CN108762088B - Sliding mode control method for hysteresis nonlinear servo motor system - Google Patents

Sliding mode control method for hysteresis nonlinear servo motor system Download PDF

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CN108762088B
CN108762088B CN201810634210.4A CN201810634210A CN108762088B CN 108762088 B CN108762088 B CN 108762088B CN 201810634210 A CN201810634210 A CN 201810634210A CN 108762088 B CN108762088 B CN 108762088B
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hysteresis
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高学辉
孙波
张成元
李英建
祝长生
孙步胜
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Shandong University of Science and Technology
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Abstract

The invention discloses a sliding mode control method of a hysteresis nonlinear servo motor system, which relates to the technical field of electromechanical control, designs an unknown state of an observation system of a sliding mode state observer, and solves the problem that state variables of the hysteresis servo motor system, such as angular velocity, angular acceleration, load angular velocity, load angular acceleration, hysteresis links and the like of a servo motor, are difficult to directly measure, so that the design of a controller is influenced; the other unknown parts of the system are regarded as disturbance, and the unknown disturbance of the system is estimated by using the Chebyshev neural network with only one layer, so that a disturbance observer and a state observer are avoided being designed simultaneously, the control difficulty is reduced, and the estimation problem of the unknown disturbance of the hysteresis servo motor system is solved; the sliding mode controller is designed, accurate tracking control of the hysteresis servo motor system is achieved by adjusting the tracking error and the sliding mode surface, the precision is high, the robustness is strong, the algorithm difficulty is reduced, the model is unified, and the method has generality.

