CN110134014A - The equivalent disturbance compensation method of period servo-system power attraction Repetitive controller - Google Patents
The equivalent disturbance compensation method of period servo-system power attraction Repetitive controller Download PDFInfo
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Abstract
A kind of period servo-system power attracts the equivalent disturbance compensation method of Repetitive controller, including given module to generate periodic reference signal, introduces period feedforward link, defines equivalent disturbance signal, estimated using observer equivalent disturbance；Attract rule building perfect error dynamic based on 1/4 (or 3/4) power, and according to perfect error dynamic design controller, is inputted the signal being calculated as the control of servo-system；Specific attitude conirol can be carried out according to characterization system convergence performance indicator, and give the monotone decreasing region of characterization tracking error convergence process, absolute attractable layer, steady-state error first enter the calculation formula of steady-state error band maximum step number with boundary and tracking error.Power provided by the invention with equivalent disturbance compensation attracts repetitive controller, by the estimation to equivalent disturbance, can be improved systematic tracking accuracy and complete inhibition periodic perturbation.
Description
Technical field
The present invention relates to the powers using equivalent disturbance compensation to attract repetitive control, and this method is used for period servo system
System Repetitive controller, is also applied for the industrial occasions of other periodic duty processes.
Background technique
When designing controller using internal model principle, it is desirable that include the mathematical model of external input signal in closed-loop system, i.e.,
By input signal model implant controller, high-precision feedback control system is constituted.Repetitive Control Technique provides a kind of based on internal model
The controller design of principle, i.e. mathematical model in internal model describe periodic signal, and closed-loop system can be realized free from errors
Corresponding reference signal is tracked, to reach control purpose.Period internal model is achieved in that, is added to the input signal of controll plant
In addition to current time deviation signal, it is also superimposed with the control signal in a period.Repetitive Control Technique has been applied to power electronics line
The high accuracy servo systems such as road, industrial robot and hard drive.
Rule method is attracted to provide a kind of Control System Design method for directly utilizing tracking error, controller design is more
Directly, succinctly.It is conventional to attract rule that reflect error attenuated feature, but independently of system performance, therefore systematic uncertainty is not considered.
Therefore direct basis attracts the controller of rule design often to cannot achieve.Solution is by the former suction of interference suppression measure " insertion "
Draw rule, constructs the perfect error dynamic with Disturbance Rejection effect, and the perfect error dynamic design controller according to construction.This
Sample, closed-loop system dynamic process are determined there is its expectation tracking performance for being characterized by perfect error dynamic.
Continuously attract rule by discretization, designs digitial controller, analyzed via error performance, provide and portray tracking error
The performance indicator of transient state and stable state behavior.Specifically there is following four index: steady-state error band, absolute attractable layer, monotone decreasing area
Domain and tracking error first enter maximum step number needed for steady-state error band.The specific value of these indexs depends on controller
The constituent element of parameter and equivalent interference signal.Therefore, controller parameter is different, and four index values are also with variation；Once
Given perfect error dynamic-form, provides the expression of indices, for instructing attitude conirol in advance.
Core cell of the extended state observer as Active Disturbance Rejection Control system, basic principle are that will influence to be controlled
The disturbance part of output expands into new state variable, i.e., overall disturbance (disturb and outside disturb including interior) is defined as new state,
And the basic thought based on state observation, extended state observer is constructed using feedback mechanism.It can not only estimating system shape
State, moreover it is possible to which the real-time effect amount of overall disturbance in estimating system model, this estimation are used in controller, disturbance cancelling signal pair
The influence of system performance.Since overall disturbance includes the uncertainty in system model, system model is simplified, controls gain
It regards known as, is convenient for controller design.
