CN109683631A - A kind of unmanned vehicle robust H ∞ reduced order control method - Google Patents
A kind of unmanned vehicle robust H ∞ reduced order control method Download PDFInfo
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Abstract
The present invention provides a kind of cascade unmanned vehicle robust H∞Reduced order control method is a kind of based on robust H∞The reduced order control method of control theory and information theory.It is main, and there are two steps, use robust H first∞Control algolithm generates H to various dimensions complex aircraft system∞Controller guarantees controller disturbance rejection.By controller cascade depression of order device of the input based on information theory of generation to remove redundancy, hardware controls difficulty is reduced.The present invention carries out simulation study by controlling a few class unmanned vehicles, it was confirmed that the validity of this method, simultaneously, it was confirmed that this method is adaptable, and hardware cost is low, and control performance is good under the premise of retaining strong robustness.
Description
Technical field
The present invention relates to a kind of unmanned vehicle control methods, more particularly to one kind to have robust H∞It control ability and is based on
The multi-model unmanned vehicle anti-interference flowing control method of information theory angle depression of order, the invention belong to aerospace unmanned air vehicle technique
Field.
Background technique
In modern scientist field, the physical object faced is often the complication system of high order, H∞Controlling is earliest
Grow up from frequency domain, with internal uncertain and external disturbance system, thus it effectively can handle and analyze
The controller that Theoretical Design goes out can guarantee the stability of closed-loop system and make interference to the smallest effect of systematic influence, in the modern times
Attempt to sum up problem in Control System Design and is converted to the H for making closed loop transfer function,∞Norm minimum, or it is less than some just
Number, i.e. H∞Norm optimization's problem, with robust H in recent years∞The mature development and extensive use of control method, utilize robust H∞Control
Controller order designed by method processed is often not less than generalized object, it is contemplated that the very high problem of order, either from programming
Or for the angle of Project Realization, or economic cost, larger difficulty can be all caused, therefore, it is desirable to H∞The order of controller is most
Possible reduction.
Last century 80 arrives the nineties, this concept of Controller order-reduction is suggested, it is desirable to which higher order controller K (s) passes through
Degree Reduction Algorithm can obtain lower order controller Kr(s), and the two is approached under certain meaning.Enns proposition in 1984 will stablize
Controller order-reduction method of the property as an important criteria, but be difficult to obtain the error and performance loss of depression of order closed-loop system.From
This Controller order-reduction obtains the concern on control circle, and nineteen ninety Liu and Anderson are by introducing method of weighting for Controller order-reduction
The problem of being converted to model reduction proposes the relatively prime factor Controller order-reduction algorithm of weighting, but systematic error problem does not obtain yet
To solution.Mustafa is for regular H∞Controller order-reduction proposes the method based on priori performance bound, will be regular mutual
Matter factor is used for H∞In the Controller order-reduction of Loop analysis.Vinnicombe estimates approximation using gap and makees on this basis
Subsequent improvement.Subsequent Wang and Sreeram proposes that a kind of additive disturbance by closed loop transfer function, obtains low order control
The method of device, but control effect and closed loop characteristic are all not fully up to expectations in biggish system.
Summary of the invention
In order to solve the problems, such as this kind of it cannot be guaranteed that closed-loop characteristic and control effect are short of, the present invention provides it is a kind of nobody
Aircraft robust H∞Reduced order control method, this method are a kind of effective cascade robust H∞Reduced order control method guarantees depression of order control
While device robustness processed, redundancy is eliminated, preferable control effect can be obtained.
To achieve the goals above, the invention adopts the following technical scheme:
A kind of unmanned vehicle robust H∞Reduced order control method, comprising the following steps:
1) it according to the transfer function matrix model for outputting and inputting data and obtaining control channel of control object system, will obtain
The transfer function model obtained is converted into state space description model；
2) robust H is used∞Controller method carries out higher order controller design to control object, generates high-order H∞Controller；
3) by the high-order H of generation∞Depression of order device of the controller cascade input based on information theory is to remove redundancy, output
Lower order controller state equation.