Description

Sliding mode control method for hysteresis nonlinear servo motor system
Technical Field
The invention relates to the technical field of electromechanical control, in particular to a sliding mode control method of a hysteresis nonlinear servo motor system.
Background
With the development and innovation of science and technology, the requirement on the control precision of the servo motor is higher and higher, the servo motor model is required to be accurate firstly, but in a hysteresis servo motor system, the existence of hysteresis nonlinearity causes great difficulty on model establishment and control strategy research, the control precision of the hysteresis servo motor is seriously influenced, even oscillation is caused in serious cases, and the control system is unstable. Therefore, precise control of the hysteresis servo motor system is an urgent problem to be solved.
There are many hysteresis models in a hysteresis servo motor system at present, a pure physical model is a Jiles-Atherton model and the like, the physical model is closely related to actual physical parameters, and different materials or systems are not universal. More general hysteresis models are mathematical models, and commonly used models include Preisach models, P-I models, Bouc-Wen models, Backlash-like models and the like. The mathematical model has strong universality and wide application range, but the model is complex and has numerous parameters. The Backlash-like model is adopted, compared with other mathematical models, the Backlash-like model has relatively few parameters, and an analytic solution can be obtained.
Macki proposed a Backlash-like hysteresis model in 1993, described by a piecewise function, and g.tao further developed the model and proposed a model-based adaptive control algorithm. On the basis, the Chun-Yi Su formally changes the Backlash-like model into a current universal form, and provides a complete process of analytic solution. After that, the Backlash-like model becomes one of the important models for describing hysteresis. Recently, HeWei proposes an adaptive neural network control algorithm for a 3-degree-of-freedom robot hysteresis system, adopts two neural networks to estimate a dynamic system and hysteresis nonlinearity, and designs a high-gain observer to observe the state of the system. And Yu ZHaoxu designs a Backlash-like random nonlinear hysteresis system controlled by an adaptive neural network controller based on an input-drive observer according to a Nussbaum gain function. The inventor also researches preset precision self-adaptive control based on a Backlash-like hysteresis model, converts vector errors into scalar errors by adopting a Laplace variation method, provides a new preset precision function, and designs a model reference self-adaptive controller control system.
Disclosure of Invention
In order to solve the technical problems, the invention provides a sliding mode control method of a hysteresis nonlinear servo motor system, which is characterized in that a Backlash-like model is integrated into a hysteresis servo motor system model, a sliding mode state observer is designed by depending on expected output data, unknown states and disturbance of the system are estimated by utilizing a Chebyshev neural network, and then a sliding mode controller is designed by error regulation input, so that high-precision hysteresis servo motor control is obtained, the algorithm complexity is reduced, and the algorithm robustness is improved.
The technical scheme adopted by the invention for solving the technical problems is as follows:
a sliding mode control method of a hysteresis nonlinear servo motor system is realized by the following steps:
1) modeling a hysteresis nonlinear servo motor system:
the Backlash-like model is adopted to describe a model of the hysteresis nonlinear motor system as
Figure GDA0002833922890000021
Wherein, thetamRepresenting the angle of the servomotor and the load, J, respectivelymRespectively representing the rotational inertia of a servo motor and the rotational inertia of a load, b is a coefficient of angular velocity of the servo motor, gamma (u) represents a hysteresis nonlinear link, tau is a transfer torque, and u is an input signal;
converting the model of formula (1) into a state space model of
Figure GDA0002833922890000022
Wherein,
Figure GDA0002833922890000023
alpha, beta and gamma are hysteresis-like model parameters, alpha>0,β>0, and β>Gamma, the actual lag model function is estimated on-line by a state observer, x in the model5The expression of (a) is a Backlash-like hysteresis model, and the estimation of an observer is given by formula (4);
2) designing a sliding mode state observer:
in order to observe unknown states of a hysteresis servo motor system, such as a motor angle, a motor angular velocity, a load angle, a load angular velocity and hysteresis characteristics, the sliding mode state observer is designed as follows:
Figure GDA0002833922890000031
wherein λ isiI is a designed gain coefficient, y represents a desired output signal, and the gain coefficient λ is adjustediThe sliding mode state observer can observe the unknown state of the hysteresis servo motor system;
3) disturbance estimation:
the state space model (2) of the hysteresis servo motor system is rewritten as follows:
Figure GDA0002833922890000032
wherein,
Figure GDA0002833922890000033
and taking T as system disturbance, estimating unknown disturbance by adopting a Chebyshev neural network, and defining the Chebyshev neural network as follows:
F(τ)＝W*Φ(τ)+ε (7)
wherein, W*Is a weight matrix of the neural network, epsilon represents the estimation error,
Figure GDA0002833922890000041
and quantity D of neural network kernel functionkDetermined by chebyshev polynomials:
Dk(τ)＝2τDk―1(τ)―Dk―2(τ)(9)
Figure GDA0002833922890000042
wherein D1(τ)＝1,D2(τ)＝τ,Dk(τ), k is 1,2, …, n is determined online by formula (9), D1
Figure GDA0002833922890000043
Determined online by equation (10);
4) designing a sliding mode controller:
through modeling of the hysteresis servo motor system, establishment of a state space model, design of a sliding mode state observer and disturbance estimation, a sliding mode controller is designed to control the hysteresis servo motor system, and the defined error is as follows:
Figure GDA0002833922890000044
the slip form is defined as follows:
s＝Ce (11)
wherein, C ═ C1,c2,c3,c4,c5]For the purpose of the designed coefficient vector or vectors,
definition of
Figure GDA0002833922890000045
Wherein, κ>0,
Figure GDA0002833922890000046
The sliding mode controller is designed as follows:
Figure GDA0002833922890000051
and the sliding mode controller is utilized to realize accurate tracking control of the hysteresis servo motor system by adjusting the tracking error and the sliding mode surface.
The sliding mode control method of the hysteresis nonlinear servo motor system, which is disclosed by the invention, has the following beneficial effects:
1) the unknown state of an observation system of the sliding mode state observer is designed, the algorithm complexity is low, the robustness is strong, and the problem that the state variables of a hysteresis servo motor system, such as the angular velocity, the angular acceleration, the load angular velocity, the load angular acceleration, the hysteresis link and the like of a servo motor, are difficult to directly measure, so that the design of a controller is influenced is solved;
