线性系统状态空间建模仿真（matlab)

Linear system course project theory manual

1

Flexible wing (FW) dynamic system analysis |

Flexible wing (FW) dynamic system analysis

Linear system course Project

Contents

Flexible wing (FW) dynamic system analysis ..............................................................................................1

3-Stability ......................................................................................................................................................6

4-State-feedback control ........................................................................................................................6

4-1Reachability ..................................................................................................................................7

4-2Controllability ..............................................................................................................................7

4-3Stabilization by State Feedback ............................................................................................8

4-4Analysis of FW .............................................................................................................................9

5-State observer ...................................................................................................................................... 11

5-1Observability ............................................................................................................................. 12

5-2Observer design ...................................................................................................................... 13

5-3Where Put Estimator Poles .................................................................................................. 14

Reference ................................................................................................................................................... 23

总结 .............................................................................................................................................................. 24

错误： ......................................................................................................................................................... 24

罗飞（Fei LUO）

Linear system course project theory manual

2

Flexible wing (FW) dynamic system analysis |

further excite the structure which forms a closed loop system. If one or more structural natural

frequencies of the flexible aircraft fall within the control bandwidth of the control system,

instability may occur. This type of instability that involves the interaction among structure,

unsteady aerodynamics and control system is called the ASE instability.

Various control analyses, design and simulations require the equations of motion to be cast

in a linear time-invariant state-space form. In order to couple the aeroelastic system with the

control system, the equations of motion of the aeroelastic system must be also cast in the

state-space form. The equations of motion of the aeroelastic system expressed in the modal

coordinates read:

(0.1)

,

and

are the generalized coordinates and the control surface deflections, respectively.

is

is the reduced frequency, L is the reference length, and V is the free steam

velocity. This GAF matrix can be computed according to following Equation:

1-1RATIONAL FUNCTION APPROXIMATION

RFA provides a convenient means of carrying out the conversion of GAF from the frequency

domain to time domain via an intermediate step wherein the frequency domain GAF are

converted to the Laplace domain. The use of RFA permits each element of the GAFs to be

written as a rational function, i.e. as a ratio of polynomials. The general expression of the RFA

reads:

(0.3)

With the RFA in hand, the state-space equations of the aeroelastic system can be readily

Linear system course project theory manual

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Flexible wing (FW) dynamic system analysis |

formed. Then, to facilitate the state-space formulation, it is convenient to define an

augmenting aerodynamic state vector as follows:

(0.4)

Substituting Equations (1.4) and (1.3) into Equation (1.1) yields:

(0.5)

Where

 

1 1 1

0 1

[ ] [ ]



 (0.9)

 (0.10)

Linear system course project theory manual

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Flexible wing (FW) dynamic system analysis |

    

recursive form

(0.15)

Linear system course project theory manual

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Flexible wing (FW) dynamic system analysis |

for internal stability here.

t

t t x



(0.16)

will stabilized at the zero point by the time gone. In theory,

to zero.

However, the simulation result is beyond our prediction within 100 the simulation steps,

Obviously, the result is wrong with the previous information of the eigenvalue of A is in left

plane of s domain.

case of zero-state response, we set back of X(0)=0.

- Free response

- Full response