CN107102544A - Global finite time Track In Track control method based on disturbance observer - Google Patents
Global finite time Track In Track control method based on disturbance observer Download PDFInfo
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- CN107102544A CN107102544A CN201710297184.6A CN201710297184A CN107102544A CN 107102544 A CN107102544 A CN 107102544A CN 201710297184 A CN201710297184 A CN 201710297184A CN 107102544 A CN107102544 A CN 107102544A
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- 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
- G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
- G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
- G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance
Abstract
The invention discloses a kind of global finite time Track In Track control method based on disturbance observer, with following steps：Set up the above water craft equation of motion for representing current ship kinetic characteristic and expect to carry transposed matrix R (ψ) in ship course model, the above water craft equation of motion；By Coordinate Conversion, by the above water craft equation of motion with expect ship course model conversion into standard second order nonlinear control system；Analysis obtains the error system in second nonlinear control system；Finite time flight tracking control rule and corresponding disturbance observer are provided, Track In Track control is completed.
Description
Technical field
The present invention relates to a kind of global finite time Track In Track control method based on disturbance observer.It is related to patent point
Class-mark G05 is controlled；Adjust the general controls of G05B or regulating system；The functional unit of this system；For this system or list
Member monitoring or test device G05B13/00 adaptive control systems, i.e. system according to some predetermined criterion adjust automaticallies from
Oneself with the system G05B13/02 electricity of optimum performance G05B13/04 including the use of model or simulator.
Background technology
In field of non-linear control, finite-time control method has obtained widely studied due to its fast convergence.
Conventional finite-time control algorithm includes adding exponential integral, terminal sliding mode etc..In addition, thering is scholar to prove, in system asymptotically stability
On the basis of, if being able to demonstrate that, its degree of homogeneity is less than zero, then closed-loop system can reach the control effect of finite time stability.
Traditional can not be to outside time-varying uncertain disturbance based on the minus finite-time control method of degree of homogeneity
Handled, when its exterior disturbance is larger, system robustness is poor, and control performance declines.The invention is limited by introducing
Time disturbance observer so that system can effectively recognize outside uncertain disturbance, and closed-loop system is when meeting global limited
Between stable control effect, improve the robustness of control system.
The content of the invention
The proposition of the invention for being directed to problem above, and a kind of global finite time flight path based on disturbance observer developed
Tracking and controlling method, with following steps：
- set up the above water craft equation of motion for representing current ship kinetic characteristic and expect ship course model, the water
Transposed matrix R (ψ) is carried in the ship equation of motion of face；
- pass through Coordinate Conversion, by the above water craft equation of motion with expect ship course model conversion into standard second order
Nonlinear control system；
- analysis obtains the error system in second nonlinear control system；
- when external disturbance meets following condition：
Wherein, n is positive integer, Hi=diag (hi,1,hi,2,hi,3), and hi,j(j=1,2,3) it is arithmetic number；
Finite time flight tracking control rule and corresponding disturbance observer are provided, Track In Track control is completed；
Described flight tracking control rate is as follows：
In formula,H is disturbance observer design parameter, H=diag (h1,h2,h3), meet h1>0,h2>
0,h3>0；WithIt is the disturbance observer quantity of state being derived by by disturbance observer；
The disturbance observer is as follows：
In formula：
Wherein, τ is derived by by flight tracking control rate formula, Τi=diag (Ti,1,Ti,2,Ti,3) (i=0,1 ..., n-1) be
Disturbance observer design parameter, andAndαi=1+ (i+1) θ, αi>0, θ ∈ (- 1/ (n+1), 0).