2) the other unknown parts of the system are regarded as disturbance, and the unknown disturbance of the system is estimated by using the Chebyshev neural network with only one layer, so that a disturbance observer and a state observer are avoided being designed simultaneously, the control difficulty is reduced, and the estimation problem of the unknown disturbance of the hysteresis servo motor system is solved;
3) after the steps of system modeling, state space model conversion, sliding mode state observer design and disturbance estimation are completed, a sliding mode controller is designed, accurate tracking control of a hysteresis servo motor system is achieved by adjusting tracking errors and sliding mode surfaces, the precision is high, the robustness is high, the algorithm difficulty is reduced, the model is unified, and the method is general.
Drawings
FIG. 1 is a schematic flow diagram of the principle of the present invention;
FIG. 2 is a diagram illustrating an angle tracking effect according to an embodiment;
FIG. 3 is a diagram illustrating the tracking effect of angular velocity in an embodiment;
FIG. 4 is a diagram illustrating the effect of the controller reaching a sliding surface in an embodiment;
FIG. 5 is a diagram illustrating the effect of controller input in an embodiment.
Detailed Description
The invention is described in detail below by means of specific examples:
as shown in fig. 1, the overall design concept of the present invention is as follows: firstly, a hysteresis servo motor system model is converted into a state space form, wherein a Backlash-like model is adopted in a hysteresis nonlinear link, and the method is different from other methods. And designing a sliding mode state observer to observe the unknown state of the hysteresis servo motor system, estimating the unknown disturbance of the system according to the Chebyshev neural network, and designing a sliding mode controller to accurately control the hysteresis servo motor system according to a defined error function and a defined sliding mode surface.
The specific design steps are as follows:
1) modeling a hysteresis nonlinear servo motor system:
the Backlash-like model is adopted to describe a model of the hysteresis nonlinear motor system as
Figure GDA0002833922890000061
Wherein, thetamRepresenting the angle of the servomotor and the load, J, respectivelymRespectively representing the rotational inertia of a servo motor and the rotational inertia of a load, b is a coefficient of angular velocity of the servo motor, gamma (u) represents a hysteresis nonlinear link, tau is a transfer torque, and u is an input signal;
converting the model of formula (1) into a state space model of formula (2)
Figure GDA0002833922890000062
It is assumed that,
Figure GDA0002833922890000063
alpha, beta and gamma are hysteresis-like model parameters, alpha>0,β>0, and β>Gamma, the actual lag model function is estimated on-line by a state observer, x in the model5The expression of (a) is a Backlash-like hysteresis model, and the estimation of an observer is given by formula (4); (ii) a
2) Designing a sliding mode state observer:
in order to observe unknown states of a hysteresis servo motor system, such as a motor angle, a motor angular velocity, a load angle, a load angular velocity and hysteresis characteristics, the sliding mode state observer is designed as follows:
Figure GDA0002833922890000071
wherein λ isiI is 1,2,3,4,5 is the designed gain coefficient, y represents the periodAdjusting gain factor lambda of output signaliThe sliding mode state observer can observe the unknown state of the hysteresis servo motor system;
3) disturbance estimation:
the state space model (2) of the hysteresis servo motor system is rewritten as follows:
Figure GDA0002833922890000072
according to the formulae (2) and (5):
Figure GDA0002833922890000073
and taking T as unknown disturbance of the system, estimating the unknown disturbance by adopting a Chebyshev neural network, and defining the Chebyshev neural network as follows:
F(τ)＝W*Φ(τ)+ε (7)
wherein, W*Is a weight matrix of the neural network, epsilon represents the estimation error,
Figure GDA0002833922890000074
and quantity D of neural network kernel functionkDetermined by chebyshev polynomials:
Dk(τ)＝2τDk―1(τ)―Dk―2(τ)(9)
Figure GDA0002833922890000081
wherein D1(τ)＝1,D2(τ)＝τ,Dk(τ), k is 1,2, …, n is determined online by formula (9), D1
Figure GDA0002833922890000082
Determined online by equation (10);
4) designing a sliding mode controller:
a sliding mode state observer is adopted to observe the unknown state of a hysteresis servo motor system, a sliding mode controller is designed according to a defined error and a sliding mode surface, the hysteresis servo motor system is controlled, and the defined error is as follows:
Figure GDA0002833922890000083
the slip form is defined as follows:
s＝Ce( 11)
wherein, C ═ C1,c2,c3,c4,c5]For the purpose of the designed coefficient vector or vectors,
definition of
Figure GDA0002833922890000084
Wherein, κ>0,
Figure GDA0002833922890000085
The sliding mode controller is designed as follows:
Figure GDA0002833922890000086
and tracking expected input by using a sliding mode controller to realize accurate tracking control of the hysteresis servo motor system.
According to the simulation of the steps, the control method provided by the invention is feasible, high in accuracy and strong in robustness according to the simulation result.
In the simulation experiment of the hysteresis nonlinear servo motor control system, the hysteresis servo motor parameter is shown in table 1, and the sliding mode surface gain C is [ 302010105 ]]，κ＝20
Figure GDA0002833922890000091
TABLE 1 hysteresis Servo Motor System parameters
Figure GDA0002833922890000092
The hysteresis nonlinear servo motor control system is simulated under the above parameters, the sine input signal is y ═ 0.5sin (2.3 pi t), and the tracking effect of the angle and the angular velocity is shown in fig. 2 and fig. 3. Fig. 4 is the situation that the sliding mode controller reaches the sliding mode surface, and fig. 5 is the effect graph of the input signal of the sliding mode controller. From the simulation results, the method provided by the invention has good control performance, namely, higher convergence rate and smaller error.
In summary, the above is provided. The method considers the control problem of the hysteresis nonlinear servo motor, establishes a state space model of the hysteresis servo motor, integrates a Backlash-like hysteresis model and a servo motor model, and provides unknown disturbance of a Chebyshev neural network estimation system; angular velocity and angular acceleration of a servo motor, load angular velocity and angular acceleration, hysteresis nonlinearity and the like which are difficult to directly measure by a sliding mode state observer observation system are designed; a sliding mode controller control hysteresis servo motor system is provided. The method adopts a pure mathematical model, does not contain physical variables, has wide application range and strong universality, can ensure quick tracking, and has the characteristics of strong robustness and high precision, and simulation results show that the method provided by the invention has good performance.
It is to be understood that the above description is not intended to limit the present invention, and the present invention is not limited to the above examples, and those skilled in the art may make modifications, alterations, additions or substitutions within the spirit and scope of the present invention.

