CN108919652B - Adaptive anti-interference shaping control method and system - Google Patents

Adaptive anti-interference shaping control method and system Download PDF

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CN108919652B
CN108919652B CN201811177228.2A CN201811177228A CN108919652B CN 108919652 B CN108919652 B CN 108919652B CN 201811177228 A CN201811177228 A CN 201811177228A CN 108919652 B CN108919652 B CN 108919652B
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魏伟
左敏
邵妍洁
马蓉
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Beijing Technology and Business University
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    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
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Abstract

The invention discloses a self-adaptive disturbance rejection shaping control system, which comprises an input shaper, a closed-loop control system and an algebraic estimator, wherein the output y expected by the systemdInput to the input shaper for the desired output ydShaping, outputting y after shapingdiOutputting a system output quantity y to a closed-loop control system by the closed-loop control system; the output quantity y of the system and the output quantity y of the input shaperdiAll the data are sent to an algebraic estimator, the algebraic estimator accurately estimates the actual closed-loop transfer function information of the system according to the received data, and the estimation result is transmitted to an input shaper.

Description

Adaptive anti-interference shaping control method and system
Technical Field
The invention relates to the technical field of advanced control, in particular to an anti-interference control and input shaping technology in the advanced control technology, and specifically relates to a novel anti-interference control method and a novel anti-interference control system based on adaptive input shaping.
Background
In an industrial site, the system output is greatly affected (the system output is deviated from a set value) by a change in a parameter inside the system, unmodeled dynamics, or by external disturbance of the system. Therefore, a control method for resisting disturbance inside/outside the system and ensuring the performance of the system is a key problem to be solved in the practical application of the automatic control system. Modern control theory is fruitful, but the classical proportional-integral-derivative control is still widely used in industrial fields due to the fact that the modern control theory is over-dependent on a system model.
In fact, any model cannot accurately describe the controlled object, and the controlled object is affected by various uncertain factors (disturbances). Therefore, the method for realizing the control target by getting rid of dependence on the model and relying on the input and output data of the controlled object instead has strong application value. Active disturbance rejection control is one such control method. The method has small dependence on a controlled object model, estimates information such as system output, output change rate, total disturbance and the like in real time by utilizing input and output data, and further constructs a control law based on the information. However, the setting of the parameters of the active disturbance rejection control depends on experience, and transient oscillation occurs in system response when the setting of the parameters is not ideal; in addition, the extended state observer in the active disturbance rejection control has a good estimation effect only on constant disturbance, and for time-varying disturbance, the estimation is biased, which also causes oscillation of the transient response of the system. Transient oscillation not only means that the output cannot be quickly set and cannot meet the high-precision control requirement, but also means that the system needs to replace the output following setting with larger energy consumption. However, these phenomena are unacceptable under the large background of high precision control requirements and energy saving and emission reduction.
Therefore, the invention provides a self-adaptive anti-interference shaping control method, which integrates the advantages of self-adaptive thought, input shaping and auto-interference-rejection control, and utilizes a self-adaptive input shaper to eliminate the transient oscillation of system response and shorten the time of a transition process; by means of the characteristics of small dependence on a model, strong robustness and simple structure of active disturbance rejection control, the robustness of the system is enhanced while the control speed and the control precision of the system are improved. Meanwhile, the problem that input shaping has large dependence on a model is overcome; the time-varying disturbance of the active disturbance rejection estimation has deviation, and when the parameter setting is not ideal, the transient oscillation and the transition process are long.
Disclosure of Invention
The invention provides a self-adaptive anti-interference shaping control method, which is a practical control technology of engineering, and comprehensively utilizes the advantages of a self-adaptive algebraic estimation technology, an active anti-interference control technology and an input shaping technology, thereby not only eliminating transient oscillation, shortening the time of a transition process, reducing the difficulty of setting the active anti-interference control parameters, but also avoiding excessive dependence of the input shaping technology on a model and improving the robustness of the system.