As preferred embodiment, the described current above water craft equation of motion：
In formula：η=[x, y, ψ]TPosition (x, y) and deflection (ψ) of the expression above water craft under terrestrial coordinate system, ν=
[u,v,r]TRepresent the linear velocity (u of ship,V) with angular speed (r), M is ship quality, meets M=MT>0, C (ν) is Ke Liao
Sharp centripetal force matrix, D (ν) is damping matrix, τ=[τ1,τ2,τ3]TIt is control input, d=[d1,d2,d3]TIt is external disturbance, R
(ψ) is a transposed matrix, is expressed as：
R (ψ) has following property：
Property 1：RT(ψ) R (ψ)=I；
Property 2：To arbitrary ψ, haveAnd RT(ψ) S (r) R (ψ)=R (ψ) S (r) RT(ψ)=S (r),
And
As preferred embodiment, ship desired course is as follows：
Wherein, ηd=[xd,yd,ψd]TAnd νd=[ud,vd,rd]TIt is to expect ship motion state.
Brief description of the drawings
, below will be to embodiment or existing for clearer explanation embodiments of the invention or the technical scheme of prior art
There is the accompanying drawing used required in technology description to do one simply to introduce, it should be apparent that, drawings in the following description are only
Some embodiments of the present invention, for those of ordinary skill in the art, on the premise of not paying creative work, may be used also
To obtain other accompanying drawings according to these accompanying drawings.
Fig. 1-6 is not consider the simulation analysis result schematic diagram of external disturbance in the embodiment of the present invention
Fig. 7-13 is the simulation analysis result schematic diagram of consideration external disturbance in the embodiment of the present invention
Figure 14 is steps flow chart schematic diagram of the present invention
Embodiment
To make the purpose, technical scheme and advantage of embodiments of the invention clearer, with reference to the embodiment of the present invention
In accompanying drawing, clear complete description is carried out to the technical scheme in the embodiment of the present invention：
As represented in figures 1 through 14：A kind of global finite time Track In Track control method based on disturbance observer, main bag
Include following steps：
First, the above water craft equation of motion for representing current ship kinetic characteristic is provided,
Consider that the above water craft equation of motion is as follows：
In formula：η=[x, y, ψ]TPosition (x, y) and deflection (ψ) of the expression above water craft under terrestrial coordinate system, ν=
[u,v,r]TThe linear velocity (u, v) and angular speed (r) of ship are represented, M is ship quality, meets M=MT>0, C (ν) is Ke Liao
Sharp centripetal force matrix, D (ν) is damping matrix, τ=[τ1,τ2,τ3]TIt is control input, d=[d1,d2,d3]TIt is external disturbance, R
(ψ) is a transposed matrix, is expressed as：
Also, R (ψ) has the following property：
Property 1：RT(ψ) R (ψ)=I；
Property 2：To arbitrary ψ, haveAnd RT(ψ) S (r) R (ψ)=R (ψ) S (r) RT(ψ)=S (r),
And：
Consider that ship desired course is as follows：、
Wherein, ηd=[xd,yd,ψd]TAnd νd=[ud,vd,rd]TIt is to expect ship motion state.
The final control targe of the present invention is one control law τ of design, and provides corresponding disturbance controller so that actual
Signal (1) can track desired signal (3) in finite time.
In order to simplify disturbance controller design, we carry out following coordinate transform：
ω=R (ψ) ν (4a)
ωd=R (ψd)νd (4b)
Wherein, ω and ωdRepresent ship movement velocity new after coordinate transform, and ω=[ω1,ω2,ω3]T,
ωd=[ωd,1,ωd,2,ωd,3]T, following table d herein expect by expression.
By property 1,2 and (1) and (4a) Shi Ke get：
Similarly, it can be obtained by property 1,2 and (3) and (4b)
Make ηe=η-ηd, ωe=ω-ωd.It can be obtained by (5) and (7)
In formula：
Γe()=Γ ()-S (ωd,3)ωd-R(ψ)M-1f(·) (9)
Wherein, ηeAnd ωeThe site error after coordinate transform and velocity error, and η are represented respectivelye=[ηe,1,
ηe,2,ηe,3]T, ωe=[ωe,1,ωe,2,ωe,3]T。
Using feedback line method, mission nonlinear Γe() can be eliminated by measurable η and ν by mathematical operation,
And then simplify the design of controller.
When not considering external disturbance, this section design obtains the nominal control law of global finite time so that error system exists
Finite-time convergence is proved it to zero point, and with Lyapunov Theory of Stability.
