CN111007728A - Motor active-disturbance-rejection self-adaptive control method considering all-state constraint - Google Patents

Motor active-disturbance-rejection self-adaptive control method considering all-state constraint Download PDF

Info

Publication number
CN111007728A
CN111007728A CN201911395827.6A CN201911395827A CN111007728A CN 111007728 A CN111007728 A CN 111007728A CN 201911395827 A CN201911395827 A CN 201911395827A CN 111007728 A CN111007728 A CN 111007728A
Authority
CN
China
Prior art keywords
state
equation
motor
disturbance
formula
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Granted
Application number
CN201911395827.6A
Other languages
Chinese (zh)
Other versions
CN111007728B (en
Inventor
徐张宝
刘庆运
孙船斌
郭永存
韩亮
何旭
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Anhui University of Technology AHUT
Original Assignee
Anhui University of Technology AHUT
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Anhui University of Technology AHUT filed Critical Anhui University of Technology AHUT
Priority to CN201911395827.6A priority Critical patent/CN111007728B/en
Publication of CN111007728A publication Critical patent/CN111007728A/en
Application granted granted Critical
Publication of CN111007728B publication Critical patent/CN111007728B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
    • G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
    • G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance

Landscapes

  • Engineering & Computer Science (AREA)
  • Health & Medical Sciences (AREA)
  • Artificial Intelligence (AREA)
  • Computer Vision & Pattern Recognition (AREA)
  • Evolutionary Computation (AREA)
  • Medical Informatics (AREA)
  • Software Systems (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Automation & Control Theory (AREA)
  • Feedback Control In General (AREA)

Abstract

The invention discloses a self-adaptive control method for motor active disturbance rejection considering full-state constraint in the technical field of motor control systems, which comprises the following steps: establishing a motor position servo system model; designing motor active-disturbance-rejection adaptive controller and control law u considering all-state constraint and adjusting parameter k of motor active-disturbance-rejection adaptive control law u considering all-state constraint1，k2，b1，b2，L1，L2Omega and delta, so that the system meets the control performance index, the scheme can effectively solve the problems of uncertain nonlinearity and uncertain parameters of the motor servo system, designs a constraint controller based on the barrier Lyapunov function, finally proves the overall stability of the system through a certificate, and has good parameter convergence and system control precision meeting the performance index under the interference condition; meanwhile, the invention simplifies the design of the controller, and the simulation result shows the effectiveness of the controller.