Preferably, step 3) includes: again
To the n rank controller (A of given controlled device (A, B, C)k, Bk, Ck),
3-1) solve the ornamental Grammian matrix Q of former controllerO；
3-2) to QOIt carries out Cholesky and decomposes QO=PTP；
3-3) to original controller system (Ak, Bk, Ck) make similarity transformationRegular controller model must be exported
Systematic steady state state covariance matrix after 3-4) solution Lyapunov equation is converted
3-5) balance system is truncated, with the reduced order system for the system performance that is maintained, is balanced with Moore method
Transformation matrix TR；
(A 3-6) is calculatedkR, BkR, CkR) it is required reduced order controller；
3-7) composition closed-loop system is tested and error point | | Φ (s)-Φr(s)||∞≤ σ, is returned.
Key problem in technology point of the invention is how to remove robust H∞Increase the redundancy of hardware burden, design in controller
Provide the low order H of standby preferable robustness and control performance∞Controller.
The present invention have it is following positive the utility model has the advantages that
Pass through the robust H to unmanned vehicle∞Reduced order control method carry out simulation study, it was confirmed that this method it is effective
Property.The description form of the invention adoption status spatial model as control channel, can preferably recognize containing the control disturbed outside
Channel pattern, using robust H∞Control algolithm generates high-order H to various dimensions complex aircraft system∞Controller ensure that control
Device disturbance rejection, then depression of order device of the controller cascade input based on information theory of generation is reduced with removing redundancy
Hardware controls difficulty.By carrying out flight control simulation research to a few class unmanned vehicles, it was confirmed that this method is adaptable, firmly
Part is at low cost, and control performance is good under the premise of retaining strong robustness.
Detailed description of the invention
Fig. 1 is standard H∞Control problem block diagram.
Fig. 2 is H∞Standard design structure diagram.
Specific embodiment
In order to enable the public to fully understand technical spirit and beneficial effect of the invention, applicant will be below in conjunction with attached drawing
Detailed description of specific embodiments of the present invention, but applicant is to the limitation that the description of example is not to technical solution, any
Design, which changes in the form rather than substance, according to the present invention all should be considered as protection scope of the present invention.
Robust H of the invention∞Reduced order control method, includes the following steps:
1, control channel, the system for obtaining state space description are directed to.Number is output and input according to control object system
The transfer function model of acquisition is converted into state space description model according to the transfer function matrix model for obtaining control channel.
2, robust H is used under the premise of step 1∞Controller method carries out higher order controller design to control object.If
Degenerative error pass through mechanism is counted, control effect, approximate error minimum value are detected.
3, it is used under the premise of preceding 2 step and combines modern control theory balance truncation algorithm and the letter based on information theory
The innovatory algorithm for ceasing loss reduction principle carries out the update of control law, by setting target error, approaches high-order control effect, defeated
Lower order controller state equation out.
The present invention is further described in detail with reference to the accompanying drawing:
The first step, robust H∞Controller design:
In Fig. 1, P is generalized object, and P11, P12, P21, P22 are the matrix in block form obtained by controllable considerable principle, and K is
Controller, wherein containing controlled device and frequency weighting function.
In formula, z ∈ RmTo be controlled output signal, y ∈ RqIt is measuring signal, external input signal ω ∈ Rr, u ∈ RpIt is control
Input signal processed.
The H of standard∞Control problem is the controller K for solving a canonical:
U=Ky
Closed-loop system can be made to stablize, and make the transmission function of ω to z:
Tzω=P11+P12K(1-P22K)-1P21H∞Norm minimum solves:
min||Tzω||∞
It is expressed as optimal H ∞ control problem.
If given γ > 0, above formula becomes | | Tzω||∞< γ
Above formula indicates suboptimum H∞Control problem.
In Fig. 2, wherein r, e, u, d and y are respectively reference input, speed error, control input, external disturbance and are
System output；G is controlled object model；K is H∞Controller, weighting function W1 indicate the constraint to system performance requirements, W2 reflection
Limitation to Additive Generator, weighting function W3 are reflected to the probabilistic limitation of multiplying property, z1、z2、z3For commenting for system
Bivalent signal.