According to homogeneous theoretical and modified feedback linearization control method, when not considering external disturbance d (t), it can obtain as follows
Global finite-time control rule：
Wherein,K1>0, K2>0,0<β1
<1,It is design parameter, sgn () is sign function, and
Prove：
Error system (8)-(9) are brought into control law (10)-(11), can be obtained
Choose Lyapunov functions as follows：
(13) derivation can be obtained along (12)
According to LaSalle invariant set theorems, closed-loop system (12) Globally asymptotic can be obtained.
System (12) can be written as
Wherein, f1()=ωe,j,It can thus be concluded that
According to homogeneity theory, the degree of homogeneity that can obtain closed-loop system (12) isWeight is accordingly
Analysis can be obtained more than, be less than zero in the secondly degree of closed-loop system Globally asymptotic, and system, thus may be used
To obtain the global finite time convergence control of system.
Traditional can not handle external disturbance based on the minus finite-time control method of degree of homogeneity, work as external disturbance
When larger, control input will not be able to ensure that systematic error converges to zero point.
Global finite time Track In Track control method based on disturbance observer
In view of it is traditional can not be to outside time-varying not based on the nominal control law of the minus finite time of degree of homogeneity
It is determined that disturbance is handled, when its exterior disturbance is larger, system robustness is poor, and control performance will decline.This section is led to
Cross introducing finite time disturbance observer so that system can effectively recognize outside uncertain disturbance, and closed-loop system is met
The control effect of global finite time stability, improves the robustness of control system
Assuming that 1：Assuming that external disturbance is met
Wherein, n is positive integer, Hi=diag (hi,1,hi,2,hi,3), and hi,j(j=1,2,3) it is arithmetic number.
Theorem 2. is met in external disturbance to be assumed in the case of 1, and with reference to modified feedback linearization control method, design robust is adaptive
Answer global finite time flight tracking control rule as follows：
In formula：
Wherein, H is disturbance observer design parameter, H=diag (h1,h2,h3), meet h1>0,h2>0,h3>0。With
It is the disturbance observer quantity of state being derived by by designed disturbance observer (20), disturbance observer is as follows：
In formula：
Wherein, τ is derived by by (10) formula, Τi=diag (Ti,1,Ti,2,Ti,3) (i=0,1 ..., n-1) seen for disturbance
Device design parameter is surveyed, andAndαi=1+ (i+1) θ, αi>0, θ ∈ (- 1/ (n+1), 0).
In order to which proof system error can be in Finite-time convergence to zero point, it is necessary to provide disturbance observer error, test
Can disturbance observation error be demonstrate,proved in Finite-time convergence to zero.
Consider following coordinate transform
It can thus be concluded that
It is as follows that can obtain disturbance observation error system by (20)-(23)：
Wherein,I.e.
By choosing suitable Ti,j, it can be ensured that (25) the global finite time stability of formula.It is furthermore noted that (25) formula is
The Homogeneous System that it is θ ＜ 0 that secondly one, which spent,.It can thus be concluded that,Can be in Finite-time convergence to zero.
That is, external disturbance d (t) and its each rank differential d(1)(t),…,d(n-1)(t) it can be observed in finite time.
It can be obtained by (8)-(9) and (18)-(19)
Wherein,Exported by (19)-(20).
Have as seen through the above analysis in some finite time pointIt can thus be concluded that
Can be obtained according to theorem 1, closed-loop system finite time stability, namely actual heading track can in finite time with
Desired trajectory on track.
Global finite time Track In Track control law (18) based on disturbance observer can not only ensure that desired signal has
Limit reference signal on time tracking, additionally it is possible to which finite time estimates external disturbance, therefore control system has stronger robustness.
Embodiment and compliance test result
When not considering external disturbance, to being designed with limited time between nominal control law model carried out simulation study.Choosing
It is K to take controller parameter1=0.24, K2=0.24, β1=1/3.Simulation result is as shown in figures 1 to 6.
Can be seen that from Fig. 1-Fig. 3 proposed in limited time between nominal control law model can cause in a short period of time
The upper reference signal of desired signal tracking, and control effect be substantially better than it is traditional based on Backstepping (β1=control 1)
Algorithm.
