CN108762088A - A kind of Hysteresis Nonlinear servo electrical machinery system sliding-mode control - Google Patents
A kind of Hysteresis Nonlinear servo electrical machinery system sliding-mode control Download PDFInfo
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Abstract
The invention discloses a kind of Hysteresis Nonlinear servo electrical machinery system sliding-mode controls, it is related to technical field of electromechanical control, devise sliding mode observer observation system unknown state, it solves sluggish servo electrical machinery system state variable such as servo motor angular speed, angular acceleration, load angular speed, load angular acceleration, sluggish link etc. to be difficult to directly measure, the problem of to influence controller design;By system, remaining unknown portions regards disturbance as, utilize only one layer of Chebyshev neural network estimating system unknown disturbance, disturbance observer and state observer are avoided while being designed, control difficulty is reduced, solves the estimation problem of sluggish servo electrical machinery system unknown disturbance;Sliding mode controller is devised, by adjusting tracking error and sliding-mode surface, realizes the accurate tracing control of sluggish servo electrical machinery system, precision is high, and strong robustness reduces algorithm difficulty, unified model, with more generality.
Description
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.
J.w. 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 backslash-like model is adopted to describe a model of the hysteresis nonlinear motor system as
Wherein,respectively representing the angle of the servo motor and the load,representing the moment of inertia of the servo motor and the load respectively,is a coefficient of the angular velocity of the servo motor,the non-linear element of the hysteresis is shown,it is the transmission of the torque that is,is an input signal;
converting the model of formula (1) into a state space model of
Wherein,
in the modelThe expression of (b) is a Backlash-like hysteresis model;
2) designing a sliding mode state observer:
in order to observe unknown states of a hysteresis servo motor system, such as motor angular velocity, load angular velocity, hysteresis characteristics and the like, the sliding mode state observer is designed as follows:
wherein,in order to design the gain factor for the device,indicating the desired output signal, adjusting the gain factorThe 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:
wherein,
will be provided withAnd (3) as system disturbance, estimating unknown disturbance by adopting a Chebyshev neural network, and defining the Chebyshev neural network as follows:
wherein,in order to be the weight matrix of the neural network,which is indicative of an estimation error that is,
and isDetermined by chebyshev polynomials:
;
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:
the slip form is defined as follows:
wherein,for the purpose of the designed coefficient vector or vectors,
definition of
Wherein,,
the sliding mode controller is designed as follows:
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 backslash-like model is adopted to describe a model of the hysteresis nonlinear motor system as
Wherein,respectively representing the angle of the servo motor and the load,representing the moment of inertia of the servo motor and the load respectively,is a coefficient of the angular velocity of the servo motor,the non-linear element of the hysteresis is shown,it is the transmission of the torque that is,is an input signal;
converting the model of formula (1) into a state space model of formula (2)
It is assumed that,
and isIn the modelThe expression of (b) is a Backlash-like hysteresis model;
2) designing a sliding mode state observer:
in order to observe unknown states of a hysteresis servo motor system, such as motor angular velocity, load angular velocity, hysteresis characteristics and the like, the sliding mode state observer is designed as follows:
wherein,in order to design the gain factor for the device,indicating the desired output signal, adjusting the gain factorThe 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:
according to the formulae (2) and (5):
will be provided withThe unknown disturbance is estimated by adopting a Chebyshev neural network and is regarded as the unknown disturbance of the system, and the Chebyshev is definedThe neural network is as follows:
wherein,in order to be the weight matrix of the neural network,which is indicative of an estimation error that is,
and isDetermined by chebyshev polynomials:
;
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:
the slip form is defined as follows:
wherein,for the purpose of the designed coefficient vector or vectors,
definition of
Wherein,,
the sliding mode controller is designed as follows:
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 parameters are shown in table 1, and the sliding mode surface gain
TABLE 1 hysteresis Servo Motor System parameters
0.8kgm2 | 7kgm2 | 40Nm | 6 | 2 | 0.7 |
The hysteresis nonlinear servo motor control system is simulated under the parameters, and the sine input signal isThe tracking effect of the angle and the angular velocity is shown in fig. 2 and 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 backslash-like model is adopted to describe a model of the hysteresis nonlinear motor system as
Wherein,respectively representing the angle of the servo motor and the load,representing the moment of inertia of the servo motor and the load respectively,is a coefficient of the angular velocity of the servo motor,the non-linear element of the hysteresis is shown,it is the transmission of the torque that is,is an input signal;
converting the model of formula (1) into a state space model of
Wherein,
the expression in the model is a Backlash-like hysteresis model;
2) designing a sliding mode state observer:
in order to observe unknown states of a hysteresis servo motor system, such as motor angular velocity, load angular velocity, hysteresis characteristics and the like, the sliding mode state observer is designed as follows:
wherein,in order to design the gain factor for the device,indicating the desired output signal, adjusting the gain factorThe 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:
wherein,
will be provided withAnd (3) as system disturbance, estimating unknown disturbance by adopting a Chebyshev neural network, and defining the Chebyshev neural network as follows:
wherein,in order to be the weight matrix of the neural network,which is indicative of an estimation error that is,
and isDetermined by chebyshev polynomials:
;
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:
the slip form is defined as follows:
wherein,for the purpose of the designed coefficient vector or vectors,
definition of
Wherein,,
the sliding mode controller is designed as follows:
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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