CN102929136B - Aircraft multi-time delay model approach and controller design method - Google Patents

Abstract

The invention discloses an aircraft multi-time delay model approach and controller design method, which is used for solving the technical problem of difficulty in directly designing an aircraft controller due to lack of a design step of the traditional robust control theory. In the technical scheme, robust stabilizing solvable conditions of a time varying system according to segments are given, a closed loop expected poles fed back by the state of a linear system is directly utilized to select, and according to the characteristic that all real parts of the closed loop expected poles are negative numbers, a limitation conditional inequality is given to directly design a feedback matrix. By the aircraft multi-time delay model approach and controller design method, engineering technical staff in the research field obtains an aircraft model containing the uncertainty of a plurality of time delays from wind tunnel or flight tests to directly design the aircraft controller, and the technical problem that the aircraft controller cannot be directly designed and only the robust stability inequality is given by the current research is solved.

Description

Aircraft Model approximation multiple time lag and controller design method

Technical field

The present invention relates to a kind of controller design method, particularly relate to a kind of aircraft Model approximation multiple time lag and controller design method.

Background technology

Aircraft robust control is one of emphasis problem of current international airline circle research, when high performance airplane Controller gain variations, 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 described by discrete data usually; In order to reduce risks and reduce experimentation cost, usually carry out flight maneuver test according to differing heights, Mach number, like this, the discrete data describing aircraft test model is not a lot, and this model is very practical to the good aircraft of static stability.But the modern and following fighter plane all relaxes restriction to static stability to improve " agility ", and fighter plane requires to work near open loop critical temperature rise usually; So just require that flight control system can transaction module uncertain problem well; Following subject matter to be considered: test is obtained a certain approximate model of discrete data and describes by (1), there is Unmarried pregnancy in model in practical flight Control System Design; (2) wind tunnel test can not be carried out full scale model free flight, there is constraint, the input action selections of the selection of flight test discrete point, initial flight state, maneuvering flight etc. can not, by all non-linear abundant excitations, adopt System Discrimination gained model to there is various error; (3) flight environment of vehicle and experimental enviroment are had any different, and flow field change and interference etc. make actual aerodynamic force, moment model and test model have any different; (4) there is fabrication tolerance in execution unit and control element, also there is the phenomenons such as aging, wearing and tearing in system operation, not identical with the result of flight test; (5) in Practical Project problem, need controller fairly simple, reliable, usually need to simplify with being mathematics model person, remove the factor of some complexity; Therefore, when studying the control problem of present generation aircraft, just robustness problem must be considered; Particularly the aircraft angle of attack, yaw angle measures and much physics, in chemical process the time lag of various degrees uncertain, if ignore these time lags in the analysis of system or design process, just may there is the result of mistake or cause the instability of system.

After 1980, carry out the control theory research of multiple uncertain system in the world, the H-infinit particularly proposed by Canadian scholar Zames is theoretical, Zames thinks, based on the LQG method of state-space model, why robustness is bad, mainly because represent that uncertain interference is unpractical with White Noise Model; Therefore, when supposing that interference belongs to a certain known signal collection, Zames proposes by the norm of its corresponding sensitivity function as index, design object is under contingent worst interference, make the error of system be issued to minimum in this norm meaning, thus AF panel problem is converted into solve closed-loop system is stablized; From then on, lot of domestic and international scholar expands the research of H-infinit control method; At aeronautical chart, the method is in the exploratory stage always, U.S. NASA, and the states such as German aerospace research institute, Holland are all studied robust control method, achieves a lot of emulation and experimental result; Domestic aviation universities and colleges have also carried out a series of research to aircraft robust control method, 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 these results and the distance of practical application also differ very large, are difficult to directly design practical flight controller and apply; Particularly a lot of research only gives uncertain time delay system Robust Stability according to Lyapunov theorem, but relate to less for the problem such as existence condition of these solution of inequality, specific implementation robust Controller Design time lag step can not be obtained, there is no to solve the technical matters of directly design robust flight controller.

Summary of the invention

Being difficult to directly design the technical deficiency of flight controller in order to overcome existing robust control theory shortage design procedure, the invention provides a kind of aircraft Model approximation multiple time lag and controller design method; The multiple time lags this method providing real system Robust Stability Controller approach design conditions, the closed loop of State Feedback for Linear Systems is directly utilized to expect the selection of poles, and expect that the real part of limit is all the feature of negative according to all closed loops, give qualifications inequality direct design of feedback matrix, what can obtain wind-tunnel or flight test directly designs flight controller containing uncertain dummy vehicle multiple time lag, solves current research and only provides robust stability inequality and the technical matters that directly cannot design flight controller.

