)0The method is not easy to select, so the invention aims to design a linear active disturbance rejection controller introducing dynamic inverse for a multi-input multi-output nonlinear uncertain strict feedback system, can estimate and compensate the total disturbance consisting of external disturbance and internal uncertainty of the system, and does not relate to b0The selection problem of the value avoids bijThe uncertainty in (t) has an effect on the stability of the closed loop system.
The specific operation of outputting the feedback control rate using the dynamic inversion-based method includes the following steps,
s1: definition of
Figure RE-GDA0002774958930000141
A sum of state errors for 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-GDA0002774958930000142
Wherein B ═ Bij)m×mParameter μiThe number of the positive lines is small and positive,
Figure RE-GDA0002774958930000143
s3: order to
Figure RE-GDA0002774958930000144
In the case of output feedback, only xii，1Can measure and
Figure RE-GDA0002774958930000145
unknown, solving xi using a generalized proportional integral observeriAnd
Figure RE-GDA0002774958930000146
Figure RE-GDA0002774958930000147
wherein the parameters
Figure RE-GDA0002774958930000148
Satisfy the requirement of
Figure RE-GDA0002774958930000149
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-GDA0002774958930000151
wherein the content of the first and second substances,
Figure RE-GDA0002774958930000152
Figure RE-GDA0002774958930000153
Figure RE-GDA0002774958930000154
furthermore, the linear active disturbance rejection control system of the multi-input multi-output nonlinear system is applied to the two-degree-of-freedom mechanical arm electromechanical servo control device with the multi-input multi-output characteristic.
Specifically, 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, wherein the first speed reducer 2 is connected with the base 3 through a bolt, an input shaft of the first speed reducer 2 is fixedly connected with an output shaft of a first permanent magnet synchronous motor 1 through a bolt, an output shaft of the first speed reducer 2 is fixedly connected with the head end of a first mechanical arm 4 through a shaft pin, the tail end of the first mechanical arm 4 is connected with a second speed reducer 6 through a bolt, an input shaft of the second speed reducer 6 is fixedly connected with an output shaft of a second permanent magnet synchronous motor 7 through a bolt, and an output shaft of the second speed reducer 6 is connected with a second mechanical arm 5 through a shaft pin;
and 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.
Further, the dynamic equation of the electromechanical servo control device of the two-degree-of-freedom mechanical arm is
Figure RE-GDA0002774958930000161
Wherein the content of the first and second substances,
M11＝a1+a2 cosθ2，
Figure RE-GDA0002774958930000162
M22＝a3，
Figure RE-GDA0002774958930000163
Figure RE-GDA0002774958930000164
G1(θ)＝a4 sinθ1+a5 sin(θ1+θ2)，
G2(θ)＝a5 sin(θ1+θ2)，
Figure RE-GDA0002774958930000165
a2＝m2l2l1，
Figure RE-GDA0002774958930000166
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-GDA0002774958930000167
Figure RE-GDA0002774958930000171
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.
Further, the specific operation of applying the linear active disturbance rejection control system of the multiple-input multiple-output nonlinear system in the two-degree-of-freedom mechanical arm electromechanical servo control device of the present invention comprises the following steps,
s5: order to
Figure RE-GDA0002774958930000172
Figure RE-GDA0002774958930000173
Figure RE-GDA0002774958930000174
Figure RE-GDA0002774958930000175
The dynamic equation of the electromechanical servo control device of the two-degree-of-freedom mechanical arm can be continuously transformed into
Figure RE-GDA0002774958930000176
S6: order to
Figure RE-GDA0002774958930000177
Wherein
Figure RE-GDA0002774958930000178
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-GDA0002774958930000181
Wherein the content of the first and second substances,
Figure RE-GDA0002774958930000182
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-GDA0002774958930000183
Wherein r is1＝[r1，1 r1，2]T，r2＝[r2，1 r2，2]T，
Figure RE-GDA0002774958930000184
Is a bounded command signal generated using a quintic fit;
s8: the active disturbance rejection controller in step S4 is designed to
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;
wherein the content of the first and second substances,
Figure RE-GDA0002774958930000192
respectively represent
Figure RE-GDA0002774958930000193
The result is outputted by the control of (1),
Figure RE-GDA0002774958930000194
respectively represent
Figure RE-GDA0002774958930000195
And (4) outputting the result.
Through the process, the linear active disturbance rejection controller of the multi-input multi-output strict feedback nonlinear system, which introduces a dynamic inverse method, can be obtained to control the rotation angles of the two permanent magnet synchronous motors of the two-degree-of-freedom mechanical arm system.
Simulation experiment:
the application effect of the linear active disturbance rejection control system in the invention in the track tracking control is verified by utilizing a two-degree-of-freedom mechanical arm experimental platform, and the experimental platform is shown in figure 2 and consists of a rotating motor, a speed reducer, a mechanical arm, a GTHD servo driver and a GT-800-SV motion control card.
Let the end of the second robot follow the trajectory of a letter R, add 1kg of load to the end of the second robot, give θ at 3s and 13s, respectively1,θ2Simultaneously increasing step signal with amplitude of 10V, comparingThe control system (dilaprc) of the present invention and the conventional lardrc have anti-interference capability under a load condition, and the result is shown in fig. 3, wherein (a) is a result of comparing the tracking trajectory in the x direction, (b) is a result of comparing the tracking error in the x direction, (c) is a result of comparing the tracking trajectory in the y direction, (d) is a result of comparing the tracking error in the y direction, and (e) is a result of comparing the tracking condition of R.
As can be seen from fig. 3 (a) (c), in 3s and 13s, whether in the x direction or the y direction, the system under the control of the conventional LADRC is affected by the disturbance to cause the tracking displacement to deviate from the desired displacement by a value larger than the dilackc, and the effect reflected on the R track is as shown in (e), and after the disturbance, the dilackc is affected by the disturbance to cause the distortion of the R track to be smaller than the LADRC. As can be seen from fig. 3 (b) (d), the tracking deviation of the system under the control of the laldrc is significantly larger at 3s and 13s than the dildrc due to the interference in both the x and y directions.
Simulation experiment results verify that the DILADRC designed by the invention has better anti-interference performance than the traditional LADRC.
The foregoing shows and describes the general principles, essential features, and advantages of the invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, which are described in the specification and illustrated only to illustrate the principle of the present invention, but that various changes and modifications may be made therein without departing from the spirit and scope of the present invention, which fall within the scope of the invention as claimed. The scope of the invention is defined by the appended claims and equivalents thereof.