Description

Motor active-disturbance-rejection self-adaptive control method considering all-state constraint
Technical Field
The invention relates to the technical field of motor control systems, in particular to a motor active-disturbance-rejection self-adaptive control method considering all-state constraint.
Background
Due to the wide range of applications in the industry, high performance control of motor driven motion systems has attracted a wide range of attention including engineers and scientists. However, it is not easy to design a high performance controller for the servo system, and since model uncertainty is widely existed in the control system, a designer is likely to encounter many model uncertainties, especially unmodeled nonlinearities such as non-structural uncertainty. These uncertainty factors can severely degrade the control performance that can be achieved, resulting in low control accuracy, limit cycle oscillations, and even instability.
The traditional control mode is difficult to meet the requirement of uncertain nonlinear tracking precision, so that a control method which is simple and practical and meets the requirement of system performance needs to be researched. In recent years, various advanced control strategies are applied to a motor servo system, such as robust adaptive control, adaptive robust and the like, and the control achieves good control accuracy. However, the high-precision control results of the above control strategies are all ensured by large feedback gains, and the high-gain feedback often excites the high-frequency dynamics of the system, which causes instability of the system.
Aiming at the characteristics of uncertain nonlinearity and parameter uncertainty in motor servo, a model of the system is established, an extended state observer and a parameter self-adaptation law of a motor position servo system are respectively designed on the basis, and the system is estimated to estimate the unmodeled interference and unknown parameters and compensate in control input. In addition, in consideration of physical constraint conditions frequently encountered by an actual system, a state constraint controller is designed on the basis of an obstacle Lyapunov function, and effective constraint is carried out on the state of the system.
Disclosure of Invention
The invention aims to provide a motor active-disturbance-rejection adaptive control method considering full-state constraint so as to solve the problems in the background technology.
In order to achieve the purpose, the invention provides the following technical scheme: a motor active-disturbance-rejection self-adaptive control method considering full-state constraint comprises the following steps:
the method comprises the following steps: establishing a motor position servo system model; according to Newton's second law, the dynamic model equation of the inertia load of the motor is as follows:
Figure BDA0002346267710000021
in the formula: y is angular displacement, m is inertial load, kfIs the torque constant, u is the system control input, b is the viscous friction coefficient,
Figure BDA0002346267710000022
for other unmodeled disturbances, non-linear friction, external disturbances, and unmodeled dynamics are referred to;
defining state variables
Figure BDA0002346267710000023
Equation (1) is written as a state space form:
Figure BDA0002346267710000024
in the formula: x ═ x1,x2]TFor the state vector of position and velocity, assume that the output state of the system is constrained in the set Ω, Ω ═ xi:|xi|≤ci,i＝1,2},ciConstant > 0, defining unknown parameter set theta ═ theta1,θ2,]TWherein theta1＝kf/m，θ2＝b/m，
Figure BDA0002346267710000025
Representing concentrated interference;
assuming d (x, t) is sufficiently smooth, i.e. | d (x, t) | ≦ δ1，
Figure BDA0002346267710000026
In the formula: delta1，δ2The method comprises the following steps of (1) knowing;
assume again that instruction x is expected1d(t) and the time i-th derivative thereof
Figure BDA0002346267710000027
i is 1,2 satisfies x1d(t)≤υ0≤c1-L1，
Figure BDA0002346267710000028
υi> 0 is a constant, L1>0 is a design parameter.
Step two: designing a motor active-disturbance-rejection adaptive controller and a control law u considering all-state constraint;
step three: parameter k of motor active-disturbance-rejection adaptive control law u considering all-state constraint1，k2，b1，b2，L1，L2ω and δ, to make the system meet the control performance criteria.
Further, the second step includes the following steps:
s1: constructing an extended state observer of the motor system;
s2: designing a motor active-disturbance-rejection adaptive controller system considering full-state constraint;
s3: and verifying the stability of the system.
Further, the step S1 includes the following steps:
s101: equation (2) is converted into the following form:
Figure BDA0002346267710000031
in the formula:
Figure BDA0002346267710000032
