CN110442026A - Extended state observer, disturbance rejection control system and design method based on error correction - Google Patents
Extended state observer, disturbance rejection control system and design method based on error correction Download PDFInfo
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Abstract
The invention discloses a kind of antidisturbance control systems, including extended state observer, controller and controlled device based on error correction, in which: the estimated value that the extended state observer is used to generate the system mode of controlled device according to the output signal of control signal and controlled device and always disturbs；The controller is used to generate the control signal u comprising interference compensation according to the system state estimation value, total disturbance estimated value and setting value r, and control signal u is inputed to controlled device.
Description
Technical field
The present invention relates to control technology fields, are the antidisturbance control technologies in Advanced Control Techniques by it, specifically
It is related to a kind of extended state observer design method and disturbance rejection control system based on error correction.
Background technique
Active Disturbance Rejection Control gets the attention and answers because of the advantages such as its strong antijamming capability, small to model information dependence
With.However, the core of Active Disturbance Rejection Control --- the estimated capacity limitation problem of extended state observer is limitation Active Disturbance Rejection Control
The key of performance boost.
The extended state observer design method and disturbance rejection control system that the invention proposes a kind of thus based on error correction
System can be improved the estimated capacity of observer, reduction evaluated error enhances observer under the premise of not introducing nonlinear
Estimate the ability of time-varying disturbance.
Summary of the invention
Purpose to realize the present invention, is achieved using following technical scheme:
A kind of antidisturbance control system, including extended state observer, controller and controlled device based on error correction,
Wherein: the system that the extended state observer is used to generate controlled device according to the output signal of control signal and controlled device
State estimation z1And z2With total disturbance estimated value z3；The controller is used to be estimated according to the system state estimation value, total disturbance
Evaluation and setting value r generate the control signal u comprising interference compensation, and control signal u is inputed to controlled device；Wherein base
It is expressed as follows in the extended state observer formula 7 of error correction:
z1,z2,z3For the output of extended state observer, output change rate and the always estimation that disturbs, β=[β1,β2,β3]T
For observer gain, p1=y,b0For adjustable control gain.
The antidisturbance control system, in which: controller is expressed as follows by formula (8), (9):
In formula, kp,kdThe respectively ratio and the differential gain of controller, r are setting value, u0It is for without interference compensation
Control signal；
Controller considers that the design of control law of total disturbance estimated value is
Wherein, controller parameter iskd=2 ωc=2.
A kind of design method of disturbance rejection control system, comprising the following steps:
Step 1: design general linear extended state observer
Design a second order single-input single-output nonlinear system:
In formula (1): y is system output,It is internal system dynamic, d is bounded external disturbance, and u is control input；
Enable b0For the estimation for controlling gain b, noteIt is always disturbed for system, defines x1=y,Formula (1) is rewritten as
In formula, x=[x1,x2,x3]TFor system state variables,
General linear extended state observer (linear extended state observer, LESO) is designed as
In formula, β=[β1,β2,β3]TFor observer gain, in the suitable situation of value, observer exports ξ=[ξ1,ξ2,
ξ3]TEnergy real-time estimation system mode, i.e. ξ → x；
Observer gain is set asTake ωo=9, system is applied sinusoidal
F=sin (t/2-30+ pi/2)+1 is disturbed, it is as follows
Step 2: the extended state observer of design point error correction
The general linear extended state observer (3) obtained according to step 1, the extended state observer (4) of design modification:
In formula (4), p1=y,z1,z2,z3Estimation exports the change rate of y, output respectivelyWith total disturbanceβ1,β2,β3For observer gain, b0For adjustable control gain, u is control signal；Wherein, state x1Observation
Error is e1=z1-x1=z1-p1；State x2Observation error takeState x3Observation error be e3
=z3-x3=z3-f；
Step 3: extended state observer of the design based on error correction
The modified extended state observer obtained according to step 2 designs total disturbance based on different conditions proportional integration
Estimate (6), form the extended state observer (7) based on error correction:
In formula (4), what is always disturbed is estimated as state x1Observation error e1=z1-x1=z1-p1It is multiplied by gain and integrates, by
Formula (4) can obtain
Consideration system (2), hasThereforeThen, new total disturbance
Estimation may be designed as
Extended state observer design based on error correction are as follows:
Wherein, z1,z2,z3For the output of extended state observer, output change rate and the always estimation that disturbs, β=[β1,β2,
β3]TFor observer gain, p1=y,b0For adjustable control gain, u is control signal；
Step 4: designing the control law of controller
In the controller, consider setting value derivative information as available feed-forward signal
In formula, kp,kdThe respectively ratio and the differential gain of controller, r are setting value, u0It is free from the control of interference compensation
Signal processed；
Consider that total design of control law for disturbing estimated value is
Wherein, controller parameter iskd=2 ωc=2；
Step 5: forming closed loop disturbance rejection control system
The control amount obtained according to step 4 is applied separately in observer and controlled device, forms closed loop disturbance rejection control
System.
Detailed description of the invention
Attached drawing 1 is the structural block diagram of disturbance rejection control system of the invention；
Attached drawing 2 is disturbance rejection control system design flow figure of the invention；
Attached drawing 3 is present invention control and estimated result comparison diagram.
Specific embodiment
Detailed description of the preferred embodiments by 1-3 with reference to the accompanying drawing.
Fig. 1 is the structural block diagram of disturbance rejection control system of the invention.The control system includes the expansion based on error correction
State observer (ECESO), controller (Controller) and controlled device (plant).The expansion based on error correction
State observer is used to generate the system state estimation value of controlled device according to the output signal of control signal and controlled device；Institute
Controller is stated for generating the control input letter comprising interference compensation according to the system state estimation value and given signal r
Number, and the control input signal is applied to controlled device.
The disturbance rejection control system designs as follows:
Step 1: design general linear extended state observer
Design a second order single-input single-output nonlinear system:
In formula (1): y is system output,It is internal system dynamic, d is bounded external disturbance, and u is control input.
Enable b0For the estimation for controlling gain b, noteIt is always disturbed for system, defines x1=y,Then formula (1) is rewritable is
In formula, x=[x1,x2,x3]TFor system state variables,
General linear extended state observer (linear extended state observer, LESO) is designed as
In formula, β=[β1,β2,β3]TFor observer gain, in the suitable situation of value, observer exports ξ=[ξ1,ξ2,
ξ3]TEnergy real-time estimation system mode, i.e. ξ → x.
Observer gain is set asωoFor observer bandwidth, ω is takeno=
9.For the estimation effect that test different types Design of Observer disturbs variety classes, time segment setting disturbance.That is: one
Start not applying disturbance；In t=20s, simplified system concatenated to two-integrator applies unit step and disturbs f=1；In t=
When 40s, applies the slope changed over time to system and disturb f=0.05 (t-40)+1；In t=40s, system is applied just
String disturbs f=sin (t/2-30+ pi/2)+1.Have
Step 2: modified extended state observer
The general linear extended state observer (3) obtained according to step 1, design are based on the modified expansion shape of state error
State observer (4):
It is noted that in formula (3),With ξ2,With ξ3+b0U all adoption status x1Observation error e1=ξ1-x1=ξ1- y comes
Amendment.This amendment is used for estimated state x1It is reasonable, but is used for estimated state x2It is conservative.Therefore it should reconstruct for estimating
Meter state x2Correction term.State x2Observation error be e2=ξ2-x2, but because of x2It needs to estimate, i.e. x2True value it is unknown, and ξ1Estimate
Count x1AndSo, observer internal signal can be usedApproximate x2True value, for correctingThen, state x2
Observation error beThen the extended state observer of use state error correction is designed as
In formula (4), p1=y,z1,z2,z3Estimation exports the change rate of y, output respectivelyWith total disturbanceβ1,β2,β3For observer gain, b0For adjustable control gain, u is control signal；Wherein, state x1Observation
Error is e1=z1-x1=z1-p1；State x2Observation error takeState x3Observation error be e3
=z3-x3=z3-f。
Step 3: extended state observer of the design based on error correction
The modified extended state observer obtained according to step 2 designs new total disturbance estimation (6), forms new expansion
It opens state observer (7):
In formula (4), what is always disturbed is estimated as state x1Observation error e1=z1-x1=z1-p1It is multiplied by gain and integrates.This
Kind method is stable state indifference to constant value disturbance, but is also conservative.It can be obtained by formula (4)
Consider formula (2), hasThereforeThen, new total disturbance
Estimation may be designed as
As it can be seen that new total disturbance is estimated as state x1Observation error integral and state x2Observation error ratio it
With.
To sum up, the new extended state observer based on error correction may be designed as:
Wherein, z1,z2,z3It disturbs for the output of extended state observer based on error correction, output change rate and always
Estimation, β=[β1,β2,β3]TFor observer gain, p1=y,b0For adjustable control gain, u is control signal.
Step 4: designing the control law of controller
The observer output obtained according to step 3 considers the derivative feed-forward information of setting value r, the control of design proportion differential
Device:
To obtain better tracking effect, in the controller, consider setting value derivative information as available feed-forward signal
In formula, kp,kdThe respectively ratio and the differential gain of controller, r are setting value, u0It is free from the control of interference compensation
Signal processed.
Consider that total design of control law for disturbing estimated value is
Wherein, controller parameter iskd=2 ωc=2, ωcFor controller bandwidth.
Step 5: forming closed loop
The control amount obtained according to step 4 is applied separately in observer and controlled device (system), forms closed loop system
System, to realize disturbance estimation and system closed-loop control function.
Simulation result is as shown in Figure 3, wherein figure (a) is the tracing control result of emulation；Figure (b) gives three kinds of observations
Device estimates the effect always disturbed；Figure (c) gives the partial enlargement effect on estimation slope and sinusoidal perturbation.
The root mean square of the error of three kinds of observer estimating systems, three states is listed in table 1, wherein LESO is linear expansion
State observer, POESO are the extended state observer of phase optimization, and ECESO is the expansion state observation based on error correction
Device (error correction based extended state observer, ECESO).
The data in table are compared, it is obvious that the observer proposed all has three states of system
The smallest observation error.That is, the extended state observer based on error correction has best when choosing identical parameter
Estimation effect.
The state estimation error of 1 observer of table compares
ECESO has good estimation effect, and existing brief analysis is as follows.
Compare for convenience, by ξ in formula (3)3It is denoted as z3L, by z in formula (7)3It is denoted as z3E。
Z can be obtained by formula (3)3LTransmission function is
Second equation can be written as in formula (2) again
Then f=s2y-b0U has
Z can be obtained by formula (7)3NTransmission function is
It can similarly obtain
If different observers are respectively to total disturbance evaluated errorHave
When total disturbance is the step signal, i.e. f=K/s that amplitude is K, stable state estimated bias is respectively
From formula (18) it can be seen that the constant value disturbance this kind of for step of two kinds of observers, can accomplish that stable state estimates nothing
Difference.However, the ramp signal for being K for amplitude, i.e. f=K/s ought be disturbed always2When, stable state estimated bias is respectively
This shows that linear extended state observer estimation slope disturbance has a deviation, and observer proposed by the present invention, estimation
Deviation is zero.
In view of f=s2y-b0U, formula (16), (17) can be written as respectively
By formula (20), (21), with j ω replace s can be to the phase of total disturbance evaluated error
Phase difference is
Due toIt can obtainThat is, observer is to the estimation z always disturbed3NPhase is ahead of z3L。
For continuous cycles uncertain disturbance f (t)=Ksin (ω t), K and ω are respectively the amplitude and frequency of sinusoidal signal
Rate.Quantitatively to seek observer for the estimated bias of sinusoidal perturbation, observed deviation e=z-x is defined, by (2), (3) obtain system
Error dynamics are
It is rewritable to be
In formula
It solves (25), has
Since there is matrix A negative characteristic value to have in the case where initial error e (0) bounded
Then, the second part of selective analysis formula (26) enables
In the case that assuming that h (t)=K ω cos (ω t) has when sinusoidal interference
Integration by parts (29)
Due to matrixIt is positive definite, reversible, therefore
Then
Formula (32) shows that the upper bound of evaluated error and the frequencies omega of sinusoidal perturbation, amplitude K and matrix A are related.Due to disturbance
Frequency and amplitude ω, K determine that matrix A is determined by the construction of observer by disturbing itself.Then, quantitative analysis difference observer
When design, the boundary of sinusoidal perturbation observation error is estimated.To distinguish, the matrix of note linear expansion observer is AL；It is new to propose
Observer matrix be AE.Have
ByIt is acquired in linear extended state observer evaluated error by formula (32)
BoundaryFor
By formula (2), (7) are obtained
Similarly, the observer evaluated error upper bound of proposition is acquired by formula (32)For
Due toTherefore proposed observer estimation misses
First and second of difference are less than linear extended state observer, and comparison result is consistent with the data in table 1.
Using the estimated value of the error correction estimated state of estimated state, so that state estimation is more quasi-, therefore, the present invention
Advantage be faster, more quasi-ly obtain system state estimation value and always disturb estimated value, and then improve whole system
Control effect.
Claims (2)
1. a kind of antidisturbance control system, including extended state observer, controller and controlled device based on error correction,
Be characterized in that: the extended state observer is used to generate controlled device according to the output signal of control signal and controlled device
System state estimation value z1And z2With total disturbance estimated value z3；The controller is used to according to the system state estimation value, always disturb
Dynamic estimated value and setting value r generate the control signal u comprising interference compensation, and control signal u is inputed to controlled device；Its
In the extended state observer formula 7 based on error correction be expressed as follows:
z1,z2,z3For the output of extended state observer, output change rate and the always estimation that disturbs, β=[β1,β2,β3]TFor observation
Device gain, p1=y,b0For adjustable control gain.
2. a kind of design method of disturbance rejection control system, it is characterised in that the following steps are included:
Step 1: design general linear extended state observer
Step 2: the extended state observer of design point error correction
Step 3: extended state observer of the design based on error correction
Extended state observer design based on error correction are as follows:
Wherein, z1,z2,z3For the output of extended state observer, output change rate and the always estimation that disturbs, β=[β1,β2,β3]T
For observer gain, p1=y,b0For adjustable control gain, u is control signal；
Step 4: designing the control law of controller
Step 5: forming closed loop disturbance rejection control system.
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| CN113156862A (en) * | 2021-04-23 | 2021-07-23 | 广东电网有限责任公司电力科学研究院 | Bit-domain proportional observer and novel basic controller system |
| WO2022164388A1 (en) * | 2021-01-28 | 2022-08-04 | Nanyang Technological University | Active disturbance rejection control system |
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