Claims (1)

1. A sliding mode control method of a hysteresis nonlinear servo motor system is characterized by comprising the following steps:
1) modeling a hysteresis nonlinear servo motor system:
the Backlash-like model is adopted to describe a model of the hysteresis nonlinear motor system as
Figure FDA0002833922880000011
Wherein, thetamRepresenting the angle of the servomotor and the load, J, respectivelymRespectively representing the rotational inertia of a servo motor and the rotational inertia of a load, b is a coefficient of angular velocity of the servo motor, gamma (u) represents a hysteresis nonlinear link, tau is a transfer torque, and u is an input signal;
converting the model of formula (1) into a state space model of
Figure FDA0002833922880000012
Wherein,
Figure FDA0002833922880000013
alpha, beta and gamma are hysteresis-like model parameters, alpha>0,β>0, and β>Gamma, the actual lag model function is estimated on-line by a state observer, x in the model5The expression of (1) is a Backlash-like hysteresis model, and the observer estimation is given by formula (4);
2) designing a sliding mode state observer:
in order to observe unknown states of a hysteresis servo motor system, such as a motor angle, a motor angular velocity, a load angle, a load angular velocity and hysteresis characteristics, the sliding mode state observer is designed as follows:
Figure FDA0002833922880000014
wherein λ isiI is a designed gain coefficient, y represents a desired output signal, and the gain coefficient λ is adjustediSo that the sliding mode state observer can observe the unknown of the hysteresis servo motor systemA state;
3) disturbance estimation:
the state space model (2) of the hysteresis servo motor system is rewritten as follows:
Figure FDA0002833922880000021
wherein,
Figure FDA0002833922880000022
and taking T as system disturbance, estimating unknown disturbance by adopting a Chebyshev neural network, and defining the Chebyshev neural network as follows:
F(τ)＝W*Φ(τ)+ε(7)
wherein, W*Is a weight matrix of the neural network, epsilon represents the estimation error,
Figure FDA0002833922880000027
and quantity D of neural network kernel functionkDetermined by chebyshev polynomials:
Dk(τ)＝2τDk-1(τ)―Dk-2(τ) (9)
Figure FDA0002833922880000023
wherein D1(τ)＝1,D2(τ)＝τ,Dk(τ), k is 1,2, …, n is determined online by formula (9),
Figure FDA0002833922880000024
Figure FDA0002833922880000025
determined online by equation (10);
4) designing a sliding mode controller:
through modeling of the hysteresis servo motor system, establishment of a state space model, design of a sliding mode state observer and disturbance estimation, a sliding mode controller is designed to control the hysteresis servo motor system, and the defined error is as follows:
Figure FDA0002833922880000026
the slip form is defined as follows:
s＝Ce(11)
wherein, C ═ C1,c2,c3,c4,c5]For the purpose of the designed coefficient vector or vectors,
definition of
Figure FDA0002833922880000031
Wherein, κ>0,
Figure FDA0002833922880000032
The sliding mode controller is designed as follows:
Figure FDA0002833922880000033
and tracking expected input by using a sliding mode controller to realize accurate tracking control of the hysteresis servo motor system.
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