CN102929142B - Method for designing controller of time-varying aircraft model with uncertainty - Google Patents

Abstract

The invention discloses a method for designing a controller of a time-varying aircraft model with uncertainty, 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 time-varying system segmentation robust stability and solvability conditions are given, selection of desired closed-loop poles of linear time-varying 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 time-varying 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

The controller design method of the uncertain time-varying model of aircraft

Technical field

The present invention relates to a kind of controller design method, particularly relate to the controller design method of the uncertain time-varying model of a kind of aircraft.

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.

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 Robust Stability according to Lyapunov theorem, becomes robust Controller Design step when can not obtain specific implementation, does not have 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 the controller design method of the uncertain time-varying model of a kind of aircraft; This method provide the design conditions of the uncertain time-varying model Robust Stability Controller of real system, the closed loop of linear time varying system feedback of status 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, the uncertain time-varying model of aircraft that can obtain wind-tunnel or flight test directly designs flight controller, 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: the controller design method of the uncertain time-varying model of a kind of aircraft, is characterized in comprising the following steps:

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

$\stackrel{\·}{x}\left(t\right)=[A\left(t\right)+\mathrm{\ΔA}\left(t\right)]x\left(t\right)+[B\left(t\right)+\mathrm{\ΔB}\left(t\right)]u\left(t\right)---\left(1\right)$

In formula, x (t) ∈ R ⁿ, u (t) ∈ R ^mbe respectively state and input vector, A (t), B (t) are known matrix of coefficients, and Δ A (t), Δ B (t) are matrix of coefficients unknown portions; According to known A (t), the variation range classification of B (t), is namely expressed as A (t), B (t) in different time sections:

$\left\{\begin{array}{c}A\left(t\right)=A_{0i}+\mathrm{\Δ}{A}_{0i}\\ B\left(t\right)=B_{0i}+\mathrm{\Δ}{B}_{0i}\end{array}\right.t_{\mathrm{ij}}\≤t\≤t_{\mathrm{ij}}+T_{\mathrm{ij}}(i=\mathrm{1,2},...,r,j=\mathrm{1,2},...,p)$

In formula, A _0i, B _0ifor known constant matrices, Δ A _0iΔ B _0ifor unknown matrix, t _ij, T _ijfor time constant, r, p are positive integer, and i, j are that the A (t) of subscript, different time sections, B (t) expression formula form can be identical;

In time period t _ij≤ t<t _ij+ T _ijin, flight controller is: u (t)=-K _ix (t)

In formula, K _ifor constant feedback matrix;

Bring in (1) formula, have: $\stackrel{\&CenterDot;}{x}\left(t\right)=[(A_{0i}-B_{0i}{K}_i)+(\mathrm{\&Delta;}{A}_{0i}-\mathrm{\&Delta;}{B}_{0i}{K}_i)]x\left(t\right)$

Step 2, choose (A _0i-B _0ik _0i) eigenwert different and real part is negative, design of feedback matrix K _imake to satisfy condition:

${\mathrm{\&Lambda;}}_i>M_i^T{(\mathrm{\&Delta;}{A}_{0i}-\mathrm{\&Delta;}{B}_{0i}{K}_i)}^T{M}_i^{-T}{M}_i^{-1}(\mathrm{\&Delta;}{A}_{0i}-\mathrm{\&Delta;}{B}_{0i}{K}_i)M_i;$

This controller makes $\stackrel{\&CenterDot;}{x}\left(t\right)=[(A_{0i}-B_{0i}{K}_i)+(\mathrm{\&Delta;}{A}_{0i}-\mathrm{\&Delta;}{B}_{0i}{K}_i)]x\left(t\right)$ Robust stability;

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

$M_i^{-1}(A_{0i}-B_{0i}{K}_i)M_i=\mathrm{diag}\left[\begin{array}{cccc}{\mathrm{\&sigma;}}_{i1}+{\mathrm{j\&omega;}}_{i1},& {\mathrm{\&sigma;}}_{i2}+{\mathrm{j\&omega;}}_{i2},& ...,& {\mathrm{\&sigma;}}_{\mathrm{in}}+{\mathrm{j\&omega;}}_{\mathrm{in}}\end{array}\right],$

σ _ik, ω _ik(k=1,2 ..., n) be real number, j ω _ix(k=1,2 ..., n) represent imaginary number, diag is diagonal matrix symbol,

${\mathrm{\&Lambda;}}_i=\mathrm{diag}\left[\begin{array}{cccc}{\mathrm{\&sigma;}}_{i1}^2,& {\mathrm{\&sigma;}}_{i2}^2,& ...,& {\mathrm{\&sigma;}}_{\mathrm{in}}^2\end{array}\right];$

Δ A _0i-Δ B _0ik _iusually Δ A is assumed to be _0i-Δ B _0ik _i=H _if _iw _i, H _i, W _iall be assumed to be matrix, 0<F _i≤ 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 linear time varying system feedback of status 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, the engineering technical personnel of this research field are made directly to design flight controller to the uncertain time-varying model of aircraft that wind-tunnel or flight test obtain, 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