In order to realize the purpose of the invention, the following technical scheme is adopted for realizing the purpose:
an adaptive immunity shaping control system comprising an input shaper, a closed-loop control system and an algebraic estimator, wherein: desired output y of the systemdInput to the input shaper for the desired output ydShaping to obtain a shaped output ydiThe output is input to a closed-loop control system, and the closed-loop control system outputs a system output quantity y; the output quantity y of the system and the output quantity y of the input shaperdiAll the data are sent to an algebraic estimator, the algebraic estimator estimates the actual closed-loop transfer function information of the system according to the received data, and the calculated result is transmitted to an input shaper.
The control system described, wherein: actual closed loop transfer function G of closed loop control system0(s) is:
Figure BDA0001824077110000021
wherein the damping ratio xi and the angular frequency omeganUnknown, KfFor magnification, s is the laplacian operator.
The control system described, wherein:
let K in formula (6)fIs 1 and is written in the form of a differential equation with:
Figure BDA0001824077110000031
wherein y (t) is the output of the controlled object, and under the non-zero initial condition, the Laplace transform is carried out on the formula (7) by
Figure BDA0001824077110000032
At zero initial conditions, comparing equations (7) and (8), there are:
Figure BDA0001824077110000033
wherein, ω isn,estAnd xiestRespectively damping ratio omeganAnd an estimate of the angular frequency xi, alpha1Is the first coefficient to be determined; alpha is alpha2Is the second predetermined coefficient.
The control system described, wherein:
to eliminate the influence of the initial conditions, the formula (8) was differentiated twice:
Figure BDA0001824077110000034
through calculation, the following can be obtained:
Figure BDA0001824077110000035
the numerator and denominator of formula (11) are multiplied by s-2The method comprises the following steps:
Figure BDA0001824077110000036
according to
Figure BDA0001824077110000041
And
Figure BDA0001824077110000042
(where L is the Laplace transform operator, v is the order of differentiation, and σ is the integral variable), transforming equation (12) back to the time domain,
η1(t)+α1η2(t)+α2η3(t)＝0 (13)
wherein the content of the first and second substances,
Figure BDA0001824077110000043
order to
η1＝t2y+x1，η2＝x3，η3＝x5，η1=t2y+x1，η2＝x3，η3＝x5，
Figure BDA0001824077110000044
Wherein x is1,x2,x3,x4,x5,x6,η1,η2,η3Is a state variable.
Integrating equation (13) on both sides, there is:
Figure BDA0001824077110000045
as a result of this, the number of the,
Figure BDA0001824077110000046
thus, the unknown parameter ωn,estAnd xiestCan be calculated by the formula (9), and the algebraic estimator estimates the parameter omega by the formula (9)n,estAnd xiestAnd will estimate the resulting ωn,estAnd xiestThe value of (c) is passed to the shaper.
The control system described, wherein: using estimated parameters omegan,estAnd xiestAnd order KfFor 1, then equation (6) can be written as:
Figure BDA0001824077110000051
order to
Figure BDA0001824077110000052
Where K is the gain factor, tdIs a delay time.