s102: designing an extended state observer with the structure as shown in formula (4) in step S101
The following:
Figure BDA0002346267710000033
in the formula:
Figure BDA0002346267710000034
is xiI is 1,2, 3; omega>0 is a parameter of the extended state observer, order
Figure BDA0002346267710000035
i＝1,2,3；
If expanded state x3D (x, t), definition h (t) as x3The estimated error dynamics of the observer can be obtained as:
Figure BDA0002346267710000036
definition of
Figure BDA0002346267710000037
i is 1,2,3, then
Figure BDA0002346267710000038
In the formula: epsilon ═ epsilon1,ε2,ε3]T,
Figure BDA0002346267710000039
B＝[0,0,1]T,C＝[0,1,0]T；
If in an expanded state
Figure BDA00023462677100000310
Then it can be obtained:
Figure BDA00023462677100000311
since matrix a satisfies the hervetz criterion, there is a positive definite symmetry of matrix P satisfying the following equation: a. theTP+PA＝-2I (9)
In the formula: the matrix I is an identity matrix;
further, the step S2 includes the following steps: headFirst define z1＝x1-x1d，
z2＝x2-α1，α1For the virtual control law, the barrier Lyapunov function is defined again:
Figure BDA0002346267710000041
in the formula: b1>0，L1>0 is a constant, V1The time derivative of (a) is:
Figure BDA0002346267710000042
let virtual control law α1The design is as follows:
Figure BDA0002346267710000043
in the formula: k is a radical of1>0 is a feedback gain, and equation (12) is substituted for equation (11) to obtain:
Figure BDA0002346267710000044
if z is2When the value is equal to 0, then
Figure BDA0002346267710000045
Then define the barrier lyapunov function:
Figure BDA0002346267710000046
in the formula: b2>0，L2>0 is a constant; v2The time derivative of (a) is:
Figure BDA0002346267710000047
in conjunction with equation (2) one can obtain:
Figure BDA0002346267710000048
finally, based on the disturbance estimation of the extended state observer, the control input u is set as follows:
Figure BDA0002346267710000051
in the formula: u. ofaAs a model compensation term, usFor the robust term, k2>0 is a feedback gain, and equation (17) is substituted for equation (16), and the following can be obtained:
Figure BDA0002346267710000052
further, the step S3 is specifically: if (1) a suitable parameter can be selected to satisfy the following equation: c. C2≥|α1|max+L2(19)
(2) The system initial value z (0) can satisfy the following condition:
Figure BDA0002346267710000053
then, as can be seen from equation (17):
when the interference is time invariant, i.e., h (t) is 0, the adaptive law is designed to:
Figure BDA0002346267710000054
the system is asymptotically convergent, i.e., when t → ∞ z1→ 0, all signals are bounded, the system state can be effectively constrained;
when system disturbances are time-varying, all signals in a closed-loop control system are bounded, and the system state can be effectively constrained as follows defining a positive lyapunov function:
Figure BDA0002346267710000055
it satisfies:
Figure BDA0002346267710000061
further, when the interference is time invariant, the lyapunov function is defined as follows:
Figure BDA0002346267710000062
the derivation of equation (24) and the substitution of equations (7), (18) and (21) can be obtained:
Figure BDA0002346267710000063
from x1＝z1+x1d(t) and expected instruction x1d(t) and the time i-th derivative thereof
Figure BDA0002346267710000064
i is 1,2 satisfies x1d(t)≤υ0≤c1-L1，
Figure BDA0002346267710000065
υi> 0 is a constant, L1>0 is a design parameter, and | x can be obtained1|≤c1Thus x1Is bounded, and α1Is z1And
Figure BDA0002346267710000066
function of z1And
Figure BDA0002346267710000067
is bounded, can obtain α1Is bounded; from | x2|≤|α1|max+|z2I and I z2|≤L2Let x know2≤c2Is bounded; thus, it can be verified that all signals of the system are bounded, and the system state is restrainable;
when the system interference is time-varying, derivation is performed on equation (22), and equations (8), (21) are substituted to obtain:
Figure BDA0002346267710000068
in the formula:
Figure BDA0002346267710000071
integration of equation (26) can result in:
Figure BDA0002346267710000072
it is demonstrated by equation (27) that all signals in a closed loop system are bounded and the system state is constrained, so the controller is convergent and the system is stable.
