CN102929138B - Method for designing aircraft controller with nonlinearity - Google Patents

Abstract

The invention discloses a method for designing an aircraft controller with the nonlinearity, which is used for solving the technical problem that an existing robust control principle is lack of design steps, so that a flight controller is difficult to directly design. The invention adopts the technical scheme that a robust stable solvability condition of a system with an uncertain nonlinear term is given out; closed-loop expectation poles fed back by a state of a linear system are directly utilized to select; and according to the characteristic that real parts of all the closed-loop expectation poles are all negative numbers, a limiting condition inequality is given out to directly design a feedback matrix. Therefore, engineering technicians in the research field can directly design the flight controller for a flight model with the uncertain nonlinear term, which is obtained by a wind tunnel or flight test; and the technical problem that in the current research, only a robust stability inequality is given out so as not to directly design the flight controller is solved.

Description

Containing nonlinear controller of aircraft method for designing

Technical field

The present invention relates to a kind of controller design method, particularly relate to a kind of containing nonlinear controller of aircraft method for designing.

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 the Robust Stability containing uncertain nonlinearities according to Lyapunov theorem, the robust Controller Design step that specific implementation contains uncertain nonlinearities 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 containing nonlinear controller of aircraft method for designing; This method provide the design conditions of the real system Robust Stability Controller containing uncertain nonlinearities, 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 design flight controller containing the dummy vehicle of uncertain nonlinearities, 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 containing nonlinear controller of aircraft method for designing, is characterized in comprising the following steps:

Step one, the dummy vehicle obtained containing uncertain nonlinearities by wind-tunnel or flight test under assigned altitute, Mach number condition are:

$\stackrel{\·}{x}=A_{0}x+A_{\mathrm{non}}{f}_{\mathrm{\Δ}}\left(x\right)+[B+\mathrm{\ΔB}\left(x\right)]u---\left(1\right)$

In formula, x ∈ R ⁿ, u ∈ R ^mbe respectively state and input vector, A ₀, B, A _nonfor known matrix of coefficients, f _Δx (), Δ B (x) are unknown nonlinear item; According to different flight ranges and flight maneuver size, the status items of (1) formula right-hand member is expressed as:

$\left\{\begin{array}{c}{A}_{0}x+A_{\mathrm{non}}{f}_{\mathrm{\&Delta;}}\left(x\right)=A_{0i}+\mathrm{\&Delta;}{A}_{0i}\\ B+\mathrm{\&Delta;B}\left(x\right)=B_{0i}+\mathrm{\&Delta;}{B}_{0i}\end{array}\right.,x_{i\min }\&le;x<x_{i\max }(i=\mathrm{1,2},...,r),$

In formula, A _0i, B _0ifor known constant matrices, Δ A _0iΔ B _0ifor unknown matrix, x _imin, x _imaxminimum and the maximal value of the state corresponding to i-th flight range of being respectively, r is positive integer, and i is subscript;

At flight range x _imin≤ x<x _imaxin, 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,

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

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, ${\mathrm{\&Lambda;}}_i=\mathrm{diag}[{\mathrm{\&sigma;}}_{i1}^2,{\mathrm{\&sigma;}}_{i2}^2,...,{\mathrm{\&sigma;}}_{\mathrm{in}}^2];$

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 the robust stability solution conditions containing uncertain nonlinearities system 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 can be obtained wind-tunnel or flight test directly design flight controller containing the dummy vehicle of uncertain nonlinearities, solves current research and only provides robust stability inequality and the technical matters that directly cannot design flight controller.

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

Embodiment

It is as follows that the present invention contains nonlinear controller of aircraft method for designing concrete steps:

1, the dummy vehicle obtained containing uncertain nonlinearities by wind-tunnel or flight test under assigned altitute, Mach number condition is:

$\stackrel{\&CenterDot;}{x}=A_{0}x+A_{\mathrm{non}}{f}_{\mathrm{\&Delta;}}\left(x\right)+[B+\mathrm{\&Delta;B}\left(x\right)]u---\left(1\right)$

In formula, x ∈ R ⁿ, u ∈ R ^mbe respectively state and input vector, A ₀, B, A _nonfor known matrix of coefficients, f _Δx (), Δ B (x) are unknown nonlinear item; According to different flight ranges and flight maneuver size, the status items of (1) formula right-hand member is expressed as:

$\left\{\begin{array}{c}{A}_{0}x+A_{\mathrm{non}}{f}_{\mathrm{\&Delta;}}\left(x\right)=A_{0i}+\mathrm{\&Delta;}{A}_{0i}\\ B+\mathrm{\&Delta;B}\left(x\right)=B_{0i}+\mathrm{\&Delta;}{B}_{0i}\end{array}\right.,x_{i\min }\&le;x<x_{i\max }(i=\mathrm{1,2},...,r),$

In formula, A _0i, B _0ifor known constant matrices, Δ A _0iΔ B _0ifor unknown matrix, x _imin, x _imaxminimum and the maximal value of the state corresponding to i-th flight range of being respectively, r is positive integer, and i is subscript;

At flight range x _imin≤ x<x _imaxin, 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:

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

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,

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

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,

${\mathrm{\&Lambda;}}_i=\mathrm{diag}[{\mathrm{\&sigma;}}_{i1}^2,{\mathrm{\&sigma;}}_{i2}^2,...,{\mathrm{\&sigma;}}_{\mathrm{in}}^2];$

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, unit degree of being/second, and α is the air-flow angle of attack, unit is degree, and θ is the angle of pitch, unit is degree, δ _efor elevating rudder drift angle; In flight range [-50-2-2] ^t≤ x< [50 20 30] ^tin, 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., containing a nonlinear controller of aircraft method for designing, it is characterized in that comprising the following steps:

Step one, the dummy vehicle obtained containing uncertain nonlinearities by wind-tunnel or flight test under assigned altitute, Mach number condition are:

In formula, x ∈ R ⁿ, u ∈ R ^mbe respectively state and input vector, A ₀, B, A _nonfor known matrix of coefficients, f _△x (), △ B (x) are unknown nonlinear item; According to different flight ranges and flight maneuver size, the status items of (1) formula right-hand member is expressed as:

In formula, A _0i, B _0ifor known constant matrices, Δ A _0i, Δ B _0ifor unknown matrix, x _imin, x _imaxminimum and the maximal value of the state corresponding to i-th flight range of being respectively, r is positive integer, and i is subscript;

At flight range x _imin≤ x<x _imaxin, flight controller is: u (t)=-K _ix (t)

In formula, K _ifor constant feedback matrix;

Bring in (1) formula, have:

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

This controller makes robust stability;

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

σ _ik, ω _ikfor real number, j ω _ikrepresent imaginary number, wherein k=1,2 ..., n, diag are diagonal matrix symbol,

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.