The control system described, wherein: the input shaper is a zero vibration shaper that provides the desired output y to the system according to equation (18)dShaping:
Figure BDA0001824077110000053
wherein A isi,tiFor applying the amplitude and corresponding time of the pulse, the ZV shaper is a two-pulse train shaper, so that the pulse amplitude given at zero time is
Figure BDA0001824077110000054
0.5tdThe pulse applied at a time has an amplitude of
Figure BDA0001824077110000055
The control system described, wherein: the input shaper is a zero-vibration robust shaper,
the shaper expects an output y for the system according to equation (19)dShaping:
Figure BDA0001824077110000056
wherein A isi,tiAlso for the amplitude and corresponding time of the applied pulse, ZVR is a four-pulse second order robust zero vibration shaper; thus, the amplitude of the applied pulse at time zero is
Figure BDA0001824077110000057
0.5(td+ta) The pulse applied at a time has an amplitude of
Figure BDA0001824077110000058
td+taAt the moment of applying a pulse of amplitude of
Figure BDA0001824077110000059
1.5(td+ta) The pulse applied at a time has an amplitude of
Figure BDA00018240771100000510
taFor additional time, C ═ 1+3K2+K3。
An adaptive immunity shaping control method, comprising: (1) aiming at a controlled object, designing an active disturbance rejection controller; (2) establishing an algebraic estimator according to input and output data of a closed-loop control system consisting of the active disturbance rejection controller and a controlled object, and estimating the damping ratio and the angular frequency of the closed-loop system in real time; (3) using the estimated damping ratio and angular frequency, the shaper is designed to give the desired output y to the systemdAnd after shaping, inputting the shaped data into a closed-loop control system.
Drawings
FIG. 1 is a block diagram of the system of the present invention;
FIG. 2 is a flow chart of the present invention;
FIG. 3 is a schematic diagram of a conventional active disturbance rejection control system
Detailed Description
Hereinafter, a detailed description will be given of a specific embodiment of the present invention with reference to fig. 1 to 3.
In the active disturbance rejection control system, y is shown in FIG. 3dIs the system output, u is the control law, and y is the system output. The extended state observer estimates and compensates the interference signal influencing the output of the system in real time. Controlled system in second order
Figure BDA0001824077110000061
For example, the state space expression of the linear extended state observer is:
Figure BDA0001824077110000062
wherein, beta1、β2、β3Is a parameter to be determined, z1、z2、z3Is the state variable of the extended state observer, estimates the system output y respectively,
Figure BDA0001824077110000063
and the total system disturbance (denoted as f).
The control law is designed as follows:
Figure BDA0001824077110000064
wherein k isp,kd,b0Is a parameter adjustable by the controller.
Ideally then, the three outputs of the extended state observer are estimated accurately, namely: z is a radical of1＝y，
Figure BDA0001824077110000071
z3When f, the system closed-loop equation is:
Figure BDA0001824077110000072
thus, the closed loop transfer function can be written as:
Figure BDA0001824077110000073
ideally, the transfer function g(s) of the closed-loop system formed by the active disturbance rejection control and the controlled object is shown as the formula (4). However, the above-mentioned transfer function g(s) only holds in the ideal case. The accuracy of the input shaper to the closed loop transfer function is very demanding. Therefore, the auto-disturbance rejection control parameters need to be well set, so that the closed-loop system is closer to the transfer function (4).
To this end, the present invention proposes a new adaptive immunity shaping control system, as shown in fig. 1, which includes an input shaper, a closed-loop control system, and an algebraic estimator. Wherein the closed-loop control system comprises an active disturbance rejection controller and a controlled object. In fig. 1, the closed-loop control system formed by the active disturbance rejection controller and the controlled object is indicated by a dashed box. Ideally, the transfer function of the closed loop control system is g(s) as shown in equation (4). However, the transfer function of an actual closed loop control system is not. Therefore, an input shaper needs to be constructed according to the actual transfer function of the closed-loop system, so that transient oscillation is eliminated, the time of the transient process is shortened, and the control precision is improved. In addition, in the system, the input shaper is designed according to the closed-loop transfer function of the system, and the accuracy of the actual closed-loop transfer function of the system is high. However, the transfer function g(s) is only an ideal expression. Therefore, the invention designs an algebraic estimator to correct closed-loop transfer function information in real time for designing an input shaper, thereby achieving the purposes of reducing transient oscillation, shortening the time of a transition process and improving the control precision.
Finally, the adaptive anti-interference shaping control is realized, and the expected target is achieved through the adaptive anti-interference shaping control system.
