CN112214038B - 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 PDFInfo
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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
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 importance that the control target (robot arm, ship, vehicle, etc.) follows a certain desired path, with secondary concern about 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 multiple input multiple output non-lineThe dynamic equation of the sexual system is
Wherein,
is the status of each subsystem;
control input of a non-linear system, omega x ，Ω u Are respectively the set of ranges taken for the subsystem state x and the control input u, and Ω x ，Ω u Respectively containing their origin points;
the measurable output of the nonlinear system is
Showing the external disturbance to the system;
representing the overall system state, including each subsystem x i And the state in which the subsystems are coupled to each other, n ═ n 1 +n 2 +…n m For the total order of the system,
i ∈ (1, 2, …, m) represents the coupling state of the system, including the sum of external disturbances and internal uncertainties;
i, j ∈ {1, 2, … m } represents the control gain of the system;
order to
The dynamic equation of the multi-input multi-output strict feedback nonlinear system can be expressed as
Further, assume the function φ i，l (·)，i∈(1，…，m)，l∈(1，…，n i -1) at least n i The + p order is continuously differentiable, and phi i，l (0) 0, then the function
Can represent
Wherein,
representing the dynamics of the known system in a manner known,
representing unknown system dynamics and being local to arguments, state x of the system versus state x of each subsystem i Is locally applied to the body of the Lipschitz,
then, according to the assumption, there is a differential homomorphic mapping
the differential homoembryo mapping is converted into an integral tandem system
further, the target system tracked by the multi-input multi-output strict feedback nonlinear system is
Wherein,
belongs to a tight set
The target system is converted into an integral cascade system to obtain
Wherein,
is provided with
Wherein, i is 1, …, m, j is 2, …, n i Integral tandem system based on differential homoembryo mapping and integral tandem system of target systemUnified availability
Wherein,
error gain matrix
Satisfy the requirement of
Is a Hurwitz matrix and is a Hurwitz matrix,
further, the specific operation of outputting the feedback control rate using the dynamic inverse-based method includes the steps of,
s1: definition of
The sum of the state errors of the actual measured output and the expected output;
s2: according to F defined in step S1 i (ξ，ζ，w i U), the dynamic inverse can be designed as
Wherein B ═ B ij ) m×m Parameter μ i Is a small positive number, mu ═ mu 1 ，…，μ m ) T ，
S3: order to
In the case of output feedback, only xi i，1 Can measure and
unknown, solving xi by using generalized proportional-integral observer i And
wherein the parameters
Satisfy the requirements of
Is a Hurwitz polynomial, epsilon i Is a small positive number, and e ═ e 1 ，…，ε m ) 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,
wherein,
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
Wherein,
M 11 ＝a 1 +a 2 cosθ 2 ，
M 22 ＝a 3 ，
G 1 (θ)＝a 4 sinθ 1 +a 5 sin(θ 1 +θ 2 )，
G 2 (θ)＝a 5 sin(θ 1 +θ 2 )，
a 2 ＝m 2 l 2 l 1 ，
in the formula I 1 ，l 2 Respectively representing the lengths of the first and second arms, theta 1 ，θ 2 Respectively representing joint angles, m, of the first and second arms 1 ，m 2 Respectively representing the mass of the first and second arm, u 1 Is a control input of the first robot arm, u 2 For control input of the second robot arm, d 1 ，d 2 Respectively representing the external disturbance to the first mechanical arm and the second mechanical arm;
let NG 1 ＝N 1 +G 1 ，NG 2 ＝N 2 +G 2 The dynamic equation of the electromechanical servo control device of the two-degree-of-freedom mechanical arm can be transformed into
Due to M 11 ，M 22 With theta 2 The 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
The dynamic equation of the electromechanical servo control device of the two-degree-of-freedom mechanical arm can be continuously transformed into
S6: order to
Wherein
The x represents theta, and the dynamic equation of the electromechanical servo control device of the two-freedom mechanical arm is further transformed into
Wherein,
two states representing control means, w 1 Indicating that the first robot arm is subjected to d 1 ，d 2 Sum of interference, w 2 Indicating that the second robot arm is subjected to d 1 ，d 2 The 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
Wherein r is 1 ＝[r 1，1 r 1，2 ] T ，r 2 ＝[r 2，1 r 2，2 ] T ，
Is a bounded command signal generated using a quintic fit;
s8: the active disturbance rejection controller in step S4 is designed to
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,
respectively represent
The result is outputted by the control of (1),
respectively represent
The control of (2) outputs the result.
The beneficial effects of the invention are:
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
Wherein,
is the status of each subsystem;
control input of a non-linear system, omega x ，Ω u Are respectively the set of ranges taken for the subsystem state x and the control input u, and Ω x ，Ω u Respectively containing the origin thereof;
the measurable output of the nonlinear system is
Showing the external disturbance to the system;
representing the overall system state, including each subsystem x i And the state in which the subsystems are coupled to each other, n ═ n 1 +n 2 +…n m For the total order of the system,
i ∈ (1, 2, …, m) represents the coupling state of the system, including the sum of external disturbances and internal uncertainties;
i, j ∈ {1, 2, … m } represents the control gain of the system;
order to
The dynamic equation of the multi-input multi-output strict feedback nonlinear system can be expressed as
Let us assume a function phi i，l (·)，i∈(1，…，m)，l∈(1，…，n i -1) at least n i The + p order is continuously differentiable, and phi i，l (0) 0, then function
Can represent
Wherein,
representing the dynamics of the known system in a way that,
representing unknown system dynamics and being local to an argument, state x of the system versus state x of each subsystem i Is of the local type of Lipschitz,
this assumption ensures that the origin is the equilibrium point of the open loop system if
Is completely unknown, then
According to this assumption, there is a differential homomorphic mapping
Wherein,
ξ i (0)＝0，
the differential homoembryo mapping is converted into an integral tandem system
Wherein,
representing the overall system state, including the sub-systems xi i And the state of the subsystems being coupled to each other, and
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
Wherein,
belongs to a tight set
The target system is converted into an integral cascade system to obtain
Wherein,
is provided with
Wherein, i is 1, …, m, j is 2, …, n i The integral tandem system based on differential homoembryo mapping and the integral tandem system of the target system can be obtained
Wherein,
error gain matrix
Satisfy the requirement of
Is a Hurwitz matrix and is a Hurwitz matrix,
the control gain b of the nonlinear system can be known from the dynamic equation of the multi-input multi-output nonlinear system ij (t) is time-varying, so when designing a conventional LADRC for the system, b ij Nominal value b of (t) 0 The 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 b 0 Value selection problem, avoid b ij The 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
A sum of state errors for the actual measured output and the expected output … …;
s2: according to F defined in step S1 i (ξ，ζ，w i U), the dynamic inverse can be designed as
Wherein B ═ B ij ) m×m Parameter μ i The number of the positive lines is small and positive,
s3: order to
In the case of output feedback, only xi i，1 Can measure and
unknown, solving xi using a generalized proportional integral observer i And
wherein the parameters
Satisfy the requirement of
Is a Hurwitz polynomial, epsilon i Is a small positive number, and e ═ e 1 ，…，ε m ) 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,
wherein,
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
M 11 ＝a 1 +a 2 cosθ 2 ，
M 22 ＝a 3 ，
G 1 (θ)＝a 4 sinθ 1 +a 5 sin(θ 1 +θ 2 )，
G 2 (θ)＝a 5 sin(θ 1 +θ 2 )，
a 2 ＝m 2 l 2 l 1 ，
in the formula I 1 ，l 2 Respectively representing the lengths of the first and second arms, theta 1 ，θ 2 Respectively representing joint angles, m, of the first and second robot arms 1 ，m 2 Respectively representing the mass of the first and second arm, u 1 Is a control input of the first robot arm, u 2 For control input of the second robot arm, d 1 ，d 2 Respectively representing external disturbance to the first mechanical arm and the second mechanical arm;
let NG 1 ＝N 1 +G 1 ，NG 2 ＝N 2 +G 2 Electromechanical servo control of mechanical arm with two degrees of freedomThe dynamic equation of the device can be transformed into
Due to M 11 ，M 22 With theta 2 The 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
The dynamic equation of the electromechanical servo control device of the two-degree-of-freedom mechanical arm can be continuously transformed into
S6: order to
Wherein
The x represents theta, and the dynamic equation of the electromechanical servo control device of the two-degree-of-freedom mechanical arm is further converted into a dynamic equation
Wherein,
representing two states of the control device, w 1 Indicating that the first robot arm is subjected to d 1 ，d 2 Sum of interference, w 2 Indicating that the second robot arm is subjected to d 1 ，d 2 The sum of the interferences;
s7: the reference system of the dynamic equation of the electromechanical servo control device of the two-degree-of-freedom mechanical arm in the step S6 is
Wherein r is 1 ＝[r 1，1 r 1，2 ] T ，r 2 ＝[r 2，1 r 2，2 ] T ，
Is a bounded command signal generated using a quintic fit;
s8: the active disturbance rejection controller in step S4 is designed
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,
respectively represent
The result is outputted by the control of (1),
respectively represent
The control of (2) outputs 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 load to the end of the second robot, give θ at 3s and 13s, respectively 1 ,θ 2 Meanwhile, a step signal with the amplitude of 10V is added, and the anti-jamming capability of a control system (DILADRC) in the invention is compared with that of a traditional LADRC under the condition of load, and the result is shown in figure 3, wherein (a) is a tracking track comparison result in the x direction, (b) is a tracking error comparison result in the x direction, (c) is a tracking track comparison result in the y direction, (d) is a tracking error comparison result in the y direction, and (e) is a track tracking condition comparison result in the R direction.
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 (5)
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;
the active disturbance rejection controller outputs a feedback control rate by adopting a method based on dynamic inversion;
the dynamic equation of the multi-input multi-output nonlinear system is
Wherein,
is the status of each subsystem;
control input of a non-linear system, omega x ，Ω u Set of ranges taken for subsystem state x and control input u, respectively, and Ω x ，Ω u Respectively containing the origin thereof;
the measurable output of the nonlinear system is
Showing the external disturbance to the system;
representing the overall system state, including each subsystem x i And the state in which the subsystems are coupled to each other, n ═ n 1 +n 2 +…n m Is the total order of the system and,
representing the coupling state of the system, including the sum of external disturbances and internal uncertainties;
represents the control gain of the system;
order to
The dynamic equation of the multi-input multi-output strict feedback nonlinear system is expressed as
Let us assume a function phi i，l (·)，i∈(1，…，m)，l∈(1，…，n i -1) at least n i The + p order is continuously differentiable, and phi i，l (0) 0, then the function
Is shown as
then, according to the assumption, there is a differential homomorphic mapping
Wherein,
ξ i (0)＝0，
transforming differential homoembryo mapping into integral series system
Wherein,
representing the overall system state, including the sub-systems xi i And the state of the subsystems being coupled to each other, and
the target system tracked by the multi-input multi-output strict feedback nonlinear system is
Wherein,
belongs to a tight set
The target system is converted into an integral cascade system to obtain
Wherein,
is provided with
Wherein i is 1, …, m, j is 2, …, n i The integral tandem system based on differential homoembryo mapping and the integral tandem system of the target system can be obtained
Wherein,
error gain matrix
Satisfy the requirements of
Is a Hurwitz matrix and is a Hurwitz matrix,
the specific operation of outputting the feedback control rate using the dynamic inversion-based method includes the following steps,
s1: definition of
A sum of state errors for the actual measured output and the expected output;
s2: according to F defined in step S1 i (ξ，ζ，w i U) design the dynamic inverse as
Wherein B ═ B ij ) m×n Parameter μ i Is a small positive number, mu ═ u 1 ，…，μ m ) T ，
S3: order to
In the case of output feedback, only xi i，l Can measure and
unknown, solving xi using a generalized proportional integral observer i And
wherein the parameters
Satisfy the requirements of
Is a Hurwitz polynomial, epsilon i Is a small positive number, and e ═ e 1 ，…，ε m ) 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,
wherein,
2. use of the linear active disturbance rejection control system of a multiple-input multiple-output nonlinear system as claimed in claim 1 in a two-degree-of-freedom robot electromechanical servo control device with multiple-input multiple-output characteristics.
3. Use of the linear active disturbance rejection control system of a multiple-input multiple-output nonlinear system as claimed in claim 2 in a two-degree-of-freedom robot electromechanical servo control device with multiple-input multiple-output characteristics, it is characterized in that the two-degree-of-freedom mechanical arm electromechanical servo control device comprises a base (3) and a first speed reducer (2) arranged on the base (3), the input shaft of the first speed reducer (2) is fixedly connected with the output shaft of the first permanent magnet synchronous motor (1), the output shaft of the first speed reducer (2) is fixedly connected with the head end of the first mechanical arm (4), the 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), the 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.
4. The use of the linear active disturbance rejection control system of a multiple-input multiple-output nonlinear system as claimed in claim 3 in a two-degree-of-freedom robot electromechanical servo control device with multiple-input multiple-output characteristic, wherein the dynamic equation of the two-degree-of-freedom robot electromechanical servo control device is
Wherein,
M 11 ＝a 1 +a 2 cosθ 2 ，
M 22 ＝a 3 ，
G 1 (θ)＝a 4 sinθ 1 +a 5 sin(θ 1 +θ 2 )，
G 2 (θ)＝a 5 sin(θ 1 +θ 2 )，
a 2 ＝m 2 l 2 l 1 ，
in the formula I 1 ，l 2 Respectively representing the lengths of the first and second arms, theta 1 ，θ 2 Respectively representing joint angles, m, of the first and second robot arms 1 ，m 2 Respectively representing the mass of the first and second arm, u 1 Is a control input of the first robot arm, u 2 For control input of the second robot arm, d 1 ，d 2 Respectively represent the first machineExternal disturbance on the mechanical arm and the second mechanical arm;
let NG 1 ＝N 1 +G 1 ，NG 2 ＝N 2 +G 2 Then the dynamic equation of the electromechanical servo control device of the two-degree-of-freedom mechanical arm is transformed into
Due to M 11 ，M 22 With theta 2 The 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.
5. The use of the linear active disturbance rejection control system of a multiple-input multiple-output nonlinear system as claimed in claim 4 in a two-degree-of-freedom robot electromechanical servo control device having a multiple-input multiple-output characteristic, wherein said specific operation of said use comprises the steps of,
s5: order to
The dynamic equation of the electromechanical servo control device of the two-degree-of-freedom mechanical arm is continuously transformed into
S6: order to
Wherein
The x represents theta, and the dynamic equation of the electromechanical servo control device of the two-freedom mechanical arm is further transformed into
Wherein,
s7: the reference system of the dynamic equation of the electromechanical servo control device of the two-degree-of-freedom mechanical arm in the step S6 is
Wherein r is 1 ＝[r 1，1 r 1，2 ] T ，r 2 ＝[r 2，1 r 2，2 ] T ，
Is a bounded command signal generated using a quintic fit;
s8: the active disturbance rejection control in step S4The device is designed as
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,
respectively represent
The result is outputted by the control of (1),
respectively represent
And (4) outputting the result.
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