The technical solution adopted for the present invention to solve the technical problems is: a kind of aircraft Model approximation multiple time lag and controller design method, be characterized in comprising the following steps:

Step one, under assigned altitute, Mach number condition by wind-tunnel or flight test obtain containing r time lag probabilistic dummy vehicle be:

$\stackrel{\·}{x}=(A_0+{\mathrm{\Δ}A}_0)x+\underset{i=1}{\overset{r}{\∑}}{A}_{\mathrm{\τi}}x(t-{\mathrm{\τ}}_i)+\mathrm{Bu}$

In formula, x ∈ R ⁿ, u ∈ R ^mbe respectively state and input vector, A ₀, A _{τ i}(i=1,2 ..., r), B is known constant coefficient matrix, τ _i(i=1,2 ..., r) be the unknown delays time, Δ A ₀for matrix of coefficients unknown portions; Symbol is identical in full;

Simultaneous $\left\{\begin{array}{c}\underset{i=1}{\overset{r}{\∑}}{A}_{\mathrm{\τi}}N=\underset{i=1}{\overset{r}{\∑}}{A}_{\mathrm{\τi}}\exp [-(A_0+\underset{i=1}{\overset{r}{\∑}}{A}_{\mathrm{\τi}}N){\mathrm{\τ}}_i]\\ \min \{x_{\mathrm{real}}\left(t\right)-\exp [(A_0+\underset{i=1}{\overset{r}{\∑}}{A}_{\mathrm{\τi}}N)t]x\left(t_0\right)-{\∫}_{t_0}^t\exp [(A_0+\underset{i=1}{\overset{r}{\∑}}{A}_{\mathrm{\τi}}N)(t-\mathrm{\ζ})]\mathrm{Bu}\left(\mathrm{\ζ}\right)\mathrm{d\ζ}{\}}^2\end{array}\right.$ Iterative N,

In formula: x _realt () is real system condition responsive;

Model tormulation is become:

$\stackrel{\·}{x}=(A+\mathrm{\ΔA})x+\mathrm{Bu}---\left(1\right)$

In formula, x ∈ R ⁿ, u ∈ R ^mbe respectively state and input vector, A=(A ₀+ A _τn), B is known matrix of coefficients, and Δ A is matrix of coefficients unknown portions;

Selection flight controller is: u=-Kx

In formula, K is feedback matrix;

Bring in (1) formula, have: $\stackrel{\·}{x}=(A-\mathrm{BK}+\mathrm{\ΔA})x$

Step 2, the eigenwert choosing (A-BK) is different and real part is negative, and design of feedback matrix K makes to satisfy condition:

Λ>M ^T(ΔA) ^TM- ^TM ^-1ΔAM；

This controller makes $\stackrel{\·}{x}=(A-\mathrm{BK}+\mathrm{\ΔA})x$ Robust stability;

In formula, M is the matrix of a linear transformation,

M ^-1(A-BK) M=diag [σ ₁+ j ω ₁, σ ₂+ j ω ₂..., σ _n+ j ω _n], σ _i, ω _i(i=1,2 ..., n) be real number, j ω _i(i=1,2 ..., n) represent imaginary number, diag is diagonal matrix symbol, $\mathrm{\Λ}=\mathrm{diag}\left[\begin{array}{cccc}{\mathrm{\σ}}_1^2,& {\mathrm{\σ}}_2^2,& ...,& {\mathrm{\σ}}_n^2\end{array}\right];$

Δ A-Δ BK is assumed to be Δ A-Δ BK=HFW usually, and H, W are all assumed to be matrix, 0<F≤I, I=diag [1,1 ..., 1] and be unit battle array.

The invention has the beneficial effects as follows: by time-varying system segmentation robust stability solution conditions provided by the invention, the closed loop of State Feedback for Linear Systems is directly utilized to expect the selection of poles, and expect that the real part of limit is all the feature of negative according to all closed loops, give qualifications inequality direct design of feedback matrix, what the engineering technical personnel of this research field were obtained wind-tunnel or flight test directly designs flight controller containing uncertain dummy vehicle multiple time lag, solve current research and only provide robust stability inequality and the technical matters that directly cannot design flight controller.

Below in conjunction with embodiment, the present invention is elaborated.