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 the content of the first and second substances,
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 the content of the first and second substances,
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 the content of the first and second substances,
Figure RE-FDA0002774958920000032
ξi(0)＝0，
Figure RE-FDA0002774958920000033
the differential homoembryo mapping is converted into an integral tandem system
Figure RE-FDA0002774958920000034
Wherein the content of the first and second substances,
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 the content of the first and second substances,
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 the content of the first and second substances,
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 the content of the first and second substances,
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 the content of the first and second substances,
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 the content of the first and second substances,
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 the content of the first and second substances,
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 the content of the first and second substances,
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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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113406971A (en) * 2021-07-13 2021-09-17 天津大学 Distributed unmanned aerial vehicle queue and dynamic obstacle avoidance control method

Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20030199997A1 (en) * 2002-04-18 2003-10-23 Zhiqiang Gao Scaling and parameterizing a controller
CN102799113A (en) * 2012-08-01 2012-11-28 中国电子科技集团公司第十研究所 Method for controlling servo system of active disturbance rejection control technology
CN103777641A (en) * 2014-02-19 2014-05-07 北京理工大学 Compound active-disturbances-rejection control method of tracking control over aircraft
CN104698845A (en) * 2015-02-10 2015-06-10 天津大学 Radar antenna servo tracking method based on active-disturbance-rejection controller and radar antenna servo tracking system
CN109507890A (en) * 2019-01-09 2019-03-22 中南大学 A kind of unmanned plane dynamic inverse generalized predictive controller based on ESO
CN110687870A (en) * 2019-08-28 2020-01-14 济南大学 Mechanical arm tracking controller and system based on nonlinear extended state observer

Patent Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20030199997A1 (en) * 2002-04-18 2003-10-23 Zhiqiang Gao Scaling and parameterizing a controller
CN102799113A (en) * 2012-08-01 2012-11-28 中国电子科技集团公司第十研究所 Method for controlling servo system of active disturbance rejection control technology
CN103777641A (en) * 2014-02-19 2014-05-07 北京理工大学 Compound active-disturbances-rejection control method of tracking control over aircraft
CN104698845A (en) * 2015-02-10 2015-06-10 天津大学 Radar antenna servo tracking method based on active-disturbance-rejection controller and radar antenna servo tracking system
CN109507890A (en) * 2019-01-09 2019-03-22 中南大学 A kind of unmanned plane dynamic inverse generalized predictive controller based on ESO
CN110687870A (en) * 2019-08-28 2020-01-14 济南大学 Mechanical arm tracking controller and system based on nonlinear extended state observer

Non-Patent Citations (6)

* Cited by examiner, † Cited by third party
Title
HUANG, ZHIJIAN, ET AL.: "A Data-driven Online ADP Control Method for Nonlinear System Based on Policy Iteration and Nonlinear MIMO Decoupling ADRC", 《NEUROCOMPUTING》 *
J. VERBERNE, ET AL.: "Robust Control Architecture for Wind Rejection in Quadrotors", 《2019 INTERNATIONAL CONFERENCE ON UNMANNED AIRCRAFT SYSTEMS (ICUAS)》 *
Z. CHEN, ET AL.: "Linear Active Disturbance Rejection Control for Nonaffine Strict-Feedback Nonlinear Systems", 《IEEE ACCESS》 *
吴超 等: "基于LADRC的无人直升机轨迹跟踪", 《航空学报》 *
徐李佳: "基于全通道耦合特征模型的高超飞行器控制研究", 《空间控制技术与应用》 *
陈志翔 等: "自适应扩张状态观测器收敛性分析与应用", 《控制理论与应用》 *

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113406971A (en) * 2021-07-13 2021-09-17 天津大学 Distributed unmanned aerial vehicle queue and dynamic obstacle avoidance control method

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