CN110989355B - Improved generation auto-disturbance-rejection controller - Google Patents
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Abstract
The invention discloses an improved active disturbance rejection controller, which particularly comprises a Tracking Differentiator, a variable gain Differentiator Exchange-High Order Differentiator, a Nonlinear State Error Feedback control law Nonlinear State Error Feedback; the tracking differentiator carries out transition on the input signal according to the bearing capacity of the control system and generates a differential signal of the input signal; observing each stage state quantity of the system by using a variable gain differentiator EHOD; finally, the differential signal of the tracking differentiator and the observation signal of the variable gain differentiator are processed by a nonlinear error feedback control law to obtain a control signal of the system to compensate the system disturbance and improve the control performance; the improved active disturbance rejection controller designed by the invention adopts the gain differentiator to replace the extended state observer to observe and feed back the system state, has less adjusting parameters and simple design, can accurately observe the state and the disturbance quantity of the controlled system, and has better measurement noise suppression capability.
Description
Technical Field
The invention belongs to the field of servo system control, and relates to an improved active disturbance rejection controller.
Background
The servo system is a motion feedback control system and is widely applied to the fields of high-precision numerical control machines, industrial robots, automobile unmanned driving, national defense and military equipment and the like. The disturbance of the nonlinear friction force causes the problems of crawling, oscillation or steady-state error and the like of the response of the servo system, and is a main factor influencing the performance of the servo system. The friction compensation control method can reduce or eliminate the influence of disturbance and improve the performance of the servo system.
The existing friction compensation control method mainly comprises two types of compensation methods: friction model based and not friction model based. The friction model-based compensation method first identifies and builds a suitable friction model, and then applies a control force to the system that opposes the friction force, thereby mitigating the effects of the frictional disturbance. A compensation method not based on a friction model adopts various control algorithms to improve the control structure or control parameters of a system to improve the interference suppression capability and reduce the influence of friction interference. Because the friction model cannot be accurately known, a compensation method which is not based on the friction model is widely adopted in practical engineering application. The proportional-Integral-derivative Controller (PID) has a simple control structure, and is widely applied to engineering without mastering advantages such as a system model, but has the problems of Integral feedback lag, poor robustness and the like, so that the control performance and the application range of the method are limited. In order to reduce or eliminate the influence of disturbance, fuzzy control, repetitive control, sliding film control and other technologies are introduced into a servo system to improve the system performance. However, fuzzy control depends on formulation of fuzzy rules, repeated control only obviously compensates for periodic disturbance and needs a certain operation period, and sliding mode control has to suppress the phenomenon of 'buffeting'. The above problems cause limitations in practical engineering applications of these methods. The active disturbance rejection control technology can estimate and compensate various external and internal disturbances suffered by the system in real time, and solves the problems of integral feedback lag, poor robustness, conflict of overshoot and rapidity caused by linear combination and the like. However, as a core part for realizing disturbance observation estimation in the active disturbance rejection control technology, the extended state observer has the problem of excessive parameters to be adjusted, increases the complexity of parameter setting, and causes great difficulty in design and implementation of the active disturbance rejection controller.
Disclosure of Invention
The invention aims to provide an improved active disturbance rejection controller which can observe and compensate the nonlinear friction force of a rotary table servo system and effectively improve the response speed and the tracking precision of the servo rotary table system.
The invention adopts the technical scheme that the improved active disturbance rejection controller specifically comprises a Tracking Differentiator, a variable gain Differentiator, a Nonlinear State Error Feedback control law Nonlinear State Error Feedback, a Tracking Differentiator, a variable gain Differentiator and a variable gain Differentiator;
the tracking differentiator carries out transition on the input signal according to the bearing capacity of the control system and generates a differential signal of the input signal;
observing each stage state quantity of the system by using the variable gain differentiator EHOD;
and finally, obtaining a control signal of the system by the differential signal of the tracking differentiator and the observation signal of the variable gain differentiator through a nonlinear error feedback control law to compensate the system disturbance and improve the control performance.
The invention is also characterized in that:
the tracking differentiator TD can smoothly track an input signal, reduce overshoot and accelerate control speed, and output a differentiated signal thereof for feedback control, and the specific function is as follows:
in the formula, v (k) is an input signal of a controlled system at the time of k; v. of 1 And v 2 For tracking the differentiator output signal, the output signal v 2 Is v is 1 For feedback control; h is a sampling step length; the slowest control function fh controls the tracking speed and the noise filtering effect of the tracking differentiator;
the expression of the fastest control function fh is as follows:
parameter r 0 For adjusting the tracking speed of the tracking differentiator; r is 0 The larger the value of (a), the faster the tracking speed. Parameter h 0 The noise filter is used for filtering noise of an input signal; h is 0 The larger the value of (A), the more obvious the noise filtering effect is;
the variable gain differentiator EHOD can observe and estimate the state quantity of the system according to the output signal of the controlled system, and outputs each stage state signal and disturbance signal of the controlled system for control and compensation, and the specific functions are as follows:
wherein: y is an output signal of a controlled system; z is a radical of 1 、z 2 And z 3 Is the output signal of the variable gain differentiator, z 1 Tracking the output signal y, z of the controlled system 2 For the controlled system to output a differential signal of y, z 3 Estimating a total disturbance signal for the system for the observation; e is the error between the observation signal of the variable gain differentiator and the output signal of the controlled system; a is a i (i =1,2,3) is a positive coefficient;
the parameter 1/epsilon is called gain; when the gain is high enough, the observed estimate of the output of the variable gain differentiator is close to the actual value, i.e.:
wherein the parameter 1/epsilon is transformed according to the set noise tolerance, and the adopted transformation control function is as follows:
ε＝ε′+a·tanh[b·(d-e)] (5)
wherein epsilon' is a constant gain constant, a and b are parameters to be adjusted, and d is the selected noise tolerance;
the function a-tanh [ b- (d-e) ] is used for controlling the magnitude of the gain, when the observation error is small, the gain can be reduced to reduce the noise influence, and when the observation error is large, the gain can be increased to reduce the observation error; the parameter a controls the increment of the variable gain, and the parameter b controls the gain change rate of the variable gain, and is selected as a number between 0 and 1;
the nonlinear error feedback control law NLSEF adopts output signals of a tracking differentiator TD and a variable gain differentiator EHOD to form a combined control law, and output system control signals compensate system disturbance and improve control performance, wherein the specific functions are as follows:
wherein u is a control signal for adding disturbance compensation, u 0 For control signals not compensated for disturbance e 1 And e 2 Is the difference between the TD and EHOD output signals, i.e., the error feedback signal; parameter beta 1 And beta 2 As gain factor, parameter b 0 Is a compensation factor;
the nonlinear function fal (e, a, δ) in the formula is expressed as:
wherein, the nonlinear function fal (e, a, delta) forms a nonlinear control combination, and the parameter a to be adjusted 1 And a 2 Adjusting the non-linearity of a non-linear functionThe linearity rate delta regulates the size of a nonlinear interval of a nonlinear function, and the value is more than 0 and less than a 1 ＜1＜a 2 ，δ＞0。
The invention has the beneficial effects that:
the invention designs a variable gain differentiator which can realize accurate observation of the system state and the disturbance quantity only by properly adjusting two parameters and has better measurement noise suppression capability. Compared with the traditional active disturbance rejection controller, the improved active disturbance rejection controller based on the variable gain differentiator is easy to design and implement, has better measurement noise suppression capability, can effectively estimate and compensate nonlinear friction disturbance, and improves the tracking performance of the turntable servo system.
Drawings
Fig. 1 is a schematic diagram of a control system in an improved active disturbance rejection controller.
In the figure, 1, a tracking differentiator TD,2, a nonlinear error state feedback control law NLSEF,3, a variable gain differentiator EHOD.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.
The invention provides an improved active disturbance rejection controller, which specifically comprises a Tracking Differentiator 1, a variable gain Differentiator Exchange-High Order Differentiator3 and a Nonlinear State Error Feedback control law Nonlinear State Error Feedback2, as shown in figure 1;
the tracking differentiator TD1 can smoothly track the input signal, reduce overshoot and increase control speed, and output its differentiated signal for feedback control, with the following specific functions:
in the formula, v (k) is an input signal of a controlled system at the time of k; v. of 1 And v 2 For tracking the differentiator output signal, the output signal v 2 Is v is 1 For feedback control; h is a sampling step length;the fastest control function fh controls the tracking differentiator to track the speed and the noise filtering effect, and the expression of the fastest control function fh is as follows:
parameter r 0 For adjusting the tracking speed of the tracking differentiator; r is 0 The larger the value of (a), the faster the tracking speed. Parameter h 0 The noise filter is used for filtering the noise of the input signal; h is 0 The larger the value of (A), the more obvious the noise filtering effect is;
the tracking differentiator realizes the output signal v 1 The input signal v (k) is quickly followed without overshoot, overshoot caused by instantaneous change of the input signal is reduced, and the system regulation time is shortened;
the variable gain differentiator EHOD3 can observe and estimate the state quantity of the system according to the output signal of the controlled system, and output each stage state signal and disturbance signal of the controlled system for control and compensation, and the specific function is as follows:
wherein: y is an output signal of a controlled system; z is a radical of 1 、z 2 And z 3 Is the output signal of the variable gain differentiator, z 1 Tracking the output signal y, z of the controlled system 2 For the controlled system to output a differential signal of y, z 3 An estimated total disturbance signal for the observed system; e is the error between the observation signal of the variable gain differentiator and the output signal of the controlled system; a is i (i =1,2,3) is a positive coefficient;
the parameter 1/epsilon is called gain; when the gain is high enough, the observed estimate of the output of the variable gain differentiator is close to the actual value, i.e.:
the parameter 1/epsilon is transformed according to the set noise tolerance, and the adopted transformation control function is as follows:
ε＝ε′+a·tanh[b·(d-e)] (5)
wherein ε' is a constant gain constant, a and b are parameters to be tuned, and d is the selected noise tolerance;
the function a-tanh [ b- (d-e) ] is used for controlling the magnitude of the gain, when the observation error is small, the gain can be reduced to reduce the noise influence, and when the observation error is large, the gain can be increased to reduce the observation error; the parameter a controls the increment of the variable gain, and the parameter b controls the gain change rate of the variable gain:
after the parameter d is selected according to the engineering requirement, the observation stationarity and rapidity can be improved by increasing the parameter a; the adjustment of the parameter b needs to take precision and noise suppression capability into consideration, the observation precision can be improved by increasing the parameter b, but the noise influence can be increased, the number is generally selected to be 0-1, and the state quantity can be quickly and accurately observed and the measurement noise can be effectively suppressed by selecting proper parameters a and b;
the variable gain observer has simple parameter setting and high observation precision, can accurately output a state signal and a disturbance signal of a controlled system for feedback compensation, improves the control performance of the system, and can enable the variable gain to enable the differentiator to simultaneously meet the effects of quick tracking and noise suppression by setting a proper parameter value;
the nonlinear error feedback control law NLSEF2 adopts output signals of a tracking differentiator TD1 and a variable gain differentiator EHOD3 to form a combined control law, an output system control signal compensates system disturbance and improves control performance, and the specific function is as follows:
where u is the control signal to which the disturbance compensation is added, u 0 For control signals not compensated for disturbance e 1 And e 2 Is the difference between the TD1 and EHOD3 output signals, i.e. the error feedback signal; parameter beta 1 And beta 2 As gain factor, parameter b 0 For compensating the factor, for controlling the degree of strength compensation of the system；
The nonlinear function fal (e, a, δ) in the formula is expressed as:
wherein the nonlinear functions fal (e, a, delta) form a nonlinear control combination, and the parameter a to be adjusted 1 And a 2 Adjusting the nonlinear rate of the nonlinear function, adjusting the nonlinear interval of the nonlinear function to be 0 < a 1 ＜1＜a 2 ，δ＞0。
The nonlinear feedback control has better robustness than the traditional linear feedback, can further reduce the control overshoot, shorten the adjusting time and improve the system control precision.
In summary, the output signal v of the tracking differentiator 1 in the present invention 1 The method has the advantages that the input signal v of the system is tracked quickly and smoothly, so that the overshoot problem caused by great change of the input signal v is reduced, and the control and adjustment speed of the system is increased; output signal v 2 Is v is 1 For system feedback control; the variable gain differentiator outputs an observation signal z according to the output signal y of the controlled system 1 、z 2 And z 3 Acting on system feedback; wherein z is 1 Tracking the output signal y, z of the controlled system 2 For the controlled system to output a differential signal of y, z 3 Is the observed system total disturbance signal; the nonlinear state error feedback control law 2 forms a combined control law according to the output signal of the tracking differentiator 1 and the output signal of the variable gain differentiator3, outputs a system control signal u, compensates the disturbance of a controlled system, and improves the control speed and the control precision of the system.
The improved active disturbance rejection controller designed by the invention adopts the variable gain differentiator to replace the extended state observer to observe and feed back the system state, has less adjusting parameters and simple design, can accurately observe the controlled system state and the disturbance quantity, and has better measurement noise suppression capability.
Claims (1)
1. An improved active disturbance rejection controller is characterized by specifically comprising a Tracking Differentiator, a variable gain Differentiator, a Nonlinear State Error Feedback control law Nonlinear State Error Feedback;
the tracking differentiator carries out transition on the input signal according to the bearing capacity of the control system and generates a differential signal of the input signal;
the tracking differentiator TD can smoothly track the input signal, reduce the overshoot and accelerate the control speed, and output its differentiated signal for feedback control, and the specific function is as follows:
in the formula, v (k) is an input signal of a controlled system at the time of k; v. of 1 And v 2 For tracking the differentiator output signal, the output signal v 2 Is v is 1 For feedback control; h is a sampling step length; the slowest control function fh controls the tracking differentiator to track the speed and the noise filtering effect;
the expression of the steepest control function fh is as follows:
parameter r 0 For adjusting the tracking speed of the tracking differentiator; r is 0 The larger the value of (A), the faster the tracking speed; parameter h 0 The noise filter is used for filtering the noise of the input signal; h is 0 The larger the value of (A), the more obvious the noise filtering effect is;
the variable gain differentiator EHOD observes each stage state quantity of the system;
the variable gain differentiator EHOD can observe and estimate the state quantity of the system according to the output signal of the controlled system, and output each stage state signal and disturbance signal of the controlled system for control and compensation, and the specific function is as follows:
wherein: y is an output signal of a controlled system; z is a radical of formula 1 、z 2 And z 3 Is the output signal of the variable gain differentiator, z 1 Tracking the output signal y, z of the controlled system 2 For the controlled system to output a differential signal of y, z 3 An estimated total disturbance signal for the observed system; e is the error between the observation signal of the variable gain differentiator and the output signal of the controlled system; a is i Is a positive coefficient, i =1,2,3;
the parameter 1/epsilon is called gain; when the gain is high enough, the observed estimate of the output of the variable gain differentiator is close to the actual value, i.e.:
the parameter 1/epsilon is transformed according to the set noise tolerance, and the adopted transformation control function is as follows:
ε＝ε′+a·tanh[b·(d-e)] (5)
wherein ε' is a constant gain constant, a and b are parameters to be tuned, and d is the selected noise tolerance;
the function a-tanh [ b- (d-e) ] is used for controlling the magnitude of the gain, when the observation error is small, the gain can be reduced to reduce the noise influence, and when the observation error is large, the gain can be increased to reduce the observation error; the parameter a controls the increment of the variable gain, and the parameter b controls the gain change rate of the variable gain, and is selected as a number between 0 and 1;
finally, a differential signal of the tracking differentiator and an observation signal of the variable gain differentiator are subjected to nonlinear error feedback control law to obtain a control signal of the system, so that the system disturbance is compensated and the control performance is improved;
the nonlinear error feedback control law NLSEF adopts output signals of a tracking differentiator TD and a variable gain differentiator EHOD to jointly form a combined control law, and a control signal of an output system compensates system disturbance and improves control performance, wherein specific functions are as follows:
where u is the control signal to which the disturbance compensation is added, u 0 For control signals not compensated for disturbance e 1 And e 2 Is the difference between the TD and EHOD output signals, i.e., the error feedback signal; parameter beta 1 And beta 2 As gain factor, parameter b 0 Is a compensation factor;
the nonlinear function fal (e, a, δ) in the formula is expressed as:
wherein the nonlinear functions fal (e, a, delta) form a nonlinear control combination, and the parameter a to be adjusted 1 And a 2 Adjusting the nonlinear rate of the nonlinear function, adjusting the nonlinear interval of the nonlinear function to be 0 < a 1 ＜1＜a 2 Delta > 0 and a is the parameter to be adjusted.
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| CN113238481B (en) * | 2021-04-13 | 2022-08-16 | 安徽工程大学 | Rotary mirror servo control system based on sliding mode active disturbance rejection control |
| CN113189872A (en) * | 2021-04-14 | 2021-07-30 | 中国科学院光电技术研究所 | Photoelectric tracking system control method based on improved repetitive active-disturbance-rejection |
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