Embodiment

Aircraft of the present invention Model approximation multiple time lag and controller design method concrete steps as follows:

1, under assigned altitute, Mach number condition by wind-tunnel or flight test obtain containing r time lag probabilistic dummy vehicle be:

$\stackrel{\&CenterDot;}{x}=(A_0+{\mathrm{\&Delta;}A}_0)x+\underset{i=1}{\overset{r}{\&Sum;}}{A}_{\mathrm{\&tau;i}}x(t-{\mathrm{\&tau;}}_i)+\mathrm{Bu}$

In formula, x ∈ R ⁿ, u ∈ R ^mbe respectively state and input vector, A ₀, A _{τ i}(i=1,2 ..., r), B is known constant coefficient matrix, τ _i(i=1,2 ..., r) be the unknown delays time, Δ A ₀for matrix of coefficients unknown portions; Symbol is identical in full;

Simultaneous $\left\{\begin{array}{c}\underset{i=1}{\overset{r}{\&Sum;}}{A}_{\mathrm{\&tau;i}}N=\underset{i=1}{\overset{r}{\&Sum;}}{A}_{\mathrm{\&tau;i}}\exp [-(A_0+\underset{i=1}{\overset{r}{\&Sum;}}{A}_{\mathrm{\&tau;i}}N){\mathrm{\&tau;}}_i]\\ \min \{x_{\mathrm{real}}\left(t\right)-\exp [(A_0+\underset{i=1}{\overset{r}{\&Sum;}}{A}_{\mathrm{\&tau;i}}N)t]x\left(t_0\right)-{\&Integral;}_{t_0}^t\exp [(A_0+\underset{i=1}{\overset{r}{\&Sum;}}{A}_{\mathrm{\&tau;i}}N)(t-\mathrm{\&zeta;})]\mathrm{Bu}\left(\mathrm{\&zeta;}\right)\mathrm{d\&zeta;}{\}}^2\end{array}\right.$ Iterative N,

In formula: x _realt () is real system condition responsive;

Model tormulation is become:

$\stackrel{\&CenterDot;}{x}=(A+\mathrm{\&Delta;A})x+\mathrm{Bu}---\left(1\right)$

In formula, x ∈ R ⁿ, u ∈ R ^mbe respectively state and input vector, A=(A ₀+ A _τn), B is known matrix of coefficients, and Δ A is matrix of coefficients unknown portions;

Selection flight controller is: u=-Kx

In formula, K is feedback matrix;

Bring in (1) formula, have: $\stackrel{\&CenterDot;}{x}=(A-\mathrm{BK}+\mathrm{\&Delta;A})x$

2, the eigenwert choosing (A-B K) is different and real part is negative, and design of feedback matrix K makes to satisfy condition:

Λ>M ^T(ΔA) ^TM ^-TM ^-1ΔAM；

This controller makes $\stackrel{\&CenterDot;}{x}=(A-\mathrm{BK}+\mathrm{\&Delta;A})x$ Robust stability;

In formula, M is the matrix of a linear transformation,

M ^-1(A-BK) M=diag [σ ₁+ j ω ₁, σ ₂+ j ω ₂..., σ _n+ j ω _n], σ _i, ω _i(i=1,2 ..., n) be real number, j ω _i(i=1,2 ..., n) represent imaginary number, diag is diagonal matrix symbol, $\mathrm{\&Lambda;}=\mathrm{diag}\left[\begin{array}{cccc}{\mathrm{\&sigma;}}_1^2,& {\mathrm{\&sigma;}}_2^2,& ...,& {\mathrm{\&sigma;}}_n^2\end{array}\right];$

Δ A-Δ BK is assumed to be Δ A-Δ BK=HFW usually, and H, W are all assumed to be matrix, 0<F≤I, I=diag [1,1 ..., 1] and be unit battle array;

Getting Flight Altitude Moving state variable is x=[q α θ] ^t, input variable is u=δ _e, wherein q is rate of pitch, and α is the air-flow angle of attack, and θ is the angle of pitch, δ _efor elevating rudder drift angle; Equivalent state equation coefficient matrix is:

$A=\left[\begin{array}{ccc}-0.5000& -8.6500& 0\\ 1.0000& -0.3800& 0\\ 1.0000& 0& 0\end{array}\right],$ $B=\left[\begin{array}{c}-6.5000\\ -0.1000\\ 0\end{array}\right],$

Uncertain part is:

$\mathrm{\&Delta;A}=\left[\begin{array}{ccc}0.1000& -0.6000& 0\\ -0.3000& 0.4000& 0\\ 0& 0& 0\end{array}\right]F,$ 0<F≤I，

Select closed loop to expect eigenwert σ (the A-BK)=diag [-0.5 ,-1 ,-2] of limit and A-BK, can obtain:

$A-\mathrm{BK}=\left[\begin{array}{ccc}-3.2738& 1.3482& -4.0502\\ 0.9573& -0.2262& -0.0623\\ 1.0000& 0& 0\end{array}\right],$ $M=\left[\begin{array}{ccc}-0.8005& -0.5173& 0.2203\\ 0.4461& 0.6817& -0.8703\\ 0.4003& 0.5173& -0.4406\end{array}\right]$

Controller is: K=[-0.3794 1.5382-0.6231].

