CN110161857A - A kind of Auto-disturbance-rejection Controller Design method suitable for non-minimum phase system - Google Patents
A kind of Auto-disturbance-rejection Controller Design method suitable for non-minimum phase system Download PDFInfo
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Abstract
The invention discloses a kind of Auto-disturbance-rejection Controller Design methods suitable for non-minimum phase system, include the following steps: 1) to provide first stability non-minimum phase system model G (s)；2) closed loop reference model, the transfer function H of the closed loop reference model are setR(s)；3) with HR(s) it is target, constructs ESO；4) system always disturbs dKThe frequency domain of+f is estimated；5) disturbance compensation control rate is constructed；6) judgement of stability condition is provided；7) parameter of K (s) is designed；8) time constant is calculatedτAnd in stable regionτIn < τ < ∞, τ value is chosen, realizes ESO, and τ is adjusted, realizes expected performance.The present invention gives the Auto-disturbance-rejection Controller Design methods given suitable for non-minimum phase system, propose a kind of new disturbance rejection control rate, have the advantages of simple structure and easy realization.
Description
Technical field
The present invention relates to industrial process control systems and kinetic control system, belong to disturbance rejection control technical field, Yi Zhongshi
Auto-disturbance-rejection Controller Design method for non-minimum phase system.
Background technique
In actual industrial production, industrial system suffers from a variety of disturbing influences, and one is internal disturbances, by physics
The mismatch of model and real system causes, and another kind is external disturbance, the interference that mainly outer bound pair control system generates.It is existing
The performance of control system and required precision are continuously improved for industrial production and manufacturing process.It is real by designing disturbance rejection control device
Existing floating regulation and tracing control with significant importance and meaning.
Non-minimum phase system is widely present in industrial object, such as robot flexibility structure control, chemical process it is dense
Degree control, ship course keeping control, aircraft manufacturing technology etc..Being mainly characterized by of non-minimum phase system has right half plane
Zero point, the one-to-one relationship being unsatisfactory between amplitude-frequency and phase frequency, the design and analysis method of minimum phase system are no longer applicable in.It is right
The zero pole point of half-plane can have an adverse effect to the stability of system, robustness and dynamic property etc..So non-minimum phase
The control of system is more much more difficult than minimum phase system.
External disturbance and inside for system is uncertain, and Active Disturbance Rejection Control (ADRC) is a kind of effective control plan
Slightly.Its basic thought is by the uncertainty of model, and external disturbance is even non-linear as a total disturbance, and by expansion shape
State observer carries out active estimation and compensation, gets rid of the dependence to model.Automatic disturbance rejection controller is initially for minimum phase
What system proposed, by adjusting two bandwidth parameters and input gain parameter, realizes that the linearisation of control system is adjusted, there is Shandong
Disturbance rejection control theoretical developments and application are greatly facilitated in the features such as stick is strong, and structure is simple, fast response time, overshoot is small.It is right
In non-minimum phase system, conventional automatic disturbance rejection controller is easy to keep system unstable, between controller parameter and control performance
Relationship is also not clear enough, it is difficult to promote and apply in industrial control system.
Therefore, a kind of automatic disturbance rejection controller suitable for non-minimum phase system is proposed in the present invention, and there is important meaning
Justice.
Summary of the invention
The present invention provides a kind of Auto-disturbance-rejection Controller Design methods suitable for non-minimum phase system, and which overcome back
The deficiencies in the prior art described in scape technology.