As shown in fig. 1, the desired output y of the systemdInput to the input shaper for the desired output ydShaping, the shaped output ydiInputting an active disturbance rejection controller, and simultaneously generating a control signal to control a controlled object according to the output y of the controlled object by the active disturbance rejection controller so as to obtain the output y of the controlled object; the algebraic estimator depends on the system output y and the output y of the input shaperdiAccurately estimating the actual closed loop transfer function of the system, and transmitting the calculation result to the input shaper, which is used for y according to the resultdAnd (6) shaping.
The working principle of the invention is illustrated as follows:
actual closed loop transfer function G formed by active disturbance rejection controller and controlled object0(s) is:
Figure BDA0001824077110000081
wherein the damping ratio xi and the angular frequency omeganUnknown, KfFor magnification, s is LaplaceAn operator; get Kf1, there is:
Figure BDA0001824077110000082
wherein, y(s) and ydi(s) are the laplace transform of the system output and the input shaper output, respectively. Writing equation (6) in the form of a differential equation, there is:
Figure BDA0001824077110000083
wherein y (t) is the output of the controlled object, and under the non-zero initial condition, the Laplace transform is carried out on the formula (7) by
Figure BDA0001824077110000084
At zero initial conditions, comparing equations (7) and (8), there are:
Figure BDA0001824077110000091
wherein, ω isn,estAnd xiestRespectively damping ratio omeganAnd an estimate of the angular frequency xi, alpha1Is the first coefficient to be determined; alpha is alpha2Is the second predetermined coefficient;
to eliminate the influence of the initial conditions, the formula (8) was differentiated twice:
Figure BDA0001824077110000092
through calculation, the following can be obtained:
Figure BDA0001824077110000093
the numerator and denominator of formula (11) are multiplied by s-2The method comprises the following steps:
Figure BDA0001824077110000094
according to
Figure BDA0001824077110000095
And
Figure BDA0001824077110000096
(where L is the Laplace transform operator, v is the order of differentiation, and σ is the integral variable), transforming equation (12) back to the time domain,
η1(t)+α1η2(t)+α2η3(t)＝0 (13)
wherein the content of the first and second substances,
Figure BDA0001824077110000097
order to
η1＝t2y+x1，η2＝x3，η3＝x5，η1=t2y+x1，η2＝x3，η3＝x5，
Figure BDA0001824077110000101
Wherein x is1,x2,x3,x4,x5,x6,η1,η2,η3Is a state variable.
Integrating equation (13) on both sides, there is:
Figure BDA0001824077110000102
as a result of this, the number of the,
Figure BDA0001824077110000103
thus, the unknown parameter ωn,estAnd xiestIt can be calculated by equation (9), i.e.: the parameter omega is estimated by the algebraic estimator through the formula (9)n,estAnd xiestThe value of (c).
To obtain omegan,estAnd xiestThe input shaper can then be designed to eliminate transient oscillations and reduce transient process time. Also, taking a second-order system as an example, the estimated parameter ω is utilizedn,estAnd xiest. (6) The formula can be written as:
Figure BDA0001824077110000104
order to
Figure BDA0001824077110000105
Where K is the gain factor, tdIs a delay time. Then, for the closed loop control system (17),
(1) design Zero Vibration (Zero Vibration) shaper
Figure BDA0001824077110000106
Wherein A isi,tiThe amplitude and corresponding time of the applied pulse. The ZV shaper is a two-pulse train shaper, so that the pulse amplitude given at zero time is
Figure BDA0001824077110000111
0.5tdThe pulse applied at a time has an amplitude of
Figure BDA0001824077110000112
The above-mentioned ZV shaper is accurate to the system model, i.e. the damping ratio omeganAnd angular frequency xi, is highly required. If there is estimation error in damping ratio and angular frequency, the effect of the ZV shaper in suppressing transient oscillation will be affected. In order to obtain better transient oscillation suppression effect, the inventionThe following shaper is further constructed.