In addition, tracking error can converge to zero, as illustrated in figures 4-5.Corresponding control input such as Fig. 5.
Consider simulation analysis during external disturbance
Assuming that external disturbanceController parameter is chosen as follows：K1=1.0, K2=
1.0, T1=diag (10,10,10), T2=diag (32,32,32), α0=7/9, α1=5/9, α2=1/3, H1=0, H2=
diag(0.05π2,-0.09π2,-0.08π2), corresponding simulation result is as shown in figs 6-12.
It can be seen from Fig. 6-8 when there is external disturbance, the global finite time Track In Track control based on disturbance observer
Method processed is able to ensure that desired signal tracks reference signal in a short period of time, and control effect is substantially better than traditional base
In backstepping flight tracking control method.
From Fig. 9-10 as can be seen that when there is external disturbance, proposed in limited time between nominal control law model (GFTC β1
=1/3) will not be able to make tracking error to converge to zero, and the global finite time Track In Track control law based on disturbance observer
Model (ARGFTC β1=1/3) still may insure each signal errors in Finite-time convergence to zero.Corresponding disturbance observation
As a result and control input as depicted in figs. 11-12.
The foregoing is only a preferred embodiment of the present invention, but protection scope of the present invention be not limited thereto,
Any one skilled in the art the invention discloses technical scope in, technique according to the invention scheme and its
Inventive concept is subject to equivalent substitution or change, should all be included within the scope of the present invention.
Claims (3)
1. a kind of global finite time Track In Track control method based on disturbance observer, it is characterised in that with following step
Suddenly：
- set up the above water craft equation of motion for representing current ship kinetic characteristic and expect ship course model, the waterborne vessel
Transposed matrix R (ψ) is carried in the oceangoing ship equation of motion；
- pass through Coordinate Conversion, by the above water craft equation of motion with expect ship course model conversion into standard second order non-thread
Property control system；
- analysis obtains the error system in second nonlinear control system；
- when external disturbance meets following condition：
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Wherein, n is positive integer, Hi=diag (hi,1,hi,2,hi,3), and hi,j(j=1,2,3) it is arithmetic number；
Finite time flight tracking control rule and corresponding disturbance observer are provided, Track In Track control is completed；
Described flight tracking control rate is as follows：
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0；WithIt is the disturbance observer quantity of state being derived by by disturbance observer；
The disturbance observer is as follows：
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In formula：
p0=ωe, u=RM-1τ+Γe(·)
Wherein, τ is derived by by flight tracking control rate formula, Τi=diag (Ti,1,Ti,2,Ti,3) (i=0,1 ..., n-1) seen for disturbance
Survey device design parameter, and Ti,1>0,Ti,2>0,Ti,3>0。Andαi=1+ (i+1) θ, αi>0, θ ∈ (- 1/ (n+1), 0).
