CN114625012B - Improved sliding mode variable structure composite control method for continuous rotary motor system - Google Patents
Improved sliding mode variable structure composite control method for continuous rotary motor system Download PDFInfo
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Abstract
The application provides an improved sliding mode variable structure composite control method for a continuous rotary motor system, and belongs to the field of intelligent control. The control method comprises the steps of introducing a continuous friction torque model as a friction feedforward compensator and providing a sliding mode variable structure controller based on an improved power approach law. The invention has the advantages that the friction torque can be compensated, and the sliding mode variable structure controller can adaptively adjust the buffeting problem of the system according to the state of the system; meanwhile, the robustness and the anti-interference capability of the system can be improved aiming at the continuous rotary electro-hydraulic servo motor system.
Description
Technical Field
The invention relates to the field of intelligent control, and particularly designs an improved sliding mode variable structure composite control method for a continuous rotary motor system.
Background
The continuous rotation electro-hydraulic servo motor is used as important equipment in flight simulation experiments, can reproduce the attitude angle change of an aircraft, and has the advantages of high frequency response, high precision, ultralow speed and the like. However, the electro-hydraulic servo motor system has the influence of uncertain non-linear factors such as friction interference, so that a steady-state error exists in a low-speed tracking state, and a crawling phenomenon is caused in a serious case, so that a controller needs to be designed to improve the control precision of the continuous rotation electro-hydraulic servo motor system.
Eliminating friction on mechanical devices is often extremely costly and even impractical, the best method being friction compensation from a control strategy. The research on friction compensation is endless, a friction model capable of capturing different friction phenomena is established, and the friction compensation is introduced into the electro-hydraulic servo control, so that the control precision is greatly improved. Meanwhile, sliding Mode Variable Structure Control (SMC) can change the Structure of the controller according to the degree of deviation of the system state from the Sliding Mode surface and drive the controller to return to a preset track, so that the Control effect is unrelated to parameters, online identification is not needed, and the Sliding Mode Variable Structure Control (SMC) has the advantages of strong robustness and the like and is very suitable for engineering application.
However, the classical friction model is mostly obtained from a static mapping relation between the relative speed and the friction force, and the direction of the friction force is distributed by a symbolic function, and the discontinuous or piecewise continuous friction model can cause instability of the system; for the sliding mode variable structure controller, due to the function of the switching function, the system state continuously reciprocates along the sliding mode surface, and the phenomenon of 'buffeting' is generated.
Disclosure of Invention
The invention provides an improved sliding mode variable structure composite control method for a continuous rotary motor system, which is characterized by comprising the following steps of: the improved sliding mode variable structure composite controller comprises a friction feedforward compensator which is used for inputting a speed signal
And an output torque T f The composition adopts a continuous friction torque model; meanwhile, the sliding mode variable structure controller based on the improved power approach law is comprised of four input signals r and x 1 、x 2 、x 3 And an output signal u, the structure of which is formed by combining a power approach law and a variable speed approach law and comprises a system state quantity x; the control method is used for controlling the continuous rotation electro-hydraulic servo motor system, has strong robustness to uncertain nonlinear factors, can self-adaptively adjust the buffeting size of the system, meets the requirements of low-speed tracking capability and system stability, and realizes accurate control of the system.
The invention adopts the following technical scheme:
1. an improved sliding mode variable structure composite control method for a continuous rotary motor system is characterized by comprising the following steps: the improved sliding mode variable structure composite controller comprises a friction feedforward compensator which is used for inputting a speed signal
And an output torque T f The composition adopts a continuous friction torque model; meanwhile, the sliding mode variable structure controller based on the improved power approach law is comprised, and four input signals r and x 1 、x 2 、x 3 And an output signal u, which has a structure formed by combining a power approach law and a variable speed approach law and comprises a system state quantity x.
2. The improved sliding mode variable structure composite controller is as follows:
the friction feedforward compensator based on the continuous friction model has the expression:
in the formula: t is a unit of f Is the friction torque value; n.m; ki ∈ Ri =1,2, ·,6; tan h is a hyperbolic tangent function;
is the angular velocity;
the sliding mode variable structure controller expression based on the improved power approach law is as follows:
in the formula: s is a slip form surface; e.
a system tracking error; c. C 1 、c 2 Gain of sliding mode; α 、k 1 、k 2 is an approach law parameter; x is the number of 1 、x 2 、x 3 Is a system state variable;
the invention is mainly characterized in that:
(1) Aiming at the existence of unknown strong nonlinearity and uncertain strong disturbance factors in the continuous rotary electro-hydraulic servo motor system, the invention designs an improved sliding mode variable structure composite control method for the continuous rotary motor system, which can compensate friction torque, has certain strong robustness and anti-interference capability, and improves the tracking precision and response frequency of the system;
(2) Compared with the traditional sliding mode variable structure controller, the improved sliding mode variable structure composite control method for the continuous rotary motor system is adjusted by a power approach law and a speed change approach law together, and system state quantity is introduced into the speed change approach law, so that buffeting can be adjusted in a self-adaptive mode according to the system state, and the stability of the controller is improved.