Summary of the invention
To make closed-loop system that there is preset anticipation error tracking performance, attract rule construction ideal accidentally according to power
Differential state designs servo-system repetitive controller.The present invention proposes that a kind of power attracts the equivalent disturbance compensation side of Repetitive controller
Method, while realizing to the complete inhibition of periodic disturbances ingredient, it is also contemplated that there are aperiodic ingredients in disturbance, in closed-loop system
Middle introducing disturbance observer further increases control performance, so that servo-system can be realized to compensate aperiodicity interference
High precision tracking.The equivalent disturbance that the present invention will affect system output expands into new variable, constructs disturbance observer.The disturbance
Observer does not need direct estimation disturbing signal, is embedded in braking measure in the equivalent disturbance of estimation, without knowing controlled system
The accurate model of system.It is analyzed for Performance of Closed Loop System, the present invention specifically provides steady-state error band, absolute attractable layer, dullness
Subtract region and tracking error first enters the expression formula of four indexs of most step numbers needed for steady-state error band, for instructing control
Device parameter tuning.
The present invention solve above-mentioned technical problem the technical solution adopted is that:
A kind of period servo-system power attracts the equivalent disturbance compensation method of Repetitive controller, comprising the following steps:
Step 1. period demand reference signal meets
rk=rk-N (1)
Wherein, N is the period of reference signal, rkAnd rk-NRespectively indicate the reference signal at k moment and k-N moment；
Step 2. defines tracking error
ek+1=rk+1-yk+1=rk+1-yk+1-N+A1(q-1)(yk-yk-N)-q-d+1B(q-1)(uk-uk-N)-wk+1+wk+1-N
(2)
In formula,
Meet
A(q-1)yk=q-dB(q-1)uk+wk (3)
Wherein, ek+1Indicate the tracking error at k+1 moment, rk+1Indicate the reference signal at k+1 moment, yk+1、yk、yk+1-NWith
yk-NRespectively indicate the output signal at k+1, k, k+1-N and k-N moment, ukAnd uk-NRespectively indicate the input letter at k and k-N moment
Number, wk+1And wk+1-NThe interference signal at k and k-N moment is respectively indicated, d indicates delay, A (q-1) and B (q-1) it is q-1Multinomial,
q-1Indicate One-step delay operator, naIndicate A (q-1) order, nbIndicate B (q-1) order,For system
Parameter and b0≠ 0, na≥nb, d is integer, and d >=1；
Step 3. constructs equivalent disturbance
dk=wk-wk-N (4)
Wherein, N is the period of reference signal, dkIndicate the equivalent disturbance signal at k moment, wkAnd wk-NRespectively indicate the k moment
With the interference signal at k-N moment；
(4) are utilized to be expressed as tracking error
ek+1=rk+1-yk+1=rk+1-yk+1-N+A1(q-1)(yk-yk-N)-q-d+1B(q-1)(uk-uk-N)-dk+1 (5)
Wherein, dk+1Indicate the equivalent disturbance at k+1 moment；
Step 4. designs observer, estimates equivalent disturbance, and process is as follows:
Observer is designed to equivalent disturbance dk+1It is observed, and equivalent disturbance is compensated with observation.Two sights of observer
Surveying variable isWithE is estimated respectivelykAnd dk, according to error dynamics (formula (5)), design the observer of following form
Wherein,It indicates to error ek+1Estimation,It indicates to error ekEstimation,Indicate equivalent disturbance, β1Table
Show the observer gain coefficient about error, β2Indicate the observer gain coefficient about equivalent disturbance.Indicate with
The evaluated error of track error；
The evaluated error of equivalent disturbanceFor
The evaluated error of tracking error is
Formula (7) and formula (8) are write as
NoteIts characteristic equation is
| λ I-B |=0 (10)
I.e.
λ2+(β1-β2-1)λ-β1=0 (11)
Therefore, characteristic root is
By to β1And β2Parameter configured so that all characteristic roots of matrix B are all in unit circle, matrix B is
Schur stable matrix, evaluated error asymptotic convergence, i.e.,
Step 5. constructs the power with Method of suppression disturbance and attracts rule
Wherein, ρ and ε is adjustable parameter,It indicates to attract index, and 0 < ρ < 1, ε > 0,
Step 6. constructs the repetitive controller with equivalent disturbance compensation, and process is as follows:
Convolution (5) and formula (12) design the repetitive controller with equivalent disturbance compensation
Note
Repetitive controller is expressed as
uk=uk-N+vk (14)
By ukAs the controller input signal of target servo, measurement obtains servo-system output signal yk, follow with reference to letter
Number rkVariation.
Further, the parameter of the discrete repetitive controller includes velocity of approach index ρ, arrival rate ε, attracts indexParameter tuning is carried out according to the index of characterization system convergence performance；Introducing characterization system convergence performance indicator has steady-state error
Band ΔSSE, absolute attractable layer ΔAAL, monotone decreasing region ΔMDRAnd tracking error first enters most multistep needed for steady-state error band
NumberConcept is defined as follows:
1) monotone decreasing region ΔMDR: work as ekWhen greater than this boundary, ekJack per line successively decreases, that is, meets following condition:
2) absolute attractable layer ΔAAL: when the absolute value of system tracking error | ek| when being greater than this boundary, | ek| monotone decreasing,
Meet such as condition:
3) steady-state error band ΔSSE: entering the boundary once restraining when systematic error, error will be stablized in this area,
Meet following condition:
4) maximum convergence step numberTracking error is at most passed throughStepping enters steady-state error band.
Equivalent disturbance compensates error and meetsWhen, the expression formula of each index is as follows
Monotone decreasing region ΔMDR
ΔMDR=max { ΔMDR1,ΔMDR2} (19)
Wherein, ΔMDR1And ΔMDR2It is real number, and is determined by formula (18)；
Absolute attractable layer ΔAAL
ΔAAL=max { ΔAAL1,ΔAAL2} (21)
Wherein, ΔAAL1And ΔAAL2It is real number, and is determined by formula (20)；
Steady-state error band ΔSSE
Wherein, xSSEFor equationPositive real root；
In addition, providing ΔSSEAfterwards, tracking error enters the maximum step number of steady-state error band
Wherein, e0For tracking error initial value,Indicate the smallest positive integral being not less than；
For what is givenValue calculates each boundary value according to formula (18)-(23) formula, to determine Performance of Closed Loop System, foundation
Corresponding equation group is not difficult to determine ΔMDRAnd ΔAALValue should be the positive real root of maximum of corresponding equation group, determine ΔAALAfter value,
According to ΔAALDetermine ΔSSE。
Further, forTwo kinds of situations, according to Δ given aboveMDR、ΔAAL、ΔSSEExpression formula and
Convergence step number expression formula determines corresponding calculation formula；
Situation:
1) monotone decreasing region ΔMDR
In formula,
2) absolute attractable layer ΔAAL
In formula,
3) steady-state error band ΔSSE
Wherein, xSSEFor equationPositive real root；
4) step number is restrained
Wherein, e0For tracking error initial value,Indicate the smallest positive integral being not less than；
Situation:
1) monotone decreasing region ΔMDR
In formula,
In formula,
2) absolute attractable layer ΔAAL
In formula,
3) steady-state error band ΔSSE
Wherein, xSSEFor equationPositive real root；
4) step number is restrained
Wherein, e0For tracking error initial value,Indicate the smallest positive integral being not less than.
Technical concept of the invention are as follows: the equivalent disturbance compensation side that period servo-system power attracts Repetitive controller is provided
Method.It according to the equivalent disturbance of given reference signal and construction, designs interference observer and equivalent disturbance is estimated, and will interference
Braking measure be embedded in power attract rule in, formed have AF panel effect perfect error dynamically, thus design with etc.
The repetitive controller of disturbance compensation is imitated, realizes and the quick high accuracy of given reference signal is tracked.
Beneficial effects of the present invention are mainly manifested in: having equivalent disturbance compensation, fast convergence performance, periodic disturbances complete
Inhibition and high control precision.
Detailed description of the invention
Fig. 1 is the block diagram of electric machine.
Fig. 2 is equivalent disturbance observer block diagram.
Fig. 3 is that power attracts repetitive controller block diagram.
Fig. 4 is as disturbance wk=5sin (2 π fkTs)+0.15sgn (sin (π/150 2k)), controller parameter takes ε=0.2, ρ
=0.3, simulation result when Δ=0.5 marks Δ in figureMDR, ΔAALAnd ΔSSE。
Fig. 5 is as disturbance wk=-10sin (2 π fkTs)+0.15sgn (sin (π/150 2k)), controller parameter take ε=
0.2, ρ=0.3, simulation result when Δ=0.5 marks Δ in figureMDR, ΔAALAnd ΔSSE。
Fig. 6 is as disturbance wk=5sin (2 π fkTs)+0.15sgn (sin (π/150 2k)), controller parameter takes ε=0.3, ρ
=0.3, simulation result when Δ=0.5 marks Δ in figureMDR, ΔAALAnd ΔSSE。
Fig. 7 is as disturbance wk=-10sin (2 π fkTs)+0.15sgn (sin (π/150 2k)), controller parameter take ε=
0.3, ρ=0.3, simulation result when Δ=0.5 marks Δ in figureMDR, ΔAALAnd ΔSSE。
Fig. 8 is as disturbance wk=5sin (2 π fkTs)+0.15sgn (sin (π/150 2k)), controller parameter takes ε=0.3, ρ
=0.5, simulation result when Δ=0.4 marks Δ in figureMDR, ΔAALAnd ΔSSE。
Fig. 9 is as disturbance wk=-10sin (2 π fkTs)+0.15sgn (sin (π/150 2k)), controller parameter take ε=
0.3, ρ=0.5, simulation result when Δ=0.4 marks Δ in figureMDR, ΔAALAnd ΔSSE。
Figure 10-13 is that repetitive controller parameter takes ρ=0.7, when ε=0.3, the experiment knot of permanent magnet synchronous motor control device
Fruit, wherein
Figure 10 is reference position signal and actual position signal under attracting the repetitive controller of rule to act on based on power；
Figure 11 is the controller voltage signal under attracting the repetitive controller of rule to act on based on power；
Figure 12 is the location error under attracting the repetitive controller of rule to act on based on power；
Figure 13 is the location error distribution histogram under attracting the repetitive controller of rule to act on based on power.
Figure 14-17 is that repetitive controller parameter takes ρ=0.7, ε=0.3, and equivalent disturbance observer parameter takes β1=0.2, β2
When=0.5, the experimental result of permanent magnet synchronous motor control device, wherein
Figure 14 be the reference position signal that attracts the repetitive controller effect of rule and equivalent disturbance compensation lower based on power with
Actual position signal；
Figure 15 is the controller voltage signal under attracting rule and the repetitive controller of equivalent disturbance compensation to act on based on power；
Figure 16 is the location error under attracting rule and the repetitive controller of equivalent disturbance compensation to act on based on power；
Figure 17 is that the location error distribution under attracting rule and the repetitive controller of equivalent disturbance compensation to act on based on power is straight
Fang Tu.
Figure 18-21 is that repetitive controller parameter takes ρ=0.3, when ε=0.15, the experiment of permanent magnet synchronous motor control device
As a result, wherein
Figure 18 is reference position signal and actual position signal under attracting the repetitive controller of rule to act on based on power；
Figure 19 is the controller voltage signal under attracting the repetitive controller of rule to act on based on power；
Figure 20 is the location error under attracting the repetitive controller of rule to act on based on power；
Figure 21 is the location error distribution histogram under attracting the repetitive controller of rule to act on based on power.
Figure 22-25 is that repetitive controller parameter takes ρ=0.3, ε=0.15, and equivalent disturbance observer parameter takes β1=0.2, β2
When=0.5, the experimental result of permanent magnet synchronous motor control device, wherein
Figure 22 be the reference position signal that attracts the repetitive controller effect of rule and equivalent disturbance compensation lower based on power with
Actual position signal；
Figure 23 is the controller voltage signal under attracting rule and the repetitive controller of equivalent disturbance compensation to act on based on power；
Figure 24 is the location error under attracting rule and the repetitive controller of equivalent disturbance compensation to act on based on power；
Figure 25 is that the location error distribution under attracting rule and the repetitive controller of equivalent disturbance compensation to act on based on power is straight
Fang Tu.
Figure 26-29 is that feedback controller parameter takes ρ=0.7, when ε=0.3, the experiment knot of permanent magnet synchronous motor control device
Fruit, wherein
Figure 26 is reference position signal and actual position signal under attracting the feedback controller of rule to act on based on power；
Figure 27 is the controller voltage signal under attracting the feedback controller of rule to act on based on power；
Figure 28 is the location error under attracting the feedback controller of rule to act on based on power；
Figure 29 is the location error distribution histogram under attracting the feedback controller of rule to act on based on power.
Figure 30-33 is that feedback controller parameter takes ρ=0.7, ε=0.3, and equivalent disturbance observer parameter takes β1=0.2, β2
When=0.5, the experimental result of permanent magnet synchronous motor control device, wherein
Figure 30 be the reference position signal that attracts the feedback controller effect of rule and equivalent disturbance compensation lower based on power with
Actual position signal；
Figure 31 is the controller voltage signal under attracting rule and the feedback controller of equivalent disturbance compensation to act on based on power；
Figure 32 is the location error under attracting rule and the feedback controller of equivalent disturbance compensation to act on based on power；
Figure 33 is that the location error distribution under attracting rule and the feedback controller of equivalent disturbance compensation to act on based on power is straight
Fang Tu.
Figure 34-37 is that feedback controller parameter takes ρ=0.3, when ε=0.15, the experiment of permanent magnet synchronous motor control device
As a result, wherein
Figure 34 is reference position signal and actual position signal under attracting the feedback controller of rule to act on based on power；
Figure 35 is the controller voltage signal under attracting the feedback controller of rule to act on based on power；
Figure 36 is the location error under attracting the feedback controller of rule to act on based on power；
Figure 37 is the location error distribution histogram under attracting the feedback controller of rule to act on based on power.
Figure 38-41 is that feedback controller parameter takes ρ=0.3, ε=0.15, and equivalent disturbance observer parameter takes β1=0.2, β2
When=0.5, the experimental result of permanent magnet synchronous motor control device, wherein
Figure 38 be the reference position signal that attracts the feedback controller effect of rule and equivalent disturbance compensation lower based on power with
Actual position signal；
Figure 39 is the controller voltage signal under attracting rule and the feedback controller of equivalent disturbance compensation to act on based on power；
Figure 40 is the location error under attracting rule and the feedback controller of equivalent disturbance compensation to act on based on power；
Figure 41 is that the location error distribution under attracting rule and the feedback controller of equivalent disturbance compensation to act on based on power is straight
Fang Tu.
Specific embodiment
The specific embodiment of the invention is further described with reference to the accompanying drawing.
- Figure 41 referring to Fig.1, a kind of period servo-system power attract the equivalent disturbance compensation method of Repetitive controller, wherein
Fig. 1 is electric machine block diagram；Fig. 2 is equivalent disturbance observer block diagram；Fig. 3 is that power attracts repetitive controller block diagram.
The period servo-system power attract the equivalent disturbance compensation method of Repetitive controller the following steps are included:
Step 1. period demand reference signal meets (1)；
Step 2. defines tracking error, and the tracking error of system is (2)；
Step 3. constructs equivalent disturbance (4), utilizes (4) that system tracking error is expressed as (5)；
Step 4. designs observer, estimates equivalent disturbance；
Step 5. constructs the power with Method of suppression disturbance and attracts rule (12)；
Step 6. constructs the repetitive controller with equivalent disturbance compensation, convolution (5) and formula (12), and design has equivalent
The repetitive controller (13) of disturbance compensation, is expressed as (14) for repetitive controller.
Above-mentioned repetitive controller design, does following explanation:
1) power, which attracts in rule, introduces dk+1, the braking measure of the disturbing signal for period demand mode is reflected, is introduced
'sThe estimated value of equivalent disturbance is reflected, equivalent disturbance compensation is provided accordingly.
2) in formula (13), ek、yk、yk-1、yk-1-NIt is obtained by measurement, uk-1、uk-1-NFor the storage value for controlling signal, from interior
Deposit middle reading.
3) when reference signal meets rk=rk-1, which is also applied for constant value regulation problem, at this moment etc.
Effect disturbance is dk=wk-wk-1；Wherein, rk-1Indicate the reference signal at k-1 moment, wk-1Indicate the interference signal at k-1 moment；Have
Equivalent disturbance compensation feedback controller be
4) above-mentioned discrete time controller is designed for second-order system, equally provides high level in the same manner
The design result of system.
Further, steady-state error band, absolute attractable layer, monotone decreasing region and tracking error are provided and first enters stable state mistake
The expression formula of four indexs of most step numbers, for describing system tracking performance and instructs attitude conirol needed for difference band.
Further, forTwo kinds of situations, according to the Δ providedMDR、ΔAAL、ΔSSEExpression formula and convergence
Step number expression formula determines corresponding calculation formula.
The present embodiment is by taking PMSM Servo System executes repeat track task on fixed interval as an example, position
Reference signal has periodic symmetry characteristic.Using TMS320F2812DSP as controller, South Korea LS AC servo motor APM-
SB01AGN is as control object, with ELMO AC servo driver and upper structure at PMSM Servo System, into
The control of row motor position.Wherein servo-system uses three close-loop control, and electric current loop and speed ring controller ELMO driver provide, position
Ring is set to be provided by DSP development board.
It is by the mathematical model that parameter Estimation obtains target servo
yk+1-1.8949yk+0.8949yk-1=1.7908uk-0.5704uk-1+wk+1 (33)
Wherein, yk, ukThe position output of respectively positional servosystem is inputted with control, wkFor interference signal.
It will illustrate that the present invention provides the validity of repetitive controller by numerical simulation and experimental result in the embodiment.
Numerical simulation the present embodiment using sinusoidal signal as system reference signal, write as by corresponding repetitive controller expression formula
Given position reference signal is rk=20 (sin (2 π fkTs- 1/2 π)+1), unit is to spend (deg), frequency f=1Hz,
Sampling period Ts=0.002s, sampling number N=1000.The disturbance quantity w chosen when emulationk, it by periodic perturbation and it is aperiodic with
Machine interference is constituted.
Patent is about monotone decreasing region Δ to illustrate the inventionMDR, absolute attractable layer ΔAALWith steady-state error band ΔSSEReason
By correctness, withFor carried out numerical simulation.Under repetitive controller (34) effect, different controller ginsengs is chosen
Number ρ, three boundary layers of ε, servo-system are also different.
1) as controller parameter ε=0.2, ρ=0.3, when Δ=0.5,
ΔSSE=ΔAAL=ΔMDR=1
2) as controller parameter ε=0.3, ρ=0.3, when Δ=0.5,
ΔSSE=ΔAAL=0.7394, ΔMDR=1.1590
3) as controller parameter ε=0.3, ρ=0.5, when Δ=0.4,
ΔSSE=0.7946, ΔAAL=0.4964, ΔMDR=1.6834
Simulation result is shown in Fig. 4-9, and wherein Fig. 4, Fig. 6 and Fig. 8 are disturbance quantity wk=5sin (2 π fkTs)+0.15sgn(2k
π/150) simulation result, Fig. 5, Fig. 7 and Fig. 9 are disturbance quantity wk=-10sin (2 π fkTs)+0.15sgn (π/150 2k) it is imitative
True result.
In the case where given system model, reference signal and interference signal, above-mentioned numerical result demonstrate this patent to
Repetitive controller out acts on the monotone decreasing region Δ of lower system tracking errorMDR, absolute attractable layer ΔAALWith steady-state error band
ΔSSEAccuracy.
Experimental verification tests the block diagram of electric machine used as shown in Figure 1.By the way that different controller parameters, verifying is arranged
Attract the tracking performance of the discrete controller of rule based on power.Reference signal rk=A (sin (2 π × (k-200)/N)+1),
In, amplitude A=135deg, sampling period Ts=2.5ms, k are sampling number, N=800.WithFor test
Card.
The following form of the repetitive controller of use
The following form of repetitive controller based on equivalent disturbance compensation used
The feedback controller of use takes following form
The following form of feedback controller based on equivalent disturbance compensation used
1) controller (35) are used, controller parameter takes ρ=0.7, when ε=0.3, experimental result as shown in figures 10-13, figure
Middle ΔSSE=0.13deg.
2) controller (36) are used, controller parameter takes ρ=0.7, ε=0.3, and equivalent disturbance observer parameter takes β1=
0.2, β2When=0.5, experimental result as shown in figures 14-17, Δ in figureSSE=0.09deg.
3) controller (35) are used, controller parameter takes ρ=0.3, when ε=0.15, experimental result as shown in figs. 18-21,
Δ in figureSSE=0.1deg.
4) controller (36) are used, controller parameter takes ρ=0.3, ε=0.15, and equivalent disturbance observer parameter takes β1=
0.2, β2When=0.5, experimental result as illustrated in figs. 22-25, Δ in figureSSE=0.07deg.
5) controller (37) are used, controller parameter takes ρ=0.7, when ε=0.3, experimental result as illustrated in figures 26-29, figure
Middle ΔSSE=0.15deg.
6) controller (38) are used, controller parameter takes ρ=0.7, ε=0.3, and equivalent disturbance observer parameter takes β1=
0.2, β2When=0.5, experimental result as shown in figs. 30-33, Δ in figureSSE=0.14deg.
7) controller (37) are used, controller parameter takes ρ=0.3, when ε=0.15, experimental result as shown in Figure 34-37,
Δ in figureSSE=0.14deg.
8) controller (38) are used, controller parameter takes ρ=0.3, ε=0.15, and equivalent disturbance observer parameter takes β1=
0.2, β2When=0.5, experimental result is as shown in Figure 38-41, Δ in figureSSE=0.11deg.
It is above-mentioned the experimental results showed that, introduce equivalent disturbance, it is estimated with equivalent interference observer, is provided for being
The compensation of unmodeled characteristic of uniting and external unknown disturbance, can effectively inhibit influence of the unknown disturbance to tracking performance；Using weight
Periodic perturbation is realized in multiple control to be completely inhibited, the further control performance for improving system.
Claims (3)
1. a kind of period servo-system power attracts the equivalent disturbance compensation method of Repetitive controller, controlled device is period servo system
System, which is characterized in that the described method comprises the following steps:
Step 1. period demand reference signal meets
rk=rk-N (1)
Wherein, N is the period of reference signal, rkAnd rk-NRespectively indicate the reference signal at k moment and k-N moment；
Step 2. defines tracking error
ek+1=rk+1-yk+1=rk+1-yk+1-N+A1(q-1)(yk-yk-N)-q-d+1B(q-1)(uk-uk-N)-wk+1+wk+1-N (2)
In formula,
Meet
A(q-1)yk=q-dB(q-1)uk+wk (3)
Wherein, ek+1Indicate the tracking error at k+1 moment, rk+1Indicate the reference signal at k+1 moment, yk+1、yk、yk+1-NAnd yk-NPoint
Not Biao Shi k+1, k, k+1-N and k-N moment output signal, ukAnd uk-NRespectively indicate the input signal at k and k-N moment, wk+1
And wk+1-NThe interference signal at k and k-N moment is respectively indicated, d indicates delay, A (q-1) and B (q-1) it is q-1Multinomial, q-1Table
Show One-step delay operator, naIndicate A (q-1) order, nbIndicate B (q-1) order,For system parameter
And b0≠ 0, na≥nb, d is integer, and d >=1；
Step 3. constructs equivalent disturbance
dk=wk-wk-N (4)
Wherein, N is the period of reference signal, dkIndicate the equivalent disturbance signal at k moment, wkAnd wk-NRespectively indicate k moment and k-N
The interference signal at moment；
(4) are utilized to be expressed as tracking error
ek+1=rk+1-yk+1=rk+1-yk+1-N+A1(q-1)(yk-yk-N)-q-d+1B(q-1)(uk-uk-N)-dk+1 (5)
Wherein, dk+1Indicate the equivalent disturbance at k+1 moment；
Step 4. designs observer, estimates equivalent disturbance, and process is as follows:
Observer is designed to equivalent disturbance dk+1It is observed, and equivalent disturbance is compensated with observation, two observations of observer become
Amount isWithIt is respectively used to estimation ekAnd dk, according to error dynamics (formula (5)), design the observer of following form
Wherein,It indicates to error ek+1Estimation,It indicates to error ekEstimation,Indicate equivalent disturbance, β1It indicates to close
In the observer gain coefficient of error, β2Indicate the observer gain coefficient about equivalent disturbance,Indicate that tracking misses
The evaluated error of difference；
The evaluated error of equivalent disturbanceFor
The evaluated error of tracking error is
Formula (7) and formula (8) are write as
NoteIts characteristic equation are as follows:
| λ I-B |=0 (10)
I.e.
λ2+(β1-β2-1)λ-β1=0 (11)
Therefore, characteristic root isTo β1And β2Parameter configured so that institute
There is characteristic root all in unit circle；
Step 5. constructs the power with Method of suppression disturbance and attracts rule
Wherein, ρ and ε is adjustable parameter,It indicates that index is attracted (to takeAnd corresponding items are being provided later
Index expression), and 0 < ρ < 1, ε > 0,
Step 6. constructs the repetitive controller with equivalent disturbance compensation, and process is as follows:
Convolution (5) and formula (12) design the repetitive controller with equivalent disturbance compensation
Note
Repetitive controller is expressed as
uk=uk-N+vk (14)
By ukAs the controller input signal of target servo, measurement obtains servo-system output signal yk, follow reference signal rk
Variation.
2. period servo-system power as described in claim 1 attracts the equivalent disturbance compensation method of Repetitive controller, feature
Be: the parameter of the discrete repetitive controller includes velocity of approach index ρ, arrival rate ε, attracts indexAccording to characterization
The index of system convergence performance carries out parameter tuning；Introducing characterization system convergence performance indicator has steady-state error band ΔSSE, absolutely
Attractable layer ΔAAL, monotone decreasing region ΔMDRAnd tracking error first enters most step numbers needed for steady-state error bandConcept,
It is defined as follows:
1) monotone decreasing region ΔMDR: work as ekWhen greater than this boundary, ekJack per line successively decreases, that is, meets following condition:
2) absolute attractable layer ΔAAL: when the absolute value of system tracking error | ek| when being greater than this boundary, | ek| monotone decreasing, i.e., it is full
The following condition of foot:
3) steady-state error band ΔSSE: entering the boundary once restraining when systematic error, error will be stablized in this area,
Meet following condition:
4) maximum convergence step numberTracking error is at most passed throughStepping enters steady-state error band；
Equivalent disturbance compensates error and meetsWhen, the expression formula of each index is as follows
Monotone decreasing region ΔMDR
ΔMDR=max { ΔMDR1,ΔMDR2} (19)
Wherein, ΔMDR1And ΔMDR2It is real number, and is determined by formula (18)；
Absolute attractable layer ΔAAL
ΔAAL=max { ΔAAL1,ΔAAL2} (21)
Wherein, ΔAAL1And ΔAAL2It is real number, and is determined by formula (20)；
Steady-state error band ΔSSE
Wherein, xSSEFor equationPositive real root；
In addition, providing ΔSSEAfterwards, tracking error enters the maximum step number of steady-state error band
Wherein, e0For tracking error initial value；Indicate the smallest positive integral being not less than；
For what is givenValue calculates each boundary value according to formula (18)-(23) formula, to determine Performance of Closed Loop System, according to corresponding
Equation group is not difficult to determine ΔMDRAnd ΔAALValue should be the positive real root of maximum of corresponding equation group, determine ΔAALAfter value, according to
According to ΔAALDetermine ΔSSE。
3. period servo-system power as claimed in claim 2 attracts the equivalent disturbance compensation method of Repetitive controller, feature
It is, forWithTwo kinds of situations, according to the monotone decreasing region Δ providedMDR, absolute attractable layer ΔAAL, stable state miss
Difference band ΔSSEAnd maximum convergence step numberExpression formula determines corresponding calculation formula；
Situation:
1) monotone decreasing region ΔMDR
In formula,
2) absolute attractable layer ΔAAL
In formula,
3) steady-state error band ΔSSE
Wherein, xSSEFor equationPositive real root；
4) step number is restrained
Wherein, e0For tracking error initial value,Indicate the smallest positive integral being not less than；
Situation:
1) monotone decreasing region ΔMDR
In formula,
In formula,
2) absolute attractable layer ΔAAL
In formula,
3) steady-state error band ΔSSE
Wherein, xSSEFor equationPositive real root；
4) step number is restrained
Wherein, e0For tracking error initial value,Indicate the smallest positive integral being not less than.
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| CN113325785A (en) * | 2021-06-11 | 2021-08-31 | 哈尔滨工业大学 | Position repetition control method based on data storage |
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