CN102929130A - Robust flight controller design method - Google Patents

Abstract

The invention discloses a robust flight controller design method which is used for solving the technical problem that the existing robust control theory lacks design steps, so the flight controller is hard to design directly. The technical scheme is as follows: the system robust stability and solvability conditions are given, selection of desired closed-loop poles of linear system state feedback is directly utilized and a constraint condition inequality direct design feedback matrix is given according to the characteristic that all the real parts of all the desired closed-loop poles are negative, so that the engineering technicians in the research field directly design the flight controller for the aircraft model with uncertainty obtained through wind tunnel or flight tests, thus solving the technical problem that the current researches only give the robust stability inequality but can not directly design the flight controller.

Description

A kind of Robust Flight Control device method for designing

Technical field

The present invention relates to a kind of controller design method, particularly relate to a kind of Robust Flight Control device method for designing.

Background technology

The aircraft robust control is one of emphasis problem of present international airline circle research, when the high performance airplane controller designs, must consider robust stability and kinds of robust control problems; Practical flight device model is the non-linear differential equation of very complicated Unknown Model structure, and in order to describe the non-linear of this complexity, people adopt wind-tunnel and flight test to obtain the test model of describing by discrete data usually; In order to reduce risks and to reduce experimentation cost, usually carry out the flight maneuver test according to differing heights, Mach number, like this, the discrete data of describing the aircraft test model is not a lot, aircraft is very practical preferably to static stability for this model.Yet the modern and following fighter plane has all relaxed restriction to static stability in order to improve " agility ", and fighter plane requires to work near open loop neutrality point usually; So just require well transaction module uncertain problem of flight control system; Will consider following subject matter in the practical flight Control System Design: (1) obtains discrete data with test and describes with a certain approximate model, exists not modeling dynamic in the model; (2) wind tunnel test can not be carried out the full scale model free flight, have constraint, the flight test discrete point is selected, the input action selection of initially state of flight, maneuvering flight etc. can not with all non-linear abundant excitations, adopt System Discrimination gained model to have various errors; (3) flight environment of vehicle and experimental enviroment are had any different, flow field change and interference etc. so that actual aerodynamic force, moment model and test model have any different; (4) there are fabrication tolerance in execution unit and control element, also have the phenomenons such as aging, wearing and tearing in system's operational process, and be not identical with the result of flight test; (5) in the Practical Project problem, need controller fairly simple, reliable, usually need to simplify for ground the mathematics model person, remove some complicated factors; Therefore, when the control problem of research present generation aircraft, just must consider robustness problem.

After 1980, carried out in the world the control theory research of multiple uncertain system, the H-infinit theory that is particularly proposed by Canadian scholar Zames, Zames thinks, why robustness is bad for the LQG method of state-based spatial model, mainly is because represent that with White Noise Model uncertain interference is unpractical; Therefore, in the situation that disturbing, supposition belongs to a certain known signal collection, Zames proposes norm with its corresponding sensitivity function as index, design object is that the error of system is issued in this norm meaning is minimum, thereby will disturb the inhibition problem to be converted into to find the solution makes closed-loop system stable; From then on, the lot of domestic and international scholar has launched the research of H-infinit control method; At aeronautical chart, the method is in the exploratory stage always, U.S. NASA, and the state such as German aerospace research institute, Holland all is studied robust control method, has obtained a lot of emulation and experimental result; Domestic aviation universities and colleges have also carried out a series of research to the aircraft robust control method, such as document (Shi Zhongke, Wu Fangxiang etc., " robust control theory ", National Defense Industry Press, in January, 2003; Su Hongye. " robust control basic theory ", Science Press, in October, 2010) introduce, but the distance of these results and practical application also differs very large, is difficult to directly the practical flight controller be designed and uses; Particularly a lot of researchs have only provided Robust Stability according to Lyapunov theorem, and for how realizing that robust controller does not have the specific design step; H _∞Very difficult when actual computation, it not only needs to choose rational weighting matrix, and, need repeatedly iterative computation, " suboptimal solution is asked in the parameter of successively decreasing γ-exploration " comes the minimum value γ of continuous approximating parameter γ repeatedly _MinLike this, choose different weighting matrixs and γ, will repeatedly calculate Riccati equation, so that uncertain problem is found the solution too complexity, on the other hand, when the state equation order of system is too high, the designing and calculating error is usually very large even occur wrong and can not use, and not have to solve the technical matters that directly designs the Robust Flight Control device.