Compared with the prior art, the invention has the beneficial effects that: the invention establishes a motor position servo system model for the characteristics of a motor position servo system; the motor active disturbance rejection adaptive controller considering the full-state constraint is designed to estimate unmodeled disturbance and carry out feedforward compensation, and meanwhile, the adaptive controller is used for estimating system position parameters, so that the problems of uncertain nonlinearity and uncertain parameters of a motor servo system can be effectively solved, the constraint controller is designed based on the barrier Lyapunov function, the overall stability of the system is finally proved through a certificate, the parameter convergence is good under the interference condition, and the system control precision meets the performance index; meanwhile, the invention simplifies the design of the controller, and the simulation result shows the effectiveness of the controller.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the description of the embodiments will be briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art that other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is a schematic diagram of a motor actuator of the present invention;
FIG. 2 is a schematic diagram of the system control strategy of the present invention;
fig. 3 is a graph of interference estimation and interference estimation error curves in accordance with the present invention;
FIG. 4 is a graph of a system parameter estimation according to the present invention;
FIG. 5 is a graph of output state curves for the design control method of the present invention;
FIG. 6 is a graph of tracking error for the desired command and two controllers according to the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Referring to fig. 1 and fig. 2, the present invention provides a technical solution: a motor active-disturbance-rejection self-adaptive control method considering full-state constraint comprises the following steps:
the method comprises the following steps: establishing a motor position servo system model; according to Newton's second law, the dynamic model equation of the inertia load of the motor is as follows:
Figure BDA0002346267710000081
in the formula: y is angular displacement, m is inertial load, kfIs the torque constant, u is the system control input, b is the viscous friction coefficient,
Figure BDA0002346267710000082
for other unmodeled disturbances, non-linear friction, external disturbances, and unmodeled dynamics are referred to;
defining state variables
Figure BDA0002346267710000083
Equation (1) is written as a state space form:
Figure BDA0002346267710000084
in the formula: x ═ x1,x2]TFor the state vector of position and velocity, assume that the output state of the system is constrained in the set Ω, Ω ═ xi:|xi|≤ci,i＝1,2},ciConstant > 0, defining unknown parameter set theta ═ theta1,θ2,]TWherein theta1＝kf/m，θ2＝b/m，
Figure BDA0002346267710000085
Representing concentrated interference;
assuming d (x, t) is sufficiently smooth, i.e. | d (x, t) | ≦ δ1，
Figure BDA0002346267710000086
In the formula: delta1，δ2The method comprises the following steps of (1) knowing;
assume again that instruction x is expected1d(t) and the time i-th derivative thereof
Figure BDA0002346267710000087
i is 1,2 satisfies x1d(t)≤υ0≤c1-L1，
Figure BDA0002346267710000088
υi> 0 is a constant, L1>0 is a design parameter.
Step two: designing a motor active-disturbance-rejection adaptive controller and a control law u considering all-state constraint;
step three: parameter k of motor active-disturbance-rejection adaptive control law u considering all-state constraint1，k2，b1，b2，L1，L2ω and δ, to make the system meet the control performance criteria.
The second step comprises the following steps:
s1: constructing an extended state observer of the motor system;
s2: designing a motor active-disturbance-rejection adaptive controller system considering full-state constraint;
s3: and verifying the stability of the system.
Step S1 includes the following steps:
s101: equation (2) is converted into the following form:
Figure BDA0002346267710000091
in the formula:
Figure BDA0002346267710000092
s102: designing an extended state observer according to formula (4) in step S101, wherein the extended state observer has the following structure:
Figure BDA0002346267710000093
in the formula:
Figure BDA0002346267710000094
is xiI is 1,2, 3; omega>0 is a parameter of the extended state observer,
order to
Figure BDA0002346267710000095
i＝1,2,3；
If expanded state x3D (x, t), definition h (t) as x3The time derivative of (2) can be obtained from the observer
The estimation error dynamics is:
Figure BDA0002346267710000096
definition of
Figure BDA0002346267710000097
i is 1,2,3, then
Figure BDA0002346267710000098
In the formula: epsilon ═ epsilon1,ε2,ε3]T,
Figure BDA0002346267710000099
B＝[0,0,1]T,C＝[0,1,0]T；
If in an expanded state
Figure BDA0002346267710000101
Then it can be obtained:
Figure BDA0002346267710000102
since matrix a satisfies the hervetz criterion, there is a positive definite symmetry of matrix P satisfying the following equation: a. theTP+PA＝-2I (9)
In the formula: the matrix I is an identity matrix;
step S2 includes the following steps: first of all, z is defined1＝x1-x1d，z2＝x2-α1，α1For virtual control
Law making, then defining the barrier Lyapunov function:
Figure BDA0002346267710000103
in the formula: b1>0，L1>0 is a constant, V1The time derivative of (a) is:
Figure BDA0002346267710000104
let virtual control law α1The design is as follows:
Figure BDA0002346267710000105
in the formula: k is a radical of1>0 is a feedback gain, and equation (12) is substituted for equation (11) to obtain:
Figure BDA0002346267710000106
if z is2When the value is equal to 0, then
Figure BDA0002346267710000107
Then define the barrier lyapunov function:
Figure BDA0002346267710000108
in the formula: b2>0，L2>0 is a constant; v2The time derivative of (a) is:
Figure BDA0002346267710000109
in conjunction with equation (2) one can obtain:
Figure BDA00023462677100001010
finally, based on the disturbance estimation of the extended state observer, the control input u is set as follows:
Figure BDA0002346267710000111
in the formula: u. ofaAs a model compensation term, usFor the robust term, k2>0 is a feedback gain, and equation (17) is substituted for equation (16), and the following can be obtained:
Figure BDA0002346267710000112
step S3 specifically includes: if (1) a suitable parameter can be selected to satisfy the following equation:
c2≥|α1|max+L2(19)
(2) the system initial value z (0) can satisfy the following condition:
Figure BDA0002346267710000113
then, as can be seen from equation (17):
when the interference is time invariant, i.e., h (t) is 0, the adaptive law is designed to:
Figure BDA0002346267710000114
the system is asymptotically convergent, i.e., when t → ∞ z1→ 0, all signals are bounded, the system state can be effectively constrained;
when system disturbances are time-varying, all signals in a closed-loop control system are bounded, and the system state can be effectively constrained as follows defining a positive lyapunov function:
Figure BDA0002346267710000115
it satisfies:
Figure BDA0002346267710000121
when the interference is time invariant, the lyapunov function is defined as follows:
Figure BDA0002346267710000122
the derivation of equation (24) and the substitution of equations (7), (18) and (21) can be obtained:
Figure BDA0002346267710000123
from x1＝z1+x1d(t) and expected instruction x1d(t) and the time i-th derivative thereof
Figure BDA0002346267710000124
i is 1,2 satisfies x1d(t)≤υ0≤c1-L1，
Figure BDA0002346267710000125
υi> 0 is a constant, L1>0 is a design parameter, and | x can be obtained1|≤c1Thus x1Is bounded, and α1Is z1And
Figure BDA0002346267710000126
function of z1And
Figure BDA0002346267710000127
is bounded, can obtain α1Is bounded; from | x2|≤|α1|max+|z2I and I z2|≤L2Let x know2≤c2Is bounded; thus, it can be verified that all signals of the system are bounded, and the system state is restrainable;
when the system interference is time-varying, derivation is performed on equation (22), and equations (8), (21) are substituted to obtain:
Figure BDA0002346267710000128
in the formula:
Figure BDA0002346267710000131
integration of equation (26) can result in:
Figure BDA0002346267710000132
it is demonstrated by equation (27) that all signals in a closed loop system are bounded and the system state is constrained, so the controller is convergent and the system is stable.
For example: the initial state of the system is x1(0)＝0.02,x2(0) In the simulation, the design controller models the system with the following parameters: m is 0.01, kg m2，kf＝5，b＝1.25N·s/m，θ1n＝600,θ2n＝80，θ3n＝0，k1＝70,k2＝0.001，b1＝2，b2＝0.01，L1＝2，L 210, ω 800, PID controller parameter kp＝110，ki＝70，kdPosition angle input signal y of 0.3d(t)＝0.2sin(πt)[1-exp(-0.01t3)]rad, d (x, t) ═ 10sin (2 pi t) N · m, the control law action effect is as shown in fig. 3-6, the algorithm provided by the invention can accurately estimate the interference value and the system state under the simulation environment, compared with the traditional PID control, the controller designed by the invention can greatly improve the control precision of the system under the condition of large interference, and has better state constraint performance; research results show that under uncertain nonlinear influence, the method provided by the scheme can meet performance indexes.
In the description herein, references to the description of "one embodiment," "an example," "a specific example" or the like are intended to mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, the schematic representations of the terms used above do not necessarily refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.
The preferred embodiments of the invention disclosed above are intended to be illustrative only. The preferred embodiments are not intended to be exhaustive or to limit the invention to the precise embodiments disclosed. Obviously, many modifications and variations are possible in light of the above teaching. The embodiments were chosen and described in order to best explain the principles of the invention and the practical application, to thereby enable others skilled in the art to best utilize the invention. The invention is limited only by the claims and their full scope and equivalents.