(2) Design Zero Vibration Robust (ZVR) shaper
Figure BDA0001824077110000113
Wherein A isi,tiAlso for the amplitude and corresponding time of the applied pulse, ZVR is a four pulse robust zero vibration shaper. Thus, the amplitude of the applied pulse at time zero is
Figure BDA0001824077110000114
0.5(td+ta) The pulse applied at a time has an amplitude of
Figure BDA0001824077110000115
td+taAt the moment of applying a pulse of amplitude of
Figure BDA0001824077110000116
1.5(td+ta) The pulse applied at a time has an amplitude of
Figure BDA0001824077110000117
taFor additional time, it depends on kpAnd kdThe size relationship of (1):
Figure BDA0001824077110000118
here, C is 1+3K2+K3K is the gain factor, Kp,kdIs an adjustable control parameter in the formula (2).
The invention comprehensively utilizes the advantages of the adaptive algebraic estimation technology, the active disturbance rejection control technology and the input shaping technology, can eliminate transient oscillation, shorten the time of a transition process, reduce the difficulty of setting the active disturbance rejection control parameters, avoid the excessive dependence of the input shaping technology on a model, and finally obtain the effects of improving the control performance of the system and enhancing the robustness of the system.
As shown in fig. 1 and fig. 3, the adaptive anti-interference shaping control method includes the following steps: aiming at a controlled object, an active disturbance rejection controller is designed, adjustable control parameters of the active disturbance rejection controller are adjusted, the estimation effect of the extended state observer is improved, and the system is better close to an ideal closed-loop transfer function; according to the input and output data of the closed-loop system formed by the active disturbance rejection control and the controlled object, an algebraic estimator is established to estimate the damping ratio omega of the closed-loop system in real timen,estSum angular frequency xiest(the specific procedure is as described above for the system); using estimated damping ratio omegan,estSum angular frequency xiestAnd a shaper is designed to reduce transient oscillation, shorten the time of a transition process and improve the control precision.

Claims (3)

1. An adaptive immunity shaping control system, comprising an input shaper, a closed-loop control system and an algebraic estimator, characterized by: desired output y of the systemdInput to the input shaper for the desired output ydShaping to obtain a shaped output ydiThe output is input to a closed-loop control system, and the closed-loop control system outputs a system output quantity y; the output quantity y of the system and the output quantity y of the input shaperdiThe data are sent to an algebraic estimator, the algebraic estimator estimates the actual closed-loop transfer function information of the system according to the received data, and the calculated result is transmitted to an input shaper; actual closed loop transfer function G of closed loop control system0(s) is:
Figure FDA0002939576870000011
wherein the damping ratio xi and the angular frequency omeganUnknown, KfIs the magnification factor, s is the Laplace operator;
let K in formula (6)fIs 1 and is written in the form of a differential equation with:
Figure FDA0002939576870000012
wherein y (t) is the output of the controlled object, and under the non-zero initial condition, the Laplace transform is carried out on the formula (7) by
Figure FDA0002939576870000013
At zero initial conditions, comparing equations (7) and (8), there are:
Figure FDA0002939576870000014
wherein, ω isn,estAnd xiestRespectively damping ratio omeganAnd an estimate of the angular frequency xi, alpha1Is the first coefficient to be determined; alpha is alpha2Is the second predetermined coefficient;
to eliminate the influence of the initial conditions, the formula (8) was differentiated twice:
Figure FDA0002939576870000021
through calculation, the following can be obtained:
Figure FDA0002939576870000022
the numerator and denominator of formula (11) are multiplied by s-2The method comprises the following steps:
Figure FDA0002939576870000023
according to
Figure FDA0002939576870000024
And
Figure FDA0002939576870000025
(wherein L is a Laplace transform operator, v is a differential order, and σ is an integral variable, the formula (12) is converted back to the time domain,
η1(t)+α1η2(t)+α2η3(t)＝0 (13)
wherein the content of the first and second substances,
Figure FDA0002939576870000026
let eta be1＝t2y+x1,η2＝x3,η3＝x5,η1＝t2y+x1,η2＝x3,η3＝x5,
Figure FDA0002939576870000027
Wherein x is1,x2,x3,x4,x5,x6,η1,η2,η3Is a state variable;
integrating equation (13) on both sides, there is:
Figure FDA0002939576870000028
as a result of this, the number of the,
Figure FDA0002939576870000031
thus, the unknown parameter ωn,estAnd xiestCan be calculated by the formula (9), and the algebraic estimator estimates the parameter omega by the formula (9)n,estAnd xiestAnd will estimate the resulting ωn,estAnd xiestThe value of (c) is passed to the shaper.
2. Control according to claim 1The system is characterized in that: using estimated parameters omegan,estAnd xiestAnd order KfFor 1, then equation (6) can be written as:
Figure FDA0002939576870000032
order to
Figure FDA0002939576870000033
Where K is the gain factor, tdIs a delay time.
3. An adaptive immunity shaping control method, comprising: (1) aiming at a controlled object, designing an active disturbance rejection controller; (2) establishing an algebraic estimator according to input and output data of a closed-loop control system consisting of the active disturbance rejection controller and a controlled object, and estimating the damping ratio and the angular frequency of the closed-loop system in real time; (3) using the estimated damping ratio and angular frequency, the shaper is designed to give the desired output y to the systemdAfter shaping, inputting the shaped data into a closed-loop control system; wherein:
actual closed loop transfer function G of closed loop control system0(s) is:
Figure FDA0002939576870000034
wherein the damping ratio xi and the angular frequency omeganUnknown, KfIs the magnification factor, s is the Laplace operator;
let K in formula (6)fIs 1 and is written in the form of a differential equation with:
Figure FDA0002939576870000041
wherein y (t) is the output of the controlled object, and under the non-zero initial condition, the Laplace transform is carried out on the formula (7) by
Figure FDA0002939576870000048
At zero initial conditions, comparing equations (7) and (8), there are:
Figure FDA0002939576870000042
wherein, ω isn,estAnd xiestRespectively damping ratio omeganAnd an estimate of the angular frequency xi, alpha1Is the first coefficient to be determined; alpha is alpha2Is the second predetermined coefficient;
to eliminate the influence of the initial conditions, the formula (8) was differentiated twice:
Figure FDA0002939576870000043
through calculation, the following can be obtained:
Figure FDA0002939576870000044
the numerator and denominator of formula (11) are multiplied by s-2The method comprises the following steps:
Figure FDA0002939576870000045
according to
Figure FDA0002939576870000046
And
Figure FDA0002939576870000047
(wherein L is a Laplace transform operator, v is a differential order, and σ is an integral variable, the formula (12) is converted back to the time domain,
η1(t)+α1η2(t)+α2η3(t)＝0 (13)
wherein the content of the first and second substances,
Figure FDA0002939576870000051
order to
η1＝t2y+x1,η2＝x3,η3＝x5,η1＝t2y+x1,η2＝x3,η3＝x5,
Figure FDA0002939576870000052
Wherein x is1,x2,x3,x4,x5,x6,η1,η2,η3Is a state variable;
integrating equation (13) on both sides, there is:
Figure FDA0002939576870000053
as a result of this, the number of the,
Figure FDA0002939576870000054
thus, the unknown parameter ωn,estAnd xiestCan be calculated by the formula (9), and the algebraic estimator estimates the parameter omega by the formula (9)n,estAnd xiestAnd will estimate the resulting ωn,estAnd xiestThe value of (d) is transmitted to the shaper;
using estimated parameters omegan,estAnd xiestAnd order KfFor 1, then equation (6) can be written as:
Figure FDA0002939576870000055
order to
Figure FDA0002939576870000056
Where K is the gain factor, tdIs a delay time.
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