The technical solution adopted by the present invention to solve the technical problems is:
A kind of Auto-disturbance-rejection Controller Design method suitable for non-minimum phase system, it includes the following steps:
1) first stability non-minimum phase system model G (s) is provided；
2) closed loop reference model, the transfer function H of the closed loop reference model are setR(s) are as follows:
With predistorter K (s), by augmented plant G (s) K (s)
It is expressed as the disturbed form of closed loop reference model, is had:
y(r)=-k0y(0)-k1y(1)-…-kr-1y(r-1)+k0(uK+dK+f)；
Wherein, closed loop reference model H is chosen with respect to order r.deg [G] according to non-minimum phase system model G (s)R(s)
The opposite order with predistorter K's (s) meets r.deg [K]+r.deg [G]=r.deg [HR]；dK=d/K, d are outside system
Portion's disturbance, K are predistorter, and f is internal system disturbance, dK+ f is that system always disturbs, and defines expansion state x(r+1)=dK+ f,
U=KuK；State-space model are as follows:
Wherein, h is that system always disturbs dKThe differential of+f；
3) with HR(s) it is target, constructs ESO, have
Wherein, xo=[xo1,xo2,…,xo(r+1)]TFor ESO state, L is observer gain, ypIt is full for system reality output
Sufficient POLE PLACEMENT USING condition:
Wherein, ωoFor ESO bandwidth, the ω of τ=1/oFor ESO time constant, I is unit matrix；
4) system always disturbs dKThe frequency domain of+f is estimated；In Active Disturbance Rejection Control, expansion state xo(r+1)The system of can be realized is disturbed
Dynamic estimation, there is x in a frequency domaino(r+1)(s)=- F1(s)uK(s)+F2(s)yp(s), in which:
5) disturbance compensation control rate u=K (s) u is constructedk=K (s) (y*-xo(r+1)), wherein y* is given input letter
Number；
6) judgement of stability condition is provided, related various pieces are write as to the form of relatively prime polynomial, are hadThe characteristic equation of closed-loop system is
pc(s, τ)=aF(τs)ak(s)ag(s)bh(s)(aF(τs)-bF(τs))+aF(τs)bk(s)bg(s)ah(s)bF(τs)
=aF(τs)ak(s)ag(s)bh(s)φ(s,τ)；
Wherein,Building S=τ s, if φ (S) is that Hurwitz is multinomial
Formula, then system in τ=∞, stablize, and there are a stability regions by systemτ< τ < ∞, system keeps stablizing, and has
Wherein,
7) parameter for designing K (s), considersWithTwo kinds of situations, wherein z, p, α, β are pre-compensating
The design parameter of device K may be designed as following two situation respectively:
Situation one:It takes λ that φ (S) is made to be Hurwitz multinomial, then has z=a0λ and p=b0；
Situation two:It takes λ that φ (S) is made to be Hurwitz multinomial, then has z=a0λ and p=b0, α and β
For undetermined parameter；
It introducing low-pass filter W (s), is matched by low frequency model, optimization calculates α and β,
8) time constant is calculatedτAnd in stable regionτIn < τ < ∞, τ value is chosen, realizes ESO, and adjust to τ
Section realizes expected performance.
The technical program compared with the background art, it has the following advantages:
1, by predistorter K (s), instead of the 1/b of conventional Active Disturbance Rejection Control0, it is capable of the dynamic of better compensation system
Step response, so that G (s) K (s) and closed loop reference model HR(s) it is matched in low-frequency range, can guarantee the stability of system, and be
Predistorter K (s) parameter designing provides theoretical foundation.
2, timeconstantτ (i.e. observer inverse bandwidth, the ω of τ=1/ of ESO are giveno), stable region calculation method.
3, a kind of new disturbance rejection control rate is given, is had the advantages of simple structure and easy realization.
4, the Auto-disturbance-rejection Controller Design method suitable for non-minimum phase system is given.
Detailed description of the invention
Present invention will be further explained below with reference to the attached drawings and examples.
Fig. 1 show the automatic disturbance rejection controller system block diagram of proposition；
Fig. 2 show Chemical process control system Φ (τ) distance map；
Fig. 3 show in Chemical process control system the nyquist diagram of L under different bandwidth (s, τ)；
Fig. 4 show Chemical process control system difference cA0Setting value and output concentration cBRelational graph.
Specific embodiment
A kind of Auto-disturbance-rejection Controller Design method suitable for non-minimum phase system, it includes the following steps:
1) first stability non-minimum phase system model G (s) is provided；
I.e. the pole of object is located at Left half-plane (object is stablized) but exists right
Half-plane zero point chooses closed loop reference model H according to system with respect to order r.deg [G]R(s) with the phase of predistorter K (s)
To order, meet r.deg [K]+r.deg [G]=r.deg [HR], so that G (s) K (s) is at zero-frequency and HR(s) approximately equal, have
G(j0)K(j0)≈HR(j0).In Active Disturbance Rejection Control,Parameter is the gain compensation before controlled device, is had
In the prior art, the parameter is not providedRational choice method in non-minimum phase system, the parameter and stability
Relationship it is also unclear.Generalized design is carried out to the parameter in the present invention, i.e. introducing dynamic compensator K (s) replaces
Augmented plant G (s) K (s) is formed, and designs predistorter K (s).