Claims (6)

1. A motor active-disturbance-rejection self-adaptive control method considering full-state constraint is characterized by comprising the following steps: the method comprises the following steps:
the method comprises the following steps: establishing a motor position servo system model; according to Newton's second law, the dynamic model equation of the inertia load of the motor is as follows:
Figure FDA0002346267700000011
in the formula: y is angular displacement, m is inertial load, kfIs the torque constant, u is the system control input, b is the viscous friction coefficient,
Figure FDA0002346267700000012
for other unmodeled disturbances, non-linear friction, external disturbances, and unmodeled dynamics are referred to;
defining state variables
Figure FDA0002346267700000013
Equation (1) is written as a state space form:
Figure FDA0002346267700000014
in the formula: x ═ x1,x2]TFor the state vector of position and velocity, assume that the output state of the system is constrained in the set Ω, Ω ═ xi:|xi|≤ci,i＝1,2},ciConstant > 0, defining unknown parameter set theta ═ theta1,θ2,]TWherein theta1＝kf/m，θ2＝b/m，
Figure FDA0002346267700000015
Representing concentrated interference;
assuming d (x, t) is sufficiently smooth, i.e. | d (x, t) | ≦ δ1，
Figure FDA0002346267700000016
In the formula: delta1，δ2The method comprises the following steps of (1) knowing;
assume again that instruction x is expected1d(t) and the time i-th derivative thereof
Figure FDA0002346267700000019
Satisfy x1d(t)≤υ0≤c1-L1，
Figure FDA0002346267700000018
υi> 0 is a constant, L1>0 is a design parameter.
Step two: designing a motor active-disturbance-rejection adaptive controller and a control law u considering all-state constraint;
step three: parameter k of motor active-disturbance-rejection adaptive control law u considering all-state constraint1，k2，b1，b2，L1，L2ω and δ, to make the system meet the control performance criteria.
2. The adaptive control method for auto-disturbance-rejection of the motor considering the full-state constraint as claimed in claim 1, wherein: the second step comprises the following steps:
s1: constructing an extended state observer of the motor system;
s2: designing a motor active-disturbance-rejection adaptive controller system considering full-state constraint;
s3: and verifying the stability of the system.
3. The adaptive control method for auto-disturbance-rejection of the motor considering the full-state constraint as claimed in claim 2, wherein: the step S1 includes the following steps:
s101: equation (2) is converted into the following form:
Figure FDA0002346267700000021
in the formula:
Figure FDA0002346267700000022
s102: designing an extended state observer according to formula (4) in step S101, wherein the extended state observer has the following structure:
Figure FDA0002346267700000023
in the formula:
Figure FDA0002346267700000024
is xiI is 1,2, 3; omega>0 is a parameter of the extended state observer,
order to
Figure FDA0002346267700000025
If expanded state x3D (x, t), definition h (t) as x3The estimated error dynamics of the observer can be obtained as:
Figure FDA0002346267700000026
definition of
Figure FDA0002346267700000027
Then
Figure FDA0002346267700000028
In the formula: epsilon ═ epsilon1,ε2,ε3]T,
Figure FDA0002346267700000029
B＝[0,0,1]T,C＝[0,1,0]T；
If in an expanded state
Figure FDA00023462677000000210
Then it can be obtained:
Figure FDA00023462677000000211
since matrix a satisfies the hervetz criterion, there is a positive definite symmetry of matrix P satisfying the following equation: a. theTP+PA＝-2I (9)
In the formula: the matrix I is an identity matrix.
4. A method of considering a full state approximation as in claim 2The self-adaptive control method for the auto-disturbance rejection of the motor is characterized by comprising the following steps: the step S2 includes the following steps: first of all, z is defined1＝x1-x1d，z2＝x2-α1，α1For the virtual control law, the barrier Lyapunov function is defined again:
Figure FDA0002346267700000031
in the formula: b1>0，L1>0 is a constant, V1The time derivative of (a) is:
Figure FDA0002346267700000032
let virtual control law α1The design is as follows:
Figure FDA0002346267700000033
in the formula: k is a radical of1>0 is a feedback gain, and equation (12) is substituted for equation (11) to obtain:
Figure FDA0002346267700000034
if z is2When the value is equal to 0, then
Figure FDA0002346267700000035
Then define the barrier lyapunov function:
Figure FDA0002346267700000036
in the formula: b2>0，L2>0 is a constant; v2The time derivative of (a) is:
Figure FDA0002346267700000037
in conjunction with equation (2) one can obtain:
Figure FDA0002346267700000038
finally, based on the disturbance estimation of the extended state observer, the control input u is set as follows:
Figure FDA0002346267700000041
in the formula: u. ofaAs a model compensation term, usFor the robust term, k2>0 is a feedback gain, and equation (17) is substituted for equation (16), and the following can be obtained:
Figure FDA0002346267700000042
。
5. the adaptive control method for auto-disturbance-rejection of the motor considering the full-state constraint as claimed in claim 2, wherein: the step S3 specifically includes: if (1) a suitable parameter can be selected to satisfy the following equation: c. C2≥|α1|max+L2(19)
(2) The system initial value z (0) can satisfy the following condition:
Figure FDA0002346267700000043
then, as can be seen from equation (17):
when the interference is time invariant, i.e., h (t) is 0, the adaptive law is designed to:
Figure FDA0002346267700000044
the system is asymptotically convergent, i.e., when t → ∞ z1→ 0, all signals are bounded, the system state can be effectively constrained;
when system disturbances are time-varying, all signals in a closed-loop control system are bounded, and the system state can be effectively constrained as follows defining a positive lyapunov function:
Figure FDA0002346267700000051
it satisfies:
Figure FDA0002346267700000052
。
6. the adaptive control method for auto-disturbance-rejection of the motor considering the full-state constraint as claimed in claim 5, wherein: when the interference is time invariant, the lyapunov function is defined as follows:
Figure FDA0002346267700000053
the derivation of equation (24) and the substitution of equations (7), (18) and (21) can be obtained:
Figure FDA0002346267700000054
from x1＝z1+x1d(t) and expected instruction x1d(t) and the time i-th derivative thereof
Figure FDA0002346267700000055
Satisfy x1d(t)≤υ0≤c1-L1，
Figure FDA0002346267700000056
υi> 0 is a constant, L1>0 is a design parameter, and | x can be obtained1|≤c1Thus x1Is bounded, and α1Is z1And
Figure FDA0002346267700000057
function of z1And
Figure FDA0002346267700000058
is bounded, can obtain α1Is bounded; from | x2|≤|α1|max+|z2I and I z2|≤L2Let x know2≤c2Is bounded; thus, it can be verified that all signals of the system are bounded, and the system state is restrainable; when the system interference is time-varying, derivation is performed on equation (22), and equations (8), (21) are substituted to obtain:
Figure FDA0002346267700000061
in the formula:
Figure FDA0002346267700000062
integration of equation (26) can result in:
Figure FDA0002346267700000063
it is demonstrated by equation (27) that all signals in a closed loop system are bounded and the system state is constrained, so the controller is convergent and the system is stable.
CN201911395827.6A 2019-12-30 2019-12-30 Motor active-disturbance-rejection self-adaptive control method considering all-state constraint Active CN111007728B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201911395827.6A CN111007728B (en) 2019-12-30 2019-12-30 Motor active-disturbance-rejection self-adaptive control method considering all-state constraint