The controller design method concrete steps of the uncertain time-varying model of aircraft of the present invention are as follows:

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

$\stackrel{\&CenterDot;}{x}\left(t\right)=[A\left(t\right)+\mathrm{\&Delta;A}\left(t\right)]x\left(t\right)+[B\left(t\right)+\mathrm{\&Delta;B}\left(t\right)]u\left(t\right)---\left(1\right)$

In formula, x (t) ∈ R ⁿ, u (t) ∈ R ^mbe respectively state and input vector, A (t), B (t) are known matrix of coefficients, and Δ A (t), Δ B (t) are matrix of coefficients unknown portions; According to known A (t), the variation range classification of B (t), is namely expressed as A (t), B (t) in different time sections:

$\left\{\begin{array}{c}A\left(t\right)=A_{0i}+\mathrm{\&Delta;}{A}_{0i}\\ B\left(t\right)=B_{0i}+\mathrm{\&Delta;}{B}_{0i}\end{array}\right.t_{\mathrm{ij}}\&le;t<t_{\mathrm{ij}}+T_{\mathrm{ij}}\left(\begin{array}{cc}i=\mathrm{1,2},...,r,& j=\mathrm{1,2},...,p\end{array}\right)$

In formula, A _0i, B _0ifor known constant matrices, Δ A _0iΔ B _0ifor unknown matrix, t _ij, T _ijfor time constant, r, p are positive integer, and i, j are that the A (t) of subscript, different time sections, B (t) expression formula form can be identical;

In time period t _ij≤ t<t _ij+ T _ijin, flight controller is: u (t)=-K _ix (t)

In formula, K _ifor constant feedback matrix;

Bring in (1) formula, have: $\stackrel{\&CenterDot;}{x}\left(t\right)=[(A_{0i}-B_{0i}{K}_i)+(\mathrm{\&Delta;}{A}_{0i}-\mathrm{\&Delta;}{B}_{0i}{K}_i)]x\left(t\right)$

2, (A is chosen _0i-B _0ik _0i) eigenwert different and real part is negative, design of feedback matrix K _imake to satisfy condition:

${\mathrm{\&Lambda;}}_i>M_i^T{(\mathrm{\&Delta;}{A}_{0i}-\mathrm{\&Delta;}{B}_{0i}{K}_i)}^T{M}_i^{-T}{M}_i^{-T}(\mathrm{\&Delta;}{A}_{0i}-\mathrm{\&Delta;}{B}_{0i}{K}_i)M_i;$

This controller makes $\stackrel{\&CenterDot;}{x}\left(t\right)=[(A_{0i}-B_{0i}{K}_i)+(\mathrm{\&Delta;}{A}_{0i}-\mathrm{\&Delta;}{B}_{0i}{K}_i)]x\left(t\right)$ Robust stability;

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

$M_i^{-1}(A_{0i}-B_{0i}{K}_i)M_i=\mathrm{diag}\left[\begin{array}{cccc}{\mathrm{\&sigma;}}_{i1}+{\mathrm{j\&omega;}}_{i1},& {\mathrm{\&sigma;}}_{i2}+{\mathrm{j\&omega;}}_{i2},& ...,& {\mathrm{\&sigma;}}_{\mathrm{in}}+j{\mathrm{\&omega;}}_{\mathrm{in}}\end{array}\right],$

σ _ik, ω _ik(k=1,2 ..., n) be real number, j ω _ik(k=1,2 ..., n) represent imaginary number, diag is diagonal matrix symbol,

${\mathrm{\&Lambda;}}_i=\mathrm{diag}\left[\begin{array}{cccc}{\mathrm{\&sigma;}}_{i1}^2,& {\mathrm{\&sigma;}}_{i2}^2,& ...,& {\mathrm{\&sigma;}}_{\mathrm{in}}^2\end{array}\right];$

Δ A _0i-Δ B _0ik _iusually Δ A is assumed to be _0i-Δ B _0ik _i=H _if _iw _i, H _i, W _iall be assumed to be matrix, 0<F _i≤ 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; In time period 20≤t<100, State Equation Coefficients matrix is:

$A_{01}=\left[\begin{array}{ccc}-0.5000& -8.6500& 0\\ 1.0000& -0.3800& 0\\ 1.0000& 0& 0\end{array}\right],$ $B_{01}=\left[\begin{array}{c}-6.5000\\ -0.1000\\ 0\end{array}\right],$

Uncertain part is:

$\mathrm{\&Delta;}{A}_{01}=\left[\begin{array}{ccc}0.1000& -0.6000& 0\\ -0.3000& 0.4000& 0\\ 0& 0& 0\end{array}\right]F_1,$ $\mathrm{\&Delta;}{B}_{01}={\mathrm{\&lambda;}}_1\left[\begin{array}{c}2.3500\\ 0.0500\\ 0\end{array}\right],0<F_1\&le;I,0\&le;{\mathrm{\&lambda;}}_1<1,$

Closed loop is selected to expect limit and A ₀₁-B ₀₁k ₁eigenwert σ (A ₀₁-B ₀₁k ₁)=diag [-0.5 ,-1 ,-2], can obtain:

$A_{01}-B_{01}{K}_1=\left[\begin{array}{ccc}-3.2738& 1.3482& -4.0502\\ 0.9573& -0.2262& -0.0623\\ 1.0000& 0& 0\end{array}\right],$ $M_1=\left[\begin{array}{ccc}-0.8005& -0.5173& 0.2203\\ 0.4461& 0.6817& -0.8703\\ 0.4003& 0.5173& -0.4406\end{array}\right]$

Controller is: K ₁=[-0.3794 1.5382-0.6231].