2) closed loop reference model, the transfer function H of the closed loop reference model are setR(s) are as follows:
With predistorter K (s), by augmented plant G (s) K (s)
It is expressed as the disturbed form of closed loop reference model, is had:
y(r)=-k0y(0)-k1y(1)-…-kr-1y(r-1)+k0(uK+dK+f)；
Wherein, dK=d/K, d are exterior disturbance, and K is predistorter, and f is internal system disturbance, dK+ f is system
Total disturbance, defines expansion state x(r+1)=dK+ f, u=KuK；State-space model are as follows:
Wherein, h is that system always disturbs dKThe differential of+f；
3) with HR(s) it is target, constructs ESO, have
Wherein, xo=[xo1,xo2,…,xo(r+1)]TFor ESO state, L is observer gain, ypIt is full for system reality output
Sufficient POLE PLACEMENT USING condition:
Wherein ωoFor ESO bandwidth, the ω of τ=1/oFor ESO time constant, I is unit matrix.
4) system always disturbs dKThe frequency domain of+f is estimated；In Active Disturbance Rejection Control, expansion state xo(r+1)The system of can be realized is disturbed
Dynamic estimation, there is x in a frequency domaino(r+1)(s)=- F1(s)uK(s)+F2(s)yp(s), in which:
5) disturbance compensation control rate u=K (s) u is constructedk=K (s) (y*-xo(r+1)), wherein y*For given input letter
Number；Compared with conventional Active Disturbance Rejection Control, which only includes the feedback compensation of expansion state, and reason is: the design of ESO is
For HR(s), rather than it is directed to controlled device G (s), system always disturbs dK+ f is by expansion state xo(r+1)It is compensated after estimation, from
And make the input/output relation of system close to HR(s), control structure is very simple.
6) judgement of stability condition is provided, related various pieces are write as to the form of relatively prime polynomial, are hadThe characteristic equation of closed-loop system is
pc(s, τ)=aF(τs)ak(s)ag(s)bh(s)(aF(τs)-bF(τs))+aF(τs)bk(s)bg(s)ah(s)bF(τs)
=aF(τs)ak(s)ag(s)bh(s)φ(s,τ)；
Wherein,Building S=τ s, τ → ∞ and s → 0 are equivalent.If φ (S) is Hurwitz multinomial, system is in τ=∞
When, system is stablized, and there are a stability region τ < τ < ∞, system keeps stablizing, and hasWherein,
7) parameter for designing K (s), considersWithTwo kinds of situations, wherein z, p, α, β are pre-compensating
The design parameter of device K may be designed as following two situation respectively:
Situation one:Design parameter z=a0λ and p=b0, so that φ (S) is Hurwitz multinomial,；
Situation two:Design parameter z=a0λ and p=b0, α and β are undetermined parameter, and corresponding value can make
Obtaining φ (S) is Hurwitz multinomial；
It introducing low-pass filter W (s), is matched by low frequency model, optimization calculates α and β,
8) timeconstantτ is calculated and in stable regionτIn < τ < ∞, τ value is chosen, realizes ESO, and adjust to τ
Section realizes expected performance.
Consider the concentration control problem of a kind of Chemical process control system, the disturbance rejection control device that the simulating, verifying invention provides
With preferable effect.The chemical system is mainly to control the concentration of product B by adjusting dilution rate F, wherein in inflow
Concentration comprising a kind of reactant A is cA0There is certain influence to reaction process, can be interfered as existing for system.Now to specific
Embodiment designs automatic disturbance rejection controller:
(1) when it is assumed that the temperature T of reaction kettle is steady state value, system is in equilibrium state, dilution F and production concentration y
=cBBetween relationship, transmission function are as follows:
And there is following input and output requirement:
cA0Variation range be 4.5mol/l≤cA0≤5.7mol/l。
It as it can be seen that there are the zero points of right half plane for the chemical industry control system, therefore is non-minimum phase system.The system it is opposite
Order is denoted as r.deg [G]=2, is chosen and is determined closed loop reference model HROpposite order is respectively with predistorter K's (s)
r.deg[HR]=r.deg [G]=2 and r.deg [K]=0, makes to meet: r.deg [K]+r.deg [G]=r.deg [HR]。
(2) desired closed loop transfer function, H is designedR(s), setup parameter ωc=50.So that closed-loop system has centainly
Response speed.The transmission function of closed loop reference model are as follows:
Augmented plant G (s) K (s) is write as the closed loop reference model form containing disturbance input, and the differential equation indicates are as follows:
y(r)=-100y(1)-2500y(0)+2500(uK+dK+f)
Wherein, dK=d/K, f are internal system disturbance, dK+ f is that system always disturbs, and is defined as expansion state x(r+1)=dK+
F, u=KuK.As shown in Figure 1, ESO carries out estimation compensation to expansion state, to carry out the elimination to disturbance.
State-space model are as follows:
(3) for closed loop reference model, with model HR(s) it is target, constructs the Active Disturbance Rejection Control structure of ESO and feedback,
Have:
Wherein xo=[xo1,xo2,xo3]TIt is system state variables, y0For the reality output of system, L is expansion state observation
Device gain, meeting POLE PLACEMENT USING condition has:
Wherein ωoIndicate ESO bandwidth, the ω of τ=1/oFor the time constant of ESO.
(4) in Active Disturbance Rejection Control, expansion state xo3It can be realized system disturbance estimation, there is x in a frequency domaino3=-F1uK+
F2yp, in which:
(5) building disturbance compensation control restrains u=K (s) uk=K (s) (y*-xo3)。
(6) judgement of stability condition: there are a time constantsτ> 0, for allτ< τ < ∞, if meet with
Lower condition, then closed-loop system has robust internal stability:
(C1) r.deg [K]+r.deg [G]=r.deg [HR]；
(C2) pole of the not no right half plane of G (s), or agIt (s) is Hurwitz multinomial；
(C3) pole of the not no right half plane of K (s), or akIt (s) is Hurwitz multinomial；
(C4) φ (S) is Hurwitz multinomial.
The form that the various pieces being related to are write as to relatively prime polynomial, has:
The proper polynomial of closed-loop system are as follows:
pc(s, τ)=aF(τs)ak(s)ag(s)bh(s)φ(s,τ)
It is therein: φ (S)=S3+3S2+ 3S+ λ, S=τ s.Due to aF(τ s) meets Hurwitz condition, a automaticallyk(s) full
Sufficient stability condition (C3), ag(s) meet stability condition (C2), bhIt (s) is a constant value, thus it is more for closed-loop system feature
Item formula meets Hurwitz condition.If K it is known that if timeconstantτ lower bound calculation formula:
WhereinFig. 3Represent nyquist plot L (s, τ) with (-
1,0) apart from the smallest point, indicate that nyquist plot passes through (- 1,0) as Φ=0, the minimum value of corresponding τ is τ.
(7) according to judgement of stability condition, the parameter of K (s) is designed,
Considerφ (S)=S in this3+3S2+ 3S+ λ need to take λ that φ (S) is made to be Hurwitz multinomial, then
There is 0 < λ < 9, enables z=a0The λ of λ=115370 and p=b0=5142.8.
In the present embodiment, λ=1, K=22.43 are taken.When Fig. 2 expression takes different λ, the value and τ of k in predistorter
Value.
(8) calculating the minimum value of timeconstantτ is τ, by calculating, in the present embodimentτ=0.0033, it determines and stablizes
Section is 0.0033 < τ < ∞, can choose suitable ESO bandwidth omegao∈ [0,303.03), it then indicates in K=in Fig. 3
When 22.43, the nyquist diagram of L (s, τ) under different bandwidth chooses ESO parameter ωo=150.Fig. 4 gives different cA0Condition
Under, the system response diagram of concentration adjustment process realizes preferable control performance.
The above is only the preferred embodiment of the present invention, the range implemented of the present invention that therefore, it cannot be limited according to, i.e., according to
Equivalent changes and modifications made by the invention patent range and description, should still be within the scope of the present invention.