Summary of the invention

Excessive and be difficult to directly design the technical deficiency of flight controller in order to overcome existing robust control theory designing and calculating error, the invention provides a kind of Robust Flight Control device method for designing; The method provides the sufficient and necessary condition of real system Design of Robust Stabilizing Controllers Based, directly utilizes the closed loop expectation the selection of poles configuration weighting matrix of State Feedback for Linear Systems, and adopts orthogonalization method to find the solution H _∞Control problem, do not need repeatedly to find the solution calculation of complex, Riccati equation that error is larger, can directly design flight controller to the uncertain dummy vehicle that contains that wind-tunnel or flight test obtain, solve that current research only provides the robust stability inequality and the technical matters that can't directly design flight controller.

The technical solution adopted for the present invention to solve the technical problems is: a kind of Robust Flight Control device method for designing is characterized in may further comprise the steps:

Step 1, under assigned altitute, Mach number condition, obtain containing probabilistic dummy vehicle by wind-tunnel or flight test

At corresponding system state revertive control rule u=Kx=-B ^TDuring Px, design flight robust controller usually runs into following problem:

A ^TP+PA+P(γ ^-2EE ^T-BR ^-1B ^T)P+C ^TC=0 (1)

In the formula, x ∈ R ⁿBe state vector, u ∈ R ^mBe control vector, w ∈ R ^lBe the Unknown Model noise vector, A, B, E are known matrix of coefficients; C ^TC, R are respectively the state that can regulate and the weighting matrix of input vector, P=P ^T0 for unknown matrix to be found the solution, and γ〉0 constant for selecting;

(1) sufficient and necessary condition of formula P existence and positive definite is: A (C ^TC) ^-1A ^T+ BR ^-1B ^T-γ ^-2EE ^T0;

Step 2, there is orthogonal matrix T, so that: NT-CAC ^-10

In the formula: NN ^T=CA (C ^TC) ^-1] A ^TC ^T+ CBR ^-1B ^TC ^T-γ ^-2CEE ^TC ^T

Step 3, find the solution positive definite matrix P by following steps:

1. general real system A then chooses suitable P without heavy limit if having ₀=δ I makes A without heavy limit after the feedback; Wherein: δ 〉=0 is positive count, and I is unit matrix;

2. CN is carried out svd and get NN ^T=SD ²S ^T, make N=SDV ₁, T ₁=V ₁S; Wherein: S, V ₁Be orthogonal matrix;

3. establish S ^TC=WM ^-1, W=diag{w ₁, w ₂..., w _nBe the diagonal angle weighting matrix, M is the matrix of a linear transformation of A, M ^-1AM=J=diag[J ₁, J ₂..., J _r]; For the real number eigenwert of A, the sub-block of corresponding J be diagonal matrix, get T ₁=I gets P=MW ^-1(D-J) ^-1(MW ^-1) ^T

4. when A has the Complex eigenvalues value, must have a conjugation Complex eigenvalues value corresponding with it, be real number matrix in order to make M, stipulate this a pair of conjugate complex number eigenwert the sub-block of corresponding J be $\left[\begin{array}{cc}\mathrm{\σ}& \mathrm{\ω}\\ -\mathrm{\ω}& \mathrm{\σ}\end{array}\right],$ Have:

$\mathrm{\Ω}={\mathrm{WM}}^{-1}{\mathrm{AMW}}^{-1}={\mathrm{WJW}}^{-1}=\mathrm{diag}\{{\mathrm{\λ}}_1,{\mathrm{\λ}}_2,\·\·\·,{\mathrm{\λ}}_r,\left[\begin{array}{cc}{\mathrm{\σ}}_1& {\mathrm{\ω}}_1(w_{r+1}/w_{r+2})\\ -{\mathrm{\ω}}_1(w_{r+2}/w_{r+1})& {\mathrm{\σ}}_1\end{array}\right],$

$\·\·\·,\left[\begin{array}{cc}{\mathrm{\σ}}_p& {\mathrm{\ω}}_p(w_{n-1}/w_n)\\ -{\mathrm{\ω}}_p(w_n/w_{n-1})& {\mathrm{\σ}}_p\end{array}\right]\};,(r+2p=n)$

S ^TCP ^-1C ^TS=DT-S ^TCAC ^-1S=DT ₁-WJW ^-1

Make T ₁=diag[1 ..., 1, T _1,1, T _1,2..., T _{1, p}]

DT then ₁-WJW ^-1=diag[d ₁-λ ₁..., d _r-λ _r, Ω ₁Ω ₂..., Ω _p]

