王立祺，周 軍，林 鵬

（西北工業(yè)