Claims (1)
1. a kind of Auto-disturbance-rejection Controller Design method suitable for non-minimum phase system, characterized by the following steps:
1) first stability non-minimum phase system model G (s) is provided；
2) closed loop reference model, the transfer function H of the closed loop reference model are setR(s) are as follows:
With predistorter K (s), augmented plant G (s) K (s) is indicated
For the disturbed form of closed loop reference model, have:
y(r)=-k0y(0)-k1y(1)-…-kr-1y(r-1)+k0(uK+dK+f)；
Wherein, closed loop reference model H is chosen with respect to order r.deg [G] according to non-minimum phase system model G (s)R(s) with before
The opposite order for setting compensator K (s) meets r.deg [K]+r.deg [G]=r.deg [HR]；dK=d/K, d disturb for exterior
Dynamic, K is predistorter, and f is internal system disturbance, dK+ f is that system always disturbs, and defines expansion state x(r+1)=dK+ f, u=
KuK；State-space model are as follows:
Wherein, h is that system always disturbs dKThe differential of+f；
3) with HR(s) it is target, constructs ESO, have
Wherein, xo=[xo1,xo2,…,xo(r+1)]TFor ESO state, L is observer gain, ypFor system reality output, meet pole
Point configuration condition:
Wherein, ωoFor ESO bandwidth, the ω of τ=1/oFor ESO time constant, I is unit matrix；
4) system always disturbs dKThe frequency domain of+f is estimated；In Active Disturbance Rejection Control, expansion state xo(r+1)It can be realized system disturbance to estimate
Meter, there is x in a frequency domaino(r+1)(s)=- F1(s)uK(s)+F2(s)yp(s), in which:
5) disturbance compensation control rate u=K (s) u is constructedk=K (s) (y*-xo(r+1)), wherein y*To give input signal；
6) judgement of stability condition is provided, related various pieces are write as to the form of relatively prime polynomial, are hadThe characteristic equation of closed-loop system is
pc(s, τ)=aF(τs)ak(s)ag(s)bh(s)(aF(τs)-bF(τs))+aF(τs)bk(s)bg(s)ah(s)bF(τs)
=aF(τs)ak(s)ag(s)bh(s)φ(s,τ)；
Wherein,Building S=τ s, if φ (S) is Hurwitz multinomial, system in τ=∞, stablize, and there are one by system
Stability regionτ< τ < ∞, system keeps stablizing, and has
Wherein,
7) parameter for designing K (s), considersWithTwo kinds of situations, wherein z, p, α, β are predistorter K's
Design parameter may be designed as following two situation respectively:
Situation one:It takes λ that φ (S) is made to be Hurwitz multinomial, then has z=a0λ and p=b0；
Situation two:It takes λ that φ (S) is made to be Hurwitz multinomial, then has z=a0λ and p=b0, α and β are undetermined
Parameter；
It introducing low-pass filter W (s), is matched by low frequency model, optimization calculates α and β,
8) time constant is calculatedτAnd in stable regionτIn < τ < ∞, τ value is chosen, realizes ESO, and τ is adjusted, it is real
Existing expected performance.
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Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN105549385A (en) * | 2015-09-03 | 2016-05-04 | 北京化工大学 | Decoupling internal die controller, control system, and control method of multivariable time-lag non-minimum-phase non-square system |
| CN106773648A (en) * | 2016-12-19 | 2017-05-31 | 华侨大学 | The Robust Guaranteed Cost design and parameter tuning method of a kind of Active Disturbance Rejection Control |
| CN106950839A (en) * | 2017-05-09 | 2017-07-14 | 厦门理工学院 | A kind of building method of Active Disturbance Rejection Control structure |
| CN109062043A (en) * | 2018-08-01 | 2018-12-21 | 西北工业大学 | Consider the spacecraft Auto-disturbance-rejection Control of network transmission and actuator saturation |
-
2019
- 2019-05-24 CN CN201910440699.6A patent/CN110161857B/en active Active
Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN105549385A (en) * | 2015-09-03 | 2016-05-04 | 北京化工大学 | Decoupling internal die controller, control system, and control method of multivariable time-lag non-minimum-phase non-square system |
| CN106773648A (en) * | 2016-12-19 | 2017-05-31 | 华侨大学 | The Robust Guaranteed Cost design and parameter tuning method of a kind of Active Disturbance Rejection Control |
| CN106950839A (en) * | 2017-05-09 | 2017-07-14 | 厦门理工学院 | A kind of building method of Active Disturbance Rejection Control structure |
| CN109062043A (en) * | 2018-08-01 | 2018-12-21 | 西北工业大学 | Consider the spacecraft Auto-disturbance-rejection Control of network transmission and actuator saturation |
Non-Patent Citations (8)
| Title |
|---|
| LIU, RJ等: "Robust disturbance rejection for a fractional-order system based on equivalent-input-disturbance approach", 《SCIENCE CHINA-INFORMATION SCIENCES 》 * |
| NIE, ZY等: "Improved disturbance rejection control for piezoelectric actuators based on combination of ESO and Q-filter", 《ELECTRONICS LETTERS 》 * |
| 刘翔等: "不稳定对象及非最小相位对象的自抗扰控制仿真研究", 《控制与决策》 * |
| 刘翔等: "水轮发电机组调速系统的自抗扰控制", 《清华大学学报(自然科学版)》 * |
| 唐茂华等: "基于自抗扰的非最小相位伺服系统控制", 《雷达科学与技术》 * |
| 张绍杰等: "MIMO非线性非最小相位系统的鲁棒跟踪控制", 《南京航空航天大学学报》 * |
| 张超等: "基于最小拍观测器的自抗扰控制器设计与性能分析", 《控制理论与应用》 * |
| 聂卓等: "复杂条件下倒立摆摆角控制设计与实验研究", 《信息与控制》 * |
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