Wherein $T_{1,j}=\left[\begin{array}{cc}\cos {\mathrm{\α}}_j& \sin {\mathrm{\α}}_j\\ -\sin {\mathrm{\α}}_j& \cos {\mathrm{\α}}_j\end{array}\right],(j=\mathrm{1,2},\·\·\·,p)$

${\mathrm{\Ω}}_j=\left[\begin{array}{cc}{d}_{r+2j-1}& 0\\ 0& d_{r+2j}\end{array}\right]\left[\begin{array}{cc}\cos {\mathrm{\α}}_j& \sin {\mathrm{\α}}_j\\ -\sin {\mathrm{\α}}_j& \cos {\mathrm{\α}}_j\end{array}\right]-\left[\begin{array}{cc}{\mathrm{\σ}}_j& {\mathrm{\ω}}_j(w_{r+2j-1}/w_{r+2j})\\ -{\mathrm{\ω}}_j(w_{r+2j}/w_{r+2j-1})& {\mathrm{\σ}}_j\end{array}\right]$

Get $\sin {\mathrm{\α}}_j=-\frac{(\frac{w_{r+2j}}{w_{r+2j-1}}+\frac{w_{r+2j-1}}{w_{r+2j}}){\mathrm{\ω}}_j}{d_{r+2j-1}+d_{r+2j}},$ Ω then _jBe symmetric matrix.

P=MW ^-1(DT1-J) ^-1(MW ^-1) ^T。

The invention has the beneficial effects as follows: can separate condition by system robust provided by the invention is stable, directly utilize the closed loop expectation the selection of poles of State Feedback for Linear Systems, and be the characteristics of negative all according to the real part of all closed loops expectation limits, provided the direct design of feedback matrix of qualifications inequality.So that the engineering technical personnel of this research field directly design flight controller to the uncertain dummy vehicle that contains that wind-tunnel or flight test obtain, solved that current research only provides the robust stability inequality and the technical matters that can't directly design flight controller.

Below in conjunction with embodiment the present invention is elaborated.

Embodiment

A kind of Robust Flight Control device of the present invention method for designing concrete steps are as follows:

1, under assigned altitute, Mach number condition, obtains containing probabilistic dummy vehicle by wind-tunnel or flight test

At corresponding system state revertive control rule u=Kx=-B ^TDuring Px, design flight robust controller usually runs into following problem:

A ^TP+PA+P(γ ^-2EE ^T-BR ^-1B ^T)P+C ^TC=0 (1)

In the formula, x ∈ R ⁿBe state vector, u ∈ R ^mBe control vector, w ∈ R ^lBe the Unknown Model noise vector, A, B, E are known matrix of coefficients; C ^TC, R are respectively the state that can regulate and the weighting matrix of input vector, P=P ^T0 for unknown matrix to be found the solution, and γ〉0 constant for selecting;

(1) sufficient and necessary condition of formula P existence and positive definite is: A (C ^TC) ^-1A ^T+ BR ^-1B ^T-γ ^-2EE ^T0;

2, there is orthogonal matrix T, so that: NT-CAC ^-10

In the formula: NN ^T=CA (C ^TC) ^-1] A ^TC ^T+ CBR ^-1B ^TC ^T-γ ^-2CEE ^TC ^T

3, find the solution positive definite matrix P by following steps:

1. general real system A then chooses suitable P without heavy limit if having ₀=δ I makes A without heavy limit after the feedback; Wherein: δ 〉=0 is positive count, and I is unit matrix;

2. CN is carried out svd and can get NN ^T=SD ²S ^T, make N=SDV ₁, T ₁=V ₁S; Wherein: S, V ₁Be orthogonal matrix;

3. establish S ^TC=WM ^-1, W=diag{w ₁, w ₂..., w _nBe the diagonal angle weighting matrix, M is the matrix of a linear transformation of A, M ^-1AM=J=diag[J ₁, J ₂..., J _r]; For the real number eigenwert of A, the sub-block of corresponding J be diagonal matrix, get T ₁=I can get P=MW ^-1(D-J) ^-1(MW ^-1) ^T

4. when A has the Complex eigenvalues value, must have a conjugation Complex eigenvalues value corresponding with it, be real number matrix in order to make M, stipulate this a pair of conjugate complex number eigenwert the sub-block of corresponding J be $\left[\begin{array}{cc}\mathrm{\σ}& \mathrm{\ω}\\ -\mathrm{\ω}& \mathrm{\σ}\end{array}\right],$ Have:

$\mathrm{\Ω}={\mathrm{WM}}^{-1}{\mathrm{AMW}}^{-1}={\mathrm{WJW}}^{-1}=\mathrm{diag}\{{\mathrm{\λ}}_1,{\mathrm{\λ}}_2,\·\·\·,{\mathrm{\λ}}_r,\left[\begin{array}{cc}{\mathrm{\σ}}_1& {\mathrm{\ω}}_1(w_{r+1}/w_{r+2})\\ -{\mathrm{\ω}}_1(w_{r+2}/w_{r+1})& {\mathrm{\σ}}_1\end{array}\right],$

$\·\·\·,\left[\begin{array}{cc}{\mathrm{\σ}}_p& {\mathrm{\ω}}_p(w_{n-1}/w_n)\\ -{\mathrm{\ω}}_p(w_n/w_{n-1})& {\mathrm{\σ}}_p\end{array}\right]\};,(r+2p=n)$

S ^TCP ^-1C ^TS＝DT-S ^TCAC ^-1S＝DT ₁-WJW ^-1

Make T ₁=diag[1 ..., 1, T _1,1, T _1,2..., T _{1, p}]

DT then ₁-WJW ^-1=diag[d ₁-λ ₁..., d _r-λ _r, Ω ₁Ω ₂..., Ω _p]

Wherein $T_{1,j}=\left[\begin{array}{cc}\cos {\mathrm{\α}}_j& \sin {\mathrm{\α}}_j\\ -\sin {\mathrm{\α}}_j& \cos {\mathrm{\α}}_j\end{array}\right],(j=\mathrm{1,2},\·\·\·,p)$

${\mathrm{\Ω}}_j=\left[\begin{array}{cc}{d}_{r+2j-1}& 0\\ 0& d_{r+2j}\end{array}\right]\left[\begin{array}{cc}\cos {\mathrm{\α}}_j& \sin {\mathrm{\α}}_j\\ -\sin {\mathrm{\α}}_j& \cos {\mathrm{\α}}_j\end{array}\right]-\left[\begin{array}{cc}{\mathrm{\σ}}_j& {\mathrm{\ω}}_j(w_{r+2j-1}/w_{r+2j})\\ -{\mathrm{\ω}}_j(w_{r+2j}/w_{r+2j-1})& {\mathrm{\σ}}_j\end{array}\right]$

Get $\sin {\mathrm{\α}}_j=-\frac{(\frac{w_{r+2j}}{w_{r+2j-1}}+\frac{w_{r+2j-1}}{w_{r+2j}}){\mathrm{\ω}}_j}{d_{r+2j-1}+d_{r+2j}},$ Ω then _jBe symmetric matrix.

P＝MW ^-1(DT ₁-J) ^-1(MW ^-1) ^T

As: $A=\left[\begin{array}{cc}1& 0\\ 0& 2\end{array}\right],$ $B=\left[\begin{array}{cc}\sqrt{3}& 0\\ -2/\sqrt{3}& \sqrt{23/3}\end{array}\right],$ $C=\left[\begin{array}{cc}1& 1\\ 0& 1\end{array}\right],$ R＝I， ${\mathrm{CAC}}^{-1}=\left[\begin{array}{cc}1& 1\\ 0& 2\end{array}\right],$ $N=\left[\begin{array}{cc}3& 1\\ 2& 3\end{array}\right]$ $T=\frac{1}{37}\left[\begin{array}{cc}35& 12\\ -12& 35\end{array}\right],$ $(\mathrm{NT}-{\mathrm{CAC}}^{-1})=\frac{1}{37}\left[\begin{array}{cc}56& 34\\ 34& 55\end{array}\right],$ $P^{-1}=\frac{1}{37}\left[\begin{array}{cc}43& -21\\ -21& 55\end{array}\right],$ $P=\frac{37}{1924}\left[\begin{array}{cc}55& 21\\ 21& 43\end{array}\right].$

Claims (1)

1. Robust Flight Control device method for designing is characterized in that may further comprise the steps:

Step 1, under assigned altitute, Mach number condition, obtain containing probabilistic dummy vehicle by wind-tunnel or flight test

At corresponding system state revertive control rule u=Kx=-B ^TDuring Px, design flight robust controller usually runs into following problem:

A ^TP+PA+P(γ ^-2EE ^T-BR ^-1B ^T)P+C ^TC＝0(1)

In the formula, x ∈ R ⁿBe state vector, u ∈ R ^mBe control vector, w ∈ R ^lBe the Unknown Model noise vector, A, B, E are known matrix of coefficients; C ^TC, R are respectively the state of adjusting and the weighting matrix of input vector, P=P ^T＞0 is unknown matrix to be found the solution, the constant of γ＞0 for selecting;