Claims (1)

1. a controller design method for the uncertain time-varying model of aircraft, is characterized in that comprising the following steps:

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

$\stackrel{\&CenterDot;}{x}\left(t\right)=[A\left(t\right)+\mathrm{\&Delta;A}\left(t\right)]x\left(t\right)+[B\left(t\right)+\mathrm{\&Delta;B}\left(t\right)]u\left(t\right)---\left(1\right)$

In formula, x (t) ∈ R ⁿ, u (t) ∈ R ^mbe respectively state and input vector, A (t), B (t) are known matrix of coefficients, and Δ A (t), Δ B (t) are matrix of coefficients unknown portions; According to known A (t), the variation range classification of B (t), is namely expressed as A (t), B (t) in different time sections:

$\left\{\begin{array}{c}A\left(t\right)=A_{0i}+{\mathrm{\&Delta;A}}_{0i}\\ B\left(t\right)=B_{0i}+{\mathrm{\&Delta;B}}_{0i}\end{array}\right.,t_{\mathrm{ij}}\&le;t\&le;t_{\mathrm{ij}}+T_{\mathrm{ij}},i=\mathrm{1,2},...,r,j=\mathrm{1,2},...,p$

In formula, A _0i, B _0ifor known constant matrices, Δ A _0iΔ B _0ifor unknown matrix, t _ij, T _ijfor time constant, r, p are positive integer, and i, j are that the A (t) of subscript, different time sections, B (t) expression formula form is identical;

In time period t _ij≤ t < t _ij+ T _ijin, flight controller is: u (t)=-K _ix (t)

In formula, K _ifor constant feedback matrix;

Bring in (1) formula, have: $\stackrel{\&CenterDot;}{x}\left(t\right)=[(A_{0i}-B_{0i}{K}_i)+({\mathrm{\&Delta;A}}_{0i}-{\mathrm{\&Delta;B}}_{0i}{K}_i)]x\left(t\right)$

Step 2, choose (A _0i-B _0ik _i) eigenwert different and real part is negative, design of feedback matrix K _imake to satisfy condition:

${\mathrm{\&Lambda;}}_i>M_i^T{({\mathrm{\&Delta;A}}_{0i}-{\mathrm{\&Delta;B}}_{0i}{K}_i)}^T{M}_i^{-T}{M}_i^{-1}({\mathrm{\&Delta;A}}_{0i}-{\mathrm{\&Delta;B}}_{0i}{K}_i)M_i;$

This controller makes $\stackrel{\&CenterDot;}{x}\left(t\right)=[(A_{0i}-B_{0i}{K}_i)+({\mathrm{\&Delta;A}}_{0i}-{\mathrm{\&Delta;B}}_{0i}{K}_i)]x\left(t\right)$ Robust stability;

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

$M_i^{-1}(A_{0i}-B_{0i}{K}_i)M_i=\mathrm{diag}\begin{array}{c}\left[\begin{array}{cccc}{\mathrm{\&sigma;}}_{i1}+{\mathrm{j\&omega;}}_{i1},& {\mathrm{\&sigma;}}_{i2}+{\mathrm{j\&omega;}}_{i2},& ...,& {\mathrm{\&sigma;}}_{\mathrm{in}}+{\mathrm{j\&omega;}}_{\mathrm{in}}\end{array}\right]\end{array},$

σ _ik, ω _ik, k=1,2 ..., n is real number, j ω _ik, k=1,2 ..., n represents imaginary number, and diag is diagonal matrix symbol,

${\mathrm{\&Lambda;}}_i=\mathrm{diag}\left[\begin{array}{cccc}{\mathrm{\&sigma;}}_{i1}^2,& {\mathrm{\&sigma;}}_{i2}^2,& ...,& {\mathrm{\&sigma;}}_{\mathrm{in}}^2\end{array}\right];$

Δ A _0i-Δ B _0ik _iusually Δ A is assumed to be _0i-Δ B _0ik _i=H _if _iw _i, H _i, W _iall be assumed to be known matrix, 0 < F _i≤ I, I=diag [1,1 ..., 1] and be unit battle array;

Getting Flight Altitude Moving state variable is $x={\left[\begin{array}{ccc}q& \mathrm{\&alpha;}& \&PartialD;\end{array}\right]}^T,$ 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.