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201911395827.6A CN111007728B (en) 2019-12-30 2019-12-30 Motor active-disturbance-rejection self-adaptive control method considering all-state constraint

Publications (2)

Publication Number Publication Date
CN111007728A true CN111007728A (en) 2020-04-14
CN111007728B CN111007728B (en) 2022-12-09

Family

ID=70118354

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201911395827.6A Active CN111007728B (en) 2019-12-30 2019-12-30 Motor active-disturbance-rejection self-adaptive control method considering all-state constraint

Country Status (1)

Country Link
CN (1) CN111007728B (en)

Citations (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20090005886A1 (en) * 2002-04-18 2009-01-01 Cleveland State University Extended Active Disturbance Rejection Controller
CN104345638A (en) * 2014-10-09 2015-02-11 南京理工大学 ADRAC (active-disturbance-rejection adaptive control) method for hydraulic motor position servo system
CN104570728A (en) * 2014-11-20 2015-04-29 南京理工大学 Self-adaptive robust output feedback control method for motor position servo system
CN108303885A (en) * 2018-01-31 2018-07-20 南京理工大学 A kind of motor position servo system self-adaptation control method based on interference observer
CN108469734A (en) * 2018-03-27 2018-08-31 安徽工业大学 Consider the motor servo system Auto-disturbance-rejection Control of state constraint
CN109995278A (en) * 2018-12-29 2019-07-09 中科院计算技术研究所南京移动通信与计算创新研究院 A kind of motor servo system self-regulation control method considering input-bound
CN110308651A (en) * 2018-03-27 2019-10-08 安徽工业大学 Electrohydraulic servo system total state about beam control method based on extended state observer