Claims (1)

1. aircraft Model approximation multiple time lag and a controller design method, is characterized in that comprising the following steps:

Step one, under assigned altitute, Mach number condition by wind-tunnel or flight test obtain containing r time lag probabilistic dummy vehicle be:

$\stackrel{.}{x}=(A_0+\mathrm{\&Delta;}{A}_0)x+\underset{i=1}{\overset{r}{\mathrm{\&Sigma;}}}{A}_{\mathrm{\&tau;i}}x(t-{\mathrm{\&tau;}}_i)+\mathrm{Bu}$

In formula, x ∈ R ⁿ, u ∈ R ^mbe respectively state and input vector, A ₀, A _{τ i}, i=1,2 ..., r, B are known constant coefficient matrix, τ _i, i=1,2 ..., r is the unknown delays time, Δ A ₀for matrix of coefficients unknown portions; Symbol is identical in full;

Simultaneous iterative N,

In formula: x _realt () is real system condition responsive;

Model tormulation is become:

$\stackrel{.}{x}=(A+\mathrm{\&Delta;A})x+\mathrm{Bu}---\left(1\right)$

In formula, x ∈ R ⁿ, u ∈ R ^mbe respectively state and input vector, A=(A ₀+ A _τn), B is known matrix of coefficients, and Δ A is matrix of coefficients unknown portions;

Selection flight controller is: u=-Kx

In formula, K is feedback matrix;

Bring in (1) formula, have: $\stackrel{.}{x}=(A-\mathrm{BK}+\mathrm{\&Delta;A})x$

Step 2, the eigenwert choosing (A-BK) is different and real part is negative, and design of feedback matrix K makes to satisfy condition:

Λ>M ^T(ΔA) ^TM ^-TM ^-1ΔAM；

This controller makes $\stackrel{.}{x}=(A-\mathrm{BK}+\mathrm{\&Delta;A})x$ Robust stability;

In formula, M is the matrix of a linear transformation,

M ^-1(A-BK) M=diag [σ ₁+ j ω ₁, σ ₂+ j ω ₂..., σ _n+ j ω _n], σ _i, ω _i, i=1,2 ..., n is real number, j ω _i, i=1,2 ..., n represents imaginary number, and diag is diagonal matrix symbol, $\mathrm{\&Lambda;}=\mathrm{diag}\left[\begin{array}{cccc}{\mathrm{\&sigma;}}_1^2,& {\mathrm{\&sigma;}}_2^2,& ...,& {\mathrm{\&sigma;}}_n^2\end{array}\right];$

Δ A-Δ BK is assumed to be Δ A-Δ BK=HFW usually, and H, W are all assumed to be known matrix, 0<F≤I, I=diag [1,1 ..., 1] and be unit battle array;

Getting Flight Altitude Moving state variable is $x={\left[\begin{array}{ccc}q& \mathrm{\&alpha;}& \mathrm{\&theta;}\end{array}\right]}^T,$ Input variable is u=δ _e, wherein q is rate of pitch, and α is the air-flow angle of attack, for the angle of pitch, δ _efor elevating rudder drift angle; Equivalent state equation coefficient matrix is:

$A=\left[\begin{array}{ccc}-0.5000& -8.6500& 0\\ 1.0000& -0.3800& 0\\ 1.0000& 0& 0\end{array}\right],B=\left[\begin{array}{c}-6.5000\\ -0.1000\\ 0\end{array}\right],$

Uncertain part is:

$\mathrm{\&Delta;A}=\left[\begin{array}{ccc}0.1000& -0.6000& 0\\ -0.3000& 0.4000& 0\\ 0& 0& 0\end{array}\right]F,0<F\&le;I,$

Closed loop is selected to expect eigenwert σ (the A-BK)=diag [-0.5 ,-1 ,-2] of limit and A-BK:

$A-\mathrm{BK}=\left[\begin{array}{ccc}-3.2738& 1.3482& -4.0502\\ 0.9573& -0.2262& -0.0623\\ 1.0000& 0& 0\end{array}\right],M=\left[\begin{array}{ccc}-0.8005& -0.5173& 0.2203\\ 0.4461& 0.6817& -0.8703\\ 0.4003& 0.5173& -0.4406\end{array}\right]$

Controller is: K=[-0.3794 1.5382-0.6231].