The state space realization of nominal transmission function is
Z=C1x+D11ω+D12u
Y=C2x+D21ω+D22u
The sensitivity function S of system are as follows:
S=(I+GK)-1
Wherein, I is unit matrix, and G is system model, and system sensitivity function can improve system to the inhibition of interference
The tracking ability of energy and input signal, | | S | |∞Inhibit the measurement of interference performance for closed-loop system.
Compensate sensitivity function T are as follows:
T=GK (I+GK)-1=I-S
Compensation sensitivity function can guarantee the robust stability of system.
The sensitivity function R of controller are as follows:
R=K (I+GK)-1=KS
Generalized object P is pushed away to obtain by Φ:
It obtains
Wherein, W1It indicates the constraint to system performance requirements, by adjusting the influence that can effectively inhibit interference, obtains
Desired output signal；Weighting function W2The limitation to Additive Generator is reflected, can be regarded as here to control signal
The constraint of amplitude；Weighting function W3It reflects to the probabilistic limitation of multiplying property, is determined by control object characteristic itself.
Second step, the application of information loss minimum principle in the controls
By information theory knowledge it is found that under the premise of system is Asymptotic Stability, the stable state shape of primal system and reduced order system
State comentropy can be expressed by the steady state covariance of system.Asymptotically stable primal system steady state information entropy are as follows:
Wherein, e is index.P (x (t)) and p is defined respectivelyr(xrIt (t)) is original and reduced order system state vector probability
Density, the two have following relationships:
Using KL minimal information Distance Theory, taken respectively about p (x (t)) and pr(xr(t)) mathematic expectaion, then makees
Difference obtains the least disadvantage information distance function of primal system and reduced order system:
IL(x(t)；xr(t))=Er{lnpr(xr(t))}-E{lnp(x(t))} (8)
It may further be expressed as:
If system be it is asymptotically stable, information loss minimum function can be obtained by formula (5) and (6):
Constant full rank controller when consideration Asymptotic Stability and controllable and considerable LINEAR CONTINUOUS:
In formula, x (t) ∈ Rn, ω (t) ∈ Rm, y (t) ∈ Rp。AK、BK、CKIt is the permanent matrix with corresponding dimension.ω(t)
It is the zero mean Gaussian white noise vector of covariance.
Assuming that controller model after depression of order are as follows:
yR(t)=CKRx(t) (12)
Wherein, xR(t)∈Rr, yR(t)∈Rr, r≤n.AKR、BKR、CKRFor the permanent matrix with corresponding dimension.
The criterion of minimum information loss method is, during obtaining reduced order system, makes to include flat in system mode
Equal information loss is minimum.
Enable the controllable and considerable Grammian matrix of system as follows:
They are respectively the positive definite symmetric solution of following Lyapnov equation:
AKPC+PCAK T+BKBK T=0
AK TQO+QOAK+CK TCK=0 (14)
Controllability information is combined with controllability information, the comentropy (Entropy) of controllability information are as follows:
Wherein, n is model order.It is similar, the comentropy of the ornamental information of system are as follows:
So the summation of controllability and ornamental information:
For the controller after depression of order, similarly have:
So, we will be such that following information loss minimizes:
Htotal(x,xR)=HΣ-HΣR=ILC(x,xR)-ILO(x,xR)(19)
Controllability information loss are as follows: ILC(x,xR)=H (PC)-H(PCR)
Controllability information loss are as follows: ILO(x,xR)=H (QO)-H(QOR)
It follows that if the Grammian product matrix P of full rank modelCQOMiddle R maximum eigenvalue is in reduced order controller
In retained, the loss of information will be minimum.System status information can be expressed by comentropy, and comentropy can lead to
System mode covariance matrix is crossed to indicate, so system status information can be described by system mode covariance matrix.?
On the basis of the smallest model reduction algorithm of information loss, it is made improvements, balance Degree Reduction Algorithm is introduced and combines, balance depression of order
Algorithm can make the inside of reduced order controller reach a kind of inner equilibrium state, can be improved the probability of stability of closed-loop system, improve
Specific step is as follows for algorithm:
To the n rank controller (A of given controlled device (A, B, C)k, Bk, Ck)
Step 1: solving the ornamental Grammian matrix Q of former controllerO。
Step 2: to QOIt carries out Cholesky and decomposes QO=PTP。
Step 3: to original controller system (Ak, Bk, Ck) make similarity transformationIt can must export regular controller
Model
Step 4: solving the steady state covariance matrix of system after Lyapunov equation is converted
Step 5: balance system is truncated, with the reduced order system for the system performance that is maintained.It is obtained with Moore method
Balanced transformation matrix TR。
Step 6: (A is calculatedkR, BkR, CkR) it is required reduced order controller.
Step 7: composition closed-loop system is tested and error point | | Φ (s)-Φr(s)||∞≤ σ, is returned.
The main problem that the present invention solves is:
(1) by unmanned aerial vehicle control system design in many problems be attributed to and make the H of a certain closed loop transfer function,∞Model
Number is minimum, or less than some specified positive number, ensure that and keep certain original product when its parameter or structure perturb
The ability of matter.
(2) Degree Reduction Algorithm part proposes the information loss minimum criteria Degree Reduction Algorithm based on information theory, and combines existing
For control theory balance truncation algorithm, solves H∞The problem of controller information redundancy causes hardware to be difficult to realize, and effectively
Main control information is had mapped, so that control effect preferably approaches former controller.
(3) network architecture of tandem type is proposed, solves the problems, such as two module information transmitting, and be conducive to error
It detects the adjustment with system regression parameter and maintains preferable closed loop characteristic, expanded convenient for the practical application in multi-model field.
Claims (2)
1. a kind of unmanned vehicle robust H∞Reduced order control method, comprising the following steps:
1) according to the transfer function matrix model for outputting and inputting data and obtaining control channel of control object system, by acquisition
Transfer function model is converted into state space description model；
2) robust H is used∞Controller method carries out higher order controller design to control object, generates high-order H∞Controller；
3) by the high-order H of generation∞Controller cascade depression of order device of the input based on information theory exports low order to remove redundancy
Controller state equation.
2. a kind of unmanned vehicle robust H according to claim 1∞Reduced order control method, which is characterized in that step 3) is again
Include:
To the n rank controller (A of given controlled device (A, B, C)k, Bk, Ck),
3-1) solve the ornamental Grammian matrix Q of former controllerO；
3-2) to QOIt carries out Cholesky and decomposes QO=PTP；
3-3) to original controller system (Ak, Bk, Ck) make similarity transformationRegular controller model must be exported
Systematic steady state state covariance matrix after 3-4) solution Lyapunov equation is converted
3-5) balance system is truncated, with the reduced order system for the system performance that is maintained, is balanced transformation with Moore method
Matrix TR；
(A 3-6) is calculatedkR, BkR, CkR) it is required reduced order controller；
3-7) composition closed-loop system is tested and error point | | Φ (s)-Φr(s)||∞≤ σ, is returned.
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Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20130124177A1 (en) * | 2009-06-13 | 2013-05-16 | Eric T. Falangas | Method of modeling dynamic characteristics of a flight vehicle |
| US20170293710A1 (en) * | 2016-04-11 | 2017-10-12 | Hamilton Sundstrand Corporation | Closed loop control and built-in test utilizing reduced order model |
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2019
- 2019-02-28 CN CN201910152868.6A patent/CN109683631A/en active Pending
Patent Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20130124177A1 (en) * | 2009-06-13 | 2013-05-16 | Eric T. Falangas | Method of modeling dynamic characteristics of a flight vehicle |
| US20170293710A1 (en) * | 2016-04-11 | 2017-10-12 | Hamilton Sundstrand Corporation | Closed loop control and built-in test utilizing reduced order model |
Non-Patent Citations (5)
| Title |
|---|
| 曹清: "用于离散时间模型降阶改进的最小信息损失方法", 《江南大学学报(自然科学版)》 * |
| 李久芹 等: "基于Hankel范数与平衡截断法的联合降阶模型", 《科技视界》 * |
| 李蒙 等: "基于鲁棒H_∞的无人机飞行控制系统设计及实现", 《北京理工大学学报》 * |
| 汪庆 等: "参数优化配置的广义奇异摄动弹性飞机模型降阶研究", 《测控技术》 * |
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