Patent Citations (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20090005886A1 (en) * 2002-04-18 2009-01-01 Cleveland State University Extended Active Disturbance Rejection Controller
CN104345638A (en) * 2014-10-09 2015-02-11 南京理工大学 ADRAC (active-disturbance-rejection adaptive control) method for hydraulic motor position servo system
CN104570728A (en) * 2014-11-20 2015-04-29 南京理工大学 Self-adaptive robust output feedback control method for motor position servo system
CN108303885A (en) * 2018-01-31 2018-07-20 南京理工大学 A kind of motor position servo system self-adaptation control method based on interference observer
CN108469734A (en) * 2018-03-27 2018-08-31 安徽工业大学 Consider the motor servo system Auto-disturbance-rejection Control of state constraint
CN110308651A (en) * 2018-03-27 2019-10-08 安徽工业大学 Electrohydraulic servo system total state about beam control method based on extended state observer
CN109995278A (en) * 2018-12-29 2019-07-09 中科院计算技术研究所南京移动通信与计算创新研究院 A kind of motor servo system self-regulation control method considering input-bound

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
ZHANGBAO XU等: "State Constraint Control for Uncertain Nonlinear Systems With Disturbance Compensation", 《IEEE ACCESS》 *

Also Published As

Publication number Publication date
CN111007728B (en) 2022-12-09

Similar Documents

Publication Publication Date Title
CN111152225B (en) Uncertain mechanical arm fixed time trajectory tracking control method with input saturation
CN108303885B (en) Self-adaptive control method of motor position servo system based on disturbance observer
CN107561935B (en) Motor position servo system friction compensation control method based on multilayer neural network
CN108875253B (en) Terminal sliding mode anti-swing control method and system of under-actuated crane system based on disturbance observer
CN107121932B (en) Motor servo system error symbol integral robust self-adaptive control method
CN108388114B (en) Flexible mechanical arm composite control method based on output redefinition
CN108628172B (en) Mechanical arm high-precision motion control method based on extended state observer
CN104333280B (en) Robustness adaptive control (RAC) method of direct driving motor system
CN110673472B (en) Adaptive robust control method based on neural network compensation dead zone inversion error
CN108469734B (en) Motor servo system active disturbance rejection control method considering state constraint
CN108155833B (en) Motor servo system asymptotic stable control method considering electrical characteristics
CN112769364B (en) Fast self-adaptive anti-interference control method of direct current motor servo system
CN111736472B (en) Motor self-adaptive preset performance asymptotic control method based on RISE
Sun et al. Research on the trajectory tracking control of a 6-DOF manipulator based on fully-actuated system models
Qiao et al. Adaptive control of missile attitude based on BP–ADRC
CN109514559B (en) Flexible mechanical arm time scale separation robust control method based on output redefinition
Xie et al. Neural network‐based adaptive control of piezoelectric actuators with unknown hysteresis
Sun et al. Active disturbance rejection adaptive control of multi‐degrees of freedom hydraulic manipulators
CN110829933A (en) Neural network output feedback self-adaptive robust control method based on transmitting platform
CN110888320B (en) Self-adaptive robust control method based on double-electric-cylinder synchronous motion error modeling
CN109324503B (en) Multilayer neural network motor system control method based on robust integration
CN109995278B (en) Motor servo system self-adjustment control method considering input limitation
CN111007728B (en) Motor active-disturbance-rejection self-adaptive control method considering all-state constraint
CN104991445B (en) A kind of motor servo system of Existence of Global Stable adaptively exports feedback robust control method
CN115047760A (en) FTAIRTSM control method for DC motor servo system

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant