CN114594688A - Improvement method of active disturbance rejection controller based on electro-hydraulic servo system - Google Patents
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Abstract
The invention discloses an improved method of an active disturbance rejection controller based on an electro-hydraulic servo system, which comprises the steps of firstly, improving a Tracking Differentiator (TD) in an Active Disturbance Rejection Controller (ADRC), and optimizing and improving the algorithm of the tracking differentiator; the Extended State Observer (ESO) is then modified by adjusting beta01、β02、β03And b to improve the performance of the ESO; and finally, improving the feedback control law (NLSEF), and modifying the fal function by a nonlinear differencing and combining method. Through the improvement of the active disturbance rejection controller, the disturbance rejection control precision of the electro-hydraulic servo system on external disturbance and internal parameter perturbation is improved.
Description
Technical Field
The invention belongs to the field of servo technical control, and particularly relates to an improved method of an active disturbance rejection controller based on an electro-hydraulic servo system.
Background
The electro-hydraulic servo system has various complex disturbance factors such as uncertain models, perturbation parameters, variable load force and the like, which greatly influences the disturbance rejection precision of the electro-hydraulic position servo system and greatly influences the tracking and control precision of the system.
The Active Disturbance Rejection Controller (ADRC) mainly comprises a Tracking Differentiator (TD), an Extended State Observer (ESO) and a feedback control law (NLSEF). The controller integrates the essence of the modern control theory and the classical PID theory, and carries out real-time estimation and compensation on unknown disturbance existing in the system by observing each stage state variable of the electro-hydraulic position servo system in real time. Unknown interference existing in the system, such as nonlinear and coupling interference of internal and external environments in the electro-hydraulic system, can be effectively suppressed through the active disturbance rejection controller. For the traditional PID control, adverse effects caused by the interference sources can be effectively inhibited only in the aspect of establishing an accurate mathematical model, which provides great challenges for controllers, but the ADRC does not depend on the specific mathematical model of a control object, so that the stability and robustness of the system can be improved, and the anti-interference control precision of the control system can be improved.
However, the conventional ADRC control algorithm also has certain defects, such as: generally, only the ESO is required to be gradually stable, the convergence rate has a space for improving, the estimation capability aiming at the fast time-varying interference is insufficient, the accuracy of the interference estimation is limited, the parameters required to be selected are numerous and are difficult to adjust, and the like. Aiming at the problems of the traditional ADRC method, the current mainstream improvement method is to linearize and parameterize the nonlinear form of ESO and set the parameters to facilitate the practical application; or the theory of variable structure control is introduced into the design of ESO in the active disturbance rejection algorithm, so that the adjustable parameters are reduced while the advantages of the original controller are ensured.
Disclosure of Invention
In view of the above, to solve the above problems, the present invention provides an improved method for an active disturbance rejection controller based on an electro-hydraulic servo system. The invention carries out optimization improvement by the algorithm of a Tracking Differentiator (TD) in an Active Disturbance Rejection Controller (ADRC); by adjusting beta01、β02、β03And b to improve the performance of the ESO; by a nonlinear differential combination method, the fal function is modified to improve the feedback control law (NLSEF), so that the improvement of the ADRC control algorithm is completed, and the method specifically comprises the following steps:
and 3, improving a feedback control law (NLSEF), and modifying the fal function by a nonlinear differencing and combining method.
Further, in step 1, the Tracking Differentiator (TD) inputs a given signal, and arranges the transition:
further, arranging the input signal v to be smooth and transitional according to the given signal v1And its differential signal v2. The second order continuous type TD is as follows:
wherein r and delta are parameters to be set, the parameter r is a convergence factor and determines the speed of tracking the input signal in the transition process, and the higher the r value is, the faster the tracking speed is. However, when r is increased to a certain degree, the tracking speed will reach a saturation state and will not increase any more, and when r is too large, the extracted tracking differential signal will oscillate. Delta is a linear interval factor, determines the size of a linear interval, and generally ranges from (0.01-1).
The algorithm for improving the post-transition process is as follows:
wherein h is the sampling step length, y is the output of the system, and e is the deviation of the two.
Further, the fhan function is a function of a non-linear combination. And optimizing the non-linear combination of the fhan function in the TD.
Further, in step 2, the estimated system state and disturbance are tracked with the system output y and input u:
wherein, beta01、β02、β03Is a set of parameters. Beta is a01、β02、β03For three important parameters of the linear extended state observer, beta is increased within a certain range01，β01Is approximately in the same order of magnitude as 1/h, beta02，β03Need to be within a certain range of values.
Further, the improved algorithm of the ESO is as follows:
wherein Z is2Is a true second order differential signal, Z, output by the system3The disturbance state quantity, which is the ESO expansion, is the core variable of the ESO. Parameter b0Is a "compensation factor" that determines the magnitude of disturbance compensation, i.e., an estimated value of the amplification factor b when the control amount u is applied to the system.
Further, in step 3, NLSEF processes u by nonlinear differencing combining method0＝β1fal(e1，a1，δ)+β2fal(e2，a2δ), the fal function in the second-order nonlinear state error feedback control law is improved as follows:
wherein, a1，a2，b1，b2，b3And delta is a parameter variable to be set. b1Similar to the proportional gain factor of a PID controller, increase b1Will increase the system running speed and reduce the static error, thereby improving the tracking accuracy, but too large b1The dynamic performance of the system is reduced, even moreTo cause unstable hunting. b2Similar to the differential gain coefficient in the PID, the increase within a certain degree can improve the tracking accuracy of the system and accelerate the dynamic response speed of the system.
Furthermore, considering that the electro-hydraulic position servo system needs to realize the goals of large error, small gain and small error and large gain, the error gain coefficient a can be made1，a2The range of (A) is as follows:
0＜a1＜1，1＜a2
when numerical simulation is carried out, in order to avoid high-frequency flutter, the fal function is modified to become a power function with a continuous linear section near the origin. The improved function fal is of the form:
wherein: δ is the interval length of the linear segment.
In general, by the above technical solution conceived by the present invention, compared to the prior art, the following beneficial results can be achieved:
1. the invention improves the tracking accuracy of the fhan function in the TD to the system by optimizing the algorithm of the tracking differentiator.
2. The invention improves the performance of ESO by adjusting the parameter values of beta 01, beta 02, beta 03 and b, reduces the estimation deviation of ESO and improves the disturbance elimination capability of ESO.
3. The invention improves the anti-interference control precision of the electro-hydraulic position servo system on external interference and internal parameter perturbation.
Drawings
FIG. 1 is a block diagram of the improved ADRC of the present invention;
FIG. 2 is a diagram illustrating nonlinear combination optimization of fhan function in TD according to an embodiment;
FIG. 3 is a simulation diagram of the extraction of a sinusoidal position signal of the fhan function in the TD in the embodiment;
FIG. 4 is a diagram of simulation of step position signal extraction for fhan function in TD in an embodiment;
FIG. 5 is a sinusoidal tracking curve in the absence of noise in an embodiment;
FIG. 6 is a tracking curve of a noise-free time step signal in an embodiment;
FIG. 7 is a trace curve of a sinusoidal signal under white noise in an embodiment;
FIG. 8 is a white noise step-down signal tracking curve in an embodiment;
FIG. 9 is a sinusoidal signal tracking curve under square wave interference in the embodiment;
fig. 10 is a tracking curve of the step signal under the square wave interference in the embodiment.
Detailed Description
The objects, technical solutions and advantages of the present invention will be clearly and completely described below with reference to the accompanying drawings. 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.
The invention aims to provide an improved method of an active disturbance rejection controller based on an electro-hydraulic servo system, which carries out optimization improvement on a Tracking Differentiator (TD) self algorithm in the Active Disturbance Rejection Controller (ADRC); by adjusting beta01、β02、β03And b to improve the performance of the ESO; by a nonlinear differential combination method, a fal function is modified to improve a feedback control law (NLSEF), so that the improvement of ADRC is completed, and the anti-interference control precision of the electro-hydraulic position servo system on external interference and internal parameter perturbation is improved, and the method specifically comprises the following steps:
Arranging a smooth and transitional input signal v according to a given signal v1And its differential signal v2. The second order continuous type TD is represented by the following formula:
in the formula: r and delta are parameters to be set, the parameter r is a convergence factor and determines the speed of tracking the input signal in the transition process, and the higher the r value is, the faster the tracking speed is. However, when r is increased to a certain degree, the tracking speed will reach a saturation state and will not increase any more, and when r is too large, the extracted tracking differential signal will oscillate. Delta is a linear interval factor, determines the size of a linear interval, and generally ranges from (0.01-1).
And the algorithm for improving the post-transition process is as follows:
as shown in the above equation, h is the sampling step, y is the output of the system, and e is the deviation between the two. The fhan function is a nonlinear combined function, and the algorithm which is the most basic of the transition process plays a role in extracting differential signals and arranging the transition process for the control system. In TD, the fhan function is important for improving the tracking accuracy. Therefore, the optimization improvement is carried out on the algorithm of the device to obtain better transition effect, and the nonlinear combination optimization diagram is shown in figure 2.
After improving and nonlinear combined optimization of the fhan function, in order to verify the change of the first-order differential signal extracted from the fhan function before and after the improvement, a sinusoidal signal and a step signal are respectively used as excitation signals, and simulation comparison is performed on the excitation signals, and the results are shown in fig. 3 and 4.
As can be seen from fig. 3, a sinusoidal excitation signal is given to the system, the blue line is the target curve, the red line is the tracking extraction signal of the fhan function before improvement, and the black line is the tracking extraction signal of the fhan function after improvement. The amplitude attenuation of the position signal of the original fhan function is 0.05mm, the phase lag is about 4%, the tracking error precision is about 0.02mm, the amplitude attenuation of the position signal of the improved fhan function is 0.04mm, the phase lag is about 3%, and the tracking error precision is about 0.01 mm. This indicates that the fhan function after the improvement design is much improved compared to that before the improvement.
A step excitation signal is given to the system, and as can be seen from fig. 4, the overshoot of the tracking curve before improvement is about 0.01mm, the response time is about 0.03s, the time to reach the steady state is about 0.5s, and the steady state error is about 0.005 mm; the overshoot of the tracking curve after improvement is about 0.01mm, the response time is about 0.01s, the time to reach the steady state is about 0.25s, and the steady state error is about 0.005mm.
And step 2, improving an Extended State Observer (ESO), and improving the performance of the ESO by adjusting the parameter values of beta 01, beta 02, beta 03 and b.
ADRC extracts the dynamic information of the system through ESO, modifies the system characteristics according to the dynamic information, cancels disturbance, and simultaneously ensures the structure and physical significance of the system.
β01、β02、β03Three important parameters of the linear extended state observer play a crucial role in steady state regulation. Wherein beta is increased within a certain range01The observation speed of the system can be improved, but the excessive system will cause violent oscillation, beta01Is approximately in the same order of magnitude as 1/h. Beta is a beta02If the value is too small, the response time of the system is delayed, and a large degree of oscillation occurs. So beta02Need to be within a certain range of values. When beta is03Too small of a device will result in too small of an observation speed of the system, which will result in a phase lag of the system, or even an inability to track the state variable in real time, when β03Too much will cause the system to see too fast and will cause severe oscillations. So beta02，β03Need to be within a certain range of values. After considering the characteristics of various parameters of the system, the improved ESO algorithm is as follows:
Z2is the true second order differential of the system outputSignal, Z3The disturbance state quantity of ESO expansion is the core variable of ESO. Parameter b0Is a "compensation factor" that determines the magnitude of disturbance compensation, i.e., an estimated value of the amplification factor b when the control amount u is applied to the system. By adjusting beta01、β02、β03And b to improve the performance of the ESO, reduce the estimated deviation of the ESO and improve the disturbance elimination capability of the ESO.
And 3, improving a feedback control law (NLSEF), and modifying the fal function by a nonlinear differencing and combining method.
The nonlinear state error feedback control law (NLSEF) is a process of performing nonlinear differencing combining processing on the first two parts of the ADRC.
The input signal v can extract each order of differential state v through the transition process1、v2、…、vn. After the input and output of the system pass through ESO, obtaining each stage state variable z of the controlled object1、z2、…、zn. The error formed by these two sets of variables before entering NLSEF is:
thus, NLSEF is processed by a nonlinear differencing combining method, and several common nonlinear functions are as follows:
a first nonlinear function is adopted, a fal function is improved, and a second-order nonlinear state error feedback control law formula is as follows:
wherein, a1，a2，b1，b2，b3And delta is a parameter variable to be set. b1Similar to the proportional gain factor of a PID controller, increase b1Will increase the system running speed and reduce the static error, thereby improving the tracking accuracy, but too large b1The dynamic performance of the system is reduced and even hunting instability may result. b is a mixture of2Similar to the differential gain coefficient in the PID, the increase within a certain degree can improve the tracking accuracy of the system and accelerate the dynamic response speed of the system. a is1，a2For the error gain coefficient, considering that the electro-hydraulic position servo system needs to realize the target of 'big error and small gain, and small error and big gain', the method can make a1，a2In the range of
0＜a1＜1，1＜a2
When numerical simulation is carried out, in order to avoid high-frequency flutter, the fal function is modified to become a power function with a continuous linear section near the origin. The improved function fal is of the form:
in the formula: δ is the interval length of the linear segment.
And 4, after setting parameters, carrying out simulation analysis and verifying the anti-interference effect of the ADRC control algorithm after improvement.
After the parameters are adjusted, sine signals and step signals are respectively used as excitation signals, and simulation results under the condition of no disturbance are shown in fig. 5 and 6.
As can be seen from fig. 5, in the case of no disturbance, the amplitude attenuation of the original ADRC sinusoid is about 1mm and the phase lag is 6%, while the amplitude attenuation of the modified auto-disturbance-rejection controller sinusoid is about 0.4mm and the phase lag is 4%. It can be seen that the improved tracking of the auto-disturbance rejection controller is better than that of the ADRC controller.
As can be seen from FIG. 6, the overshoot of the ADRC step curve is about 6mm, the response time is about 0.02s, the time to reach the steady state is about 0.5s, and the steady state error is about 0.6 mm; after improvement, the overshoot of the step curve of the active disturbance rejection controller is about 4mm, the response time is about 0.015s, the time for reaching the steady state is about 0.5s, and the steady state error is about 0.4 mm. Meanwhile, the original ADRC has a parameter perturbation problem due to a plurality of internal parameters of the controller, a certain perturbation deviation exists at the beginning, and the improved active disturbance rejection controller has a certain inhibition effect on the perturbation deviation through an improved algorithm designed in section 3.2. The perturbation deviation of the original ADRC is 0.4mm, and the perturbation deviation of the improved active disturbance rejection controller is only 0.2 mm. This shows that the stability of the designed improved auto-disturbance-rejection controller is stronger than that of the original ADRC under the condition of no disturbance.
An interference source signal of the electro-hydraulic position servo system is simulated by white noise, the white noise is given to be 0.1noise power, under the interference condition of the white noise, a sinusoidal excitation signal of 1rad/s and a step excitation signal with the amplitude of 20mm are also given, and the simulation result is shown in fig. 7 and fig. 8.
It can be seen from fig. 7 that, under the influence of white noise, the original ADRC sinusoidal following curve has a certain jitter, the improved auto-disturbance rejection controller has a sinusoidal following curve with only a slight jitter, an amplitude attenuation of about 0.4mm and a phase lag of 4%, the amplitude and the phase of the improved auto-disturbance rejection controller do not change significantly, while the original ADRC following curve has a large jitter waviness, an amplitude attenuation of about 1.2mm and a phase lag of 6.5%, and compared with a noise-free state, the amplitude is increased by 0.2mm and the phase lag amplitude is increased by 0.5%.
As can be seen from FIG. 8, in a white noise environment, the overshoot of the original ADRC step-change curve is about 6mm, the response time is about 0.02s, the time to reach the steady state is about 0.5s, and the steady state error is about 0.6 mm; the overshoot of the step curve of the improved active disturbance rejection controller is about 4mm, the response time is about 0.015s, the time to reach the steady state is about 0.5s, and the steady state error is about 0.4 mm. The step base performance index is substantially similar to that in the noise-free state. But the ADRC parameter perturbation problem is further enhanced. And locally amplifying at 0-0.2 s to obtain the maximum perturbation deviation of the original ADRC, wherein the maximum perturbation deviation is about 0.8mm at the moment, and the maximum perturbation deviation of the improved active disturbance rejection controller is about 0.7mm at the moment. The average perturbation deviation amount of the original ADRC is about 0.4mm, the average perturbation deviation amount of the improved active disturbance rejection controller is about 0.16mm, and the perturbation deviation of the improved active disturbance rejection controller under white noise interference is obviously lower than that of the ADRC. This indicates that the immunity of the improved auto-immunity controller is stronger than ADRC in the white noise condition.
Because the interference source of the electro-hydraulic position servo system is unknown, in order to further verify the anti-interference control effect of the electro-hydraulic position servo system, besides white noise, the square wave interference signal is used for simulating an interference source signal of the electro-hydraulic position servo system. The simulation results are shown in FIG. 9 and FIG. 10 for a square wave interference signal with an amplitude of 1, which is also given a sinusoidal excitation signal with a 1rad/s and a step excitation signal with an amplitude of 20 mm.
As can be seen from fig. 9, under the condition of the interference of the square wave signal, the amplitude attenuation of the original ADRC sinusoid is about 1mm, and the phase lag is 6%, while the amplitude attenuation of the modified sinusoid is about 0.4mm, and the phase lag is 4%. This is not much different from the noise-free state, but in the case of square wave interference, the system will have a following deviation at the beginning, and the maximum following deviation of the improved active disturbance rejection controller is about 0.8mm from the figure, and the maximum following deviation of the original ADRC is about 1.8 mm.
As can be seen from FIG. 10, the overshoot of the original ADRC step curve is about 6mm, the response time is about 0.02s, the time to reach steady state is about 0.5s, and the steady state error is about 0.6 mm; after improvement, the overshoot of the step curve of the active disturbance rejection controller is about 4mm, the response time is about 0.015s, the time for reaching the steady state is about 0.5s, and the steady state error is about 0.4 mm. However, under the action of the square wave interference source with the amplitude of 1, the system has two large jitter deviations. Through local amplification, the two jitter deviations are mainly concentrated in two time periods of 0-0.2 s and 0.5-0.65 s. In the time period of 0-0.2 s, the maximum jitter deviation of the improved active disturbance rejection controller is about 0.15mm, and the maximum jitter deviation of the original ADRC is about 0.2 mm. It can be calculated that the average jitter deviation of the improved ADRC is about 0.08mm, and the average jitter deviation of the original ADRC is about 0.12 mm. In the time period of 0.5-0.65 s, the maximum jitter deviation of the improved active disturbance rejection controller is about 0.12mm, and the maximum jitter deviation of the original ADRC is about 0.2 mm. It can be calculated that the average jitter deviation of the improved ADRC is about 0.04mm, and the average jitter deviation of the original ADRC is about 0.1 mm. This shows that the anti-interference effect of the improved active anti-interference controller is stronger than that of the original ADRC under the action of square wave interference.
The above embodiments are only for illustrating the present invention and not for limiting the present invention, and those skilled in the art can make various changes and modifications without departing from the spirit and scope of the present invention, therefore all equivalent technical solutions also belong to the scope of the present invention, and the protection scope of the present invention should be defined by the claims.
Claims (6)
1. An active disturbance rejection controller improvement method based on an electro-hydraulic servo system is characterized by comprising the following steps:
step 1, improving a Tracking Differentiator (TD) in Active Disturbance Rejection Control (ADRC), and optimizing and improving an algorithm of the tracking differentiator;
step 2, improvement of Extended State Observer (ESO), by adjusting beta01、β02、β03And b to improve the performance of the ESO;
and 3, improving a feedback control law (NLSEF), and modifying the fal function by a nonlinear differencing and combining method.
2. The improvement method of the active disturbance rejection controller based on the electro-hydraulic servo system, according to claim 1, is characterized in that: in step 1, an algorithm of a transition process in the TD is improved, and the improved algorithm is as follows:
in the formula, h is the sampling step length, y is the output of the system, and e is the deviation of the two.
3. The improvement method of the active disturbance rejection controller based on the electro-hydraulic servo system as claimed in claim 2, wherein: in step 1, the fhan function is a nonlinear combination function, and nonlinear combination optimization is performed on the fhan function in the TD so as to obtain a better transition effect.
4. The improvement method of the active disturbance rejection controller based on the electro-hydraulic servo system, according to claim 1, is characterized in that: in step 2,. beta.01、β02、β03For three important parameters of the linear extended state observer, beta is increased within a certain range01，β01Is approximately in the same order of magnitude as 1/h, beta02，β03Need to be within a certain range of values. After considering the characteristics of various parameters of the system, the improved ESO algorithm is as follows:
in the formula, Z2Is a true second order differential signal, Z, output by the system3The disturbance state quantity of ESO expansion is the core variable of ESO. Parameter b0Is a "compensation factor" that determines the magnitude of disturbance compensation, i.e., an estimated value of the amplification factor b when the control amount u is applied to the system.
5. The improvement method of the active disturbance rejection controller based on the electro-hydraulic servo system, according to claim 1, is characterized in that: in step 3, p is0＝β1fal(e1，a1，δ)+β2fal(e2，a2δ), improving the fal function, and the second-order nonlinear state error feedback control law formula is as follows:
in the formula, a1，a2，b1，b2，b3Delta is a parameter variable to be set; b1Similar to the proportional gain factor of a PID controller, increase b1Will increase the system running speed and reduce the static error, thereby improving the tracking accuracy, but too large b1The dynamic performance of the system is reduced, and even the oscillation performance is unstable; b is a mixture of2Similar to the differential gain coefficient in the PID, the increase in a certain degree can improve the tracking precision of the system and accelerate the dynamic response speed of the system; a is1，a2For the error gain coefficient, considering that the electro-hydraulic position servo system needs to realize the target of 'big error and small gain, and small error and big gain', the method can make a1，a2In the range of 0 < a1＜1，1＜a2。
6. The improvement method of the active disturbance rejection controller based on the electro-hydraulic servo system is characterized by comprising the following steps of: when numerical simulation is carried out, in order to avoid high-frequency flutter, the fal function is modified to become a power function with a continuous linear section near the origin. The improved function fal is of the form:
where δ is the interval length of the linear segment.
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