(1) sufficient and necessary condition of formula P existence and positive definite is: A (C ^TC) ^-1A ^T+ BR ^-1B ^T-γ ^-2EE ^T＞0;

Step 2, there is orthogonal matrix T, so that: NT-CAC ^-1＞0

In the formula: NN ^T=CA (C ^TC) ^-1] A ^TC ^T+ CBR ^-1B ^TC ^T-γ ^-2CEE ^TC ^T

Step 3, find the solution positive definite matrix P by following steps:

1. general real system A then chooses suitable P without heavy limit if having ₀=δ I makes A without heavy limit after the feedback; Wherein: δ 〉=0 is positive count, and I is unit matrix;

2. CN is carried out svd and get NN ^T=SD ²S ^T, make N=SDV ₁, T ₁=V ₁S; Wherein: S, V ₁Be orthogonal matrix;

3. establish S ^TC=WM ^-1, W=diag{w ₁, w ₂..., w _nBe the diagonal angle weighting matrix, M is the matrix of a linear transformation of A, M ^-1AM=J=diag[J ₁, J ₂..., J _r]; For the real number eigenwert of A, the sub-block of corresponding J be diagonal matrix, get T ₁=I gets P=MW ^-1(D-J) ^-1(MW ^-1) ^T

4. when A has the Complex eigenvalues value, must have a conjugation Complex eigenvalues value corresponding with it, be real number matrix in order to make M, stipulate this a pair of conjugate complex number eigenwert the sub-block of corresponding J be $\left[\begin{array}{cc}\mathrm{\σ}& \mathrm{\ω}\\ -\mathrm{\ω}& \mathrm{\σ}\end{array}\right],$ Have:

$\mathrm{\Ω}={\mathrm{WM}}^{-1}\mathrm{AM}{W}^{-1}={\mathrm{WJW}}^{-1}=\mathrm{diag}\{{\mathrm{\λ}}_1,{\mathrm{\λ}}_2,\·\·\·,{\mathrm{\λ}}_r,\left[\begin{array}{cc}{\mathrm{\σ}}_1& {\mathrm{\ω}}_1(w_{r+1}/w_{r+2})\\ -{\mathrm{\ω}}_1(w_{r+2}/w_{r+1})& {\mathrm{\σ}}_1\end{array}\right],$

$\·\·\·,\left[\begin{array}{cc}{\mathrm{\σ}}_p& {\mathrm{\ω}}_p(w_{n-1}/w_n)\\ -{\mathrm{\ω}}_p(w_n/w_{n-1})& {\mathrm{\σ}}_p\end{array}\right]\};(r+2p=n)$

S ^TCP ^-1C ^TS＝DT-S ^TCAC ^-1S＝DT ₁-WJW ^-1

Make T ₁=diag[1 ..., 1, T _1,1, T _1,2..., T _{1, p}]

DT then ₁-WJW ^-1=diag[d ₁-λ ₁..., d _r-λ _r, Ω ₁Ω ₂..., Ω _p]

Wherein $T_{1,j}=\left[\begin{array}{cc}\cos {\mathrm{\α}}_j& \sin {\mathrm{\α}}_j\\ -\sin {\mathrm{\α}}_j& \cos {\mathrm{\α}}_j\end{array}\right](j=\mathrm{1,2},\·\·\·,p)$

${\mathrm{\Ω}}_j=\left[\begin{array}{cc}{d}_{r+2j-1}& 0\\ 0& d_{r+2j}\end{array}\right]\left[\begin{array}{cc}\cos {\mathrm{\α}}_j& \sin {\mathrm{\α}}_j\\ -\sin {\mathrm{\α}}_j& \cos {\mathrm{\α}}_j\end{array}\right]-\left[\begin{array}{cc}{\mathrm{\σ}}_j& {\mathrm{\ω}}_j(w_{r+2j-1}/w_{r+2j})\\ -{\mathrm{\ω}}_j(w_{r+2j}/w_{r+2j-1})& {\mathrm{\σ}}_j\end{array}\right]$

Get $\sin {\mathrm{\α}}_j=-\frac{(\frac{w_{r+2j}}{w_{r+2j-1}}+\frac{w_{r+2j-1}}{w_{r+2j}}){\mathrm{\ω}}_j}{d_{r+2j-1}+d_{r+2j}},$ Ω then _jBe symmetric matrix.

P＝MW ^-1(DT ₁-J) ^-1(MW ^-1) ^T。