2. the global finite time Track In Track control method according to claim 1 based on disturbance observer, its feature
Also reside in：
The described current above water craft equation of motion：
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<mi>d</mi>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
In formula：η=[x, y, ψ]TPosition (x, y) and deflection (ψ) of the expression above water craft under terrestrial coordinate system, ν=[u, v,
r]TThe linear velocity (u, v) and angular speed (r) of ship are represented, M is ship quality, meets M=MT>0, C (ν) is that Coriolis is centripetal
Torque battle array, D (ν) is damping matrix, τ=[τ1,τ2,τ3]TIt is control input, d=[d1,d2,d3]TIt is external disturbance, R (ψ) is one
Individual transposed matrix, is expressed as：
<mrow>
<mi>R</mi>
<mrow>
<mo>(</mo>
<mi>&psi;</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<mrow>
<mi>c</mi>
<mi>o</mi>
<mi>s</mi>
<mrow>
<mo>(</mo>
<mi>&psi;</mi>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
<mtd>
<mrow>
<mo>-</mo>
<mi>s</mi>
<mi>i</mi>
<mi>n</mi>
<mrow>
<mo>(</mo>
<mi>&psi;</mi>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mi>s</mi>
<mi>i</mi>
<mi>n</mi>
<mrow>
<mo>(</mo>
<mi>&psi;</mi>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
<mtd>
<mrow>
<mi>cos</mi>
<mrow>
<mo>(</mo>
<mi>&psi;</mi>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>1</mn>
</mtd>
</mtr>
</mtable>
</mfenced>
</mrow>
R (ψ) has following property：
Property 1：RT(ψ) R (ψ)=I；
Property 2：To arbitrary ψ, haveAnd RT(ψ) S (r) R (ψ)=R (ψ) S (r) RT(ψ)=S (r), and
<mrow>
<mi>S</mi>
<mrow>
<mo>(</mo>
<mi>r</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mrow>
<mo>-</mo>
<mi>r</mi>
</mrow>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mi>r</mi>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>.</mo>
</mrow>
3. the global finite time Track In Track control method according to claim 1 based on disturbance observer, its feature
Also reside in：
Ship desired course is as follows：
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<msub>
<mover>
<mi>&eta;</mi>
<mo>&CenterDot;</mo>
</mover>
<mi>d</mi>
</msub>
<mo>=</mo>
<mi>R</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>&psi;</mi>
<mi>d</mi>
</msub>
<mo>)</mo>
</mrow>
<msub>
<mi>&nu;</mi>
<mi>d</mi>
</msub>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mi>M</mi>
<msub>
<mover>
<mi>&nu;</mi>
<mo>&CenterDot;</mo>
</mover>
<mi>d</mi>
</msub>
<mo>=</mo>
<mi>f</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>&eta;</mi>
<mi>d</mi>
</msub>
<mo>,</mo>
<msub>
<mi>&nu;</mi>
<mi>d</mi>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
Wherein, ηd=[xd,yd,ψd]TAnd νd=[ud,vd,rd]TIt is to expect ship motion state.
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| CN108828955A (en) * | 2018-08-16 | 2018-11-16 | 大连海事大学 | Accurate Track In Track control method based on finite time extended state observer |
| CN110377044A (en) * | 2019-07-24 | 2019-10-25 | 东南大学 | A kind of the finite time height and Attitude tracking control method of unmanned helicopter |
| CN110687799A (en) * | 2019-11-12 | 2020-01-14 | 大连海事大学 | Fuzzy self-adaptive output feedback control method and system for intelligent ship autopilot system |
| CN111338213A (en) * | 2020-03-17 | 2020-06-26 | 大连海事大学 | Self-adaptive fuzzy two-part consistent control method for multi-underwater vehicle based on event trigger mechanism |
| CN111766890A (en) * | 2020-07-24 | 2020-10-13 | 中南大学 | Spacecraft performance-guaranteeing attitude control method independent of neural network approximation |
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Cited By (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN108828955A (en) * | 2018-08-16 | 2018-11-16 | 大连海事大学 | Accurate Track In Track control method based on finite time extended state observer |
| CN110377044A (en) * | 2019-07-24 | 2019-10-25 | 东南大学 | A kind of the finite time height and Attitude tracking control method of unmanned helicopter |
| CN110687799A (en) * | 2019-11-12 | 2020-01-14 | 大连海事大学 | Fuzzy self-adaptive output feedback control method and system for intelligent ship autopilot system |
| CN110687799B (en) * | 2019-11-12 | 2022-02-11 | 大连海事大学 | Fuzzy self-adaptive output feedback control method and system for intelligent ship autopilot system |
| CN111338213A (en) * | 2020-03-17 | 2020-06-26 | 大连海事大学 | Self-adaptive fuzzy two-part consistent control method for multi-underwater vehicle based on event trigger mechanism |
| CN111766890A (en) * | 2020-07-24 | 2020-10-13 | 中南大学 | Spacecraft performance-guaranteeing attitude control method independent of neural network approximation |
| CN111766890B (en) * | 2020-07-24 | 2021-09-14 | 中南大学 | Spacecraft performance-guaranteeing attitude control method independent of neural network approximation |
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