Detailed Description
The control method of the present invention is described in detail with reference to the accompanying drawings:
as shown in fig. 1, a structural diagram of an improved sliding mode variable structure composite control method for a continuous rotary motor system; the specific control process is as follows: adopting a feedforward friction compensation strategy based on a continuous friction model to derive a command position signal r to obtain a speed signal
Obtaining friction compensation signal through continuous friction model, and outputting state quantity x by system 1 、x 2 、x 3 And the feedback input is used as the input of the sliding mode variable structure controller together with the command signal r to obtain the output u, and the output u and the friction compensation signal are used for acting on the controlled object together.
As shown in FIG. 2, the solid line is the slope input signal with the slope of 0.001/s, and the dotted line is the corresponding curve of the output of the modified sliding mode variable structure composite controller.
As shown in fig. 3, the solid line is a sinusoidal input signal with a frequency of 13Hz and an amplitude of 1 °, and the dotted line is a corresponding curve of the output of the modified sliding mode variable structure composite controller.
Description of the drawings:
FIG. 1 is a block diagram of an improved sliding mode variable structure composite control method for a continuous rotary motor system;
FIG. 2 is a graph of the corresponding characteristic of a 0.001/s ramp input signal;
fig. 3 is a graph of the response characteristic of a sinusoidal input signal of frequency 13Hz and amplitude 1 deg..
Claims (2)
1. An improved sliding mode variable structure composite control method for a continuous rotary motor system is characterized by comprising the following steps: the improved sliding mode variable structure composite controller comprises a friction feedforward compensator which is used for inputting a speed signal
And an output torque T f The composition adopts a continuous friction torque model; also comprising a power trend based on improvementThe sliding mode variable structure controller with near law is composed of four input signals r and x 1 、x 2 、x 3 And an output signal u, the structure of which is formed by combining a power approach law and a variable speed approach law and comprises a system state variable, and the expression of the sliding mode variable structure controller based on the improved power approach law is as follows:
in the formula: s is a slip form surface; e is the system tracking error; c. C 1 、c 2 Gain of sliding mode; alpha, k 1 、k 2 Is an approach law parameter; x is the number of 1 As corner position signals, x 2 Is an angular velocity signal, x 3 Is an angular acceleration signal; r is the desired position signal.
2. The improved sliding mode variable structure composite control method for the continuous rotary motor system according to claim 1, characterized in that: the continuous friction torque model avoids system instability caused by discontinuous or segmented continuous functions, is suitable for high-precision control requirements in a two-way rotation state, can capture the phenomenon that friction negative damping occurs due to large static friction coefficient when static friction is converted into dynamic friction, can describe various friction characteristics to a certain extent, covers a Stribeck friction model, a Maxwell friction model and a Coulomb friction model, and has the following expression:
in the formula: t is f Is the friction torque value, N.m; ki ∈ R i =1,2. tan h is a hyperbolic tangent function;
angular velocity, ° s;
meanwhile, the continuous friction model has the following characteristics:
(1) The model is symmetrical about the origin;
(2) When k is 6 A static friction factor when =0, wherein
Catching the Stribeck phenomenon, and reducing the friction factor along with the continuous increase of the speed;
(3)
the viscous friction is used for catching the viscous resistance generated by the viscosity of lubricating oil between the relative moving parts;
(4)
represents coulomb friction and exists in the state that the system has no viscous friction;
according to the continuous friction torque model determined by the formula, a friction compensation signal is added at the input position of a control signal, so that the friction interference is accurately estimated and compensated, and the composite control is performed with a sliding mode variable structure controller based on an improved power approach law;
on the basis of the power approach law, the advantages of the variable speed approach law are combined to determine an improved power approach law, and the mathematical expression is as follows:
in the formula: k is a radical of 1 >0,k 2 >0,α>1; x is a system state variable;
at the initial moment of system state motion, the speed change item
The power term accelerates the approach process of the system; when the system state enters a sliding mode, the power term action is weakened, and the state quantity x in the speed change term adaptively adjusts the buffeting size;
when the system approaches the equilibrium point:
therefore, the state of the improved power approach law control system is finally converged to a balance point, so that the fast adjusting speed of the power approach law is kept, and the advantage of the self-adaptive buffeting adjustment of the variable speed approach law is absorbed;
selecting a Lyapunov function V (x) = s 2 And/2, substituting the formula (2) into the formula:
therefore, the improved power approximation law meets the accessibility condition of the design of the sliding mode variable structure controller system;
assuming system initial state s (x) >0, then:
integrating to obtain:
item shifting and finishing to obtain:
according to the formula, when the system initial state s (x) >0, the control system has the accessibility in the limited time; for the same reason, s (x) <0;
there is a system state control equation:
in the formula: f (x) 2 ,x 3 )＝-5852x 2 -30x 3 Is a function of the system state; w is a control input; defining a slip form surface s:
in the formula: c. C 1 >0,c 2 >0; e is defined as follows:
taking the derivative of the above equation, introducing equation (9) can result:
and (3) combining a formula (2), and obtaining a sliding mode variable structure control law based on an improved power approach law, wherein the sliding mode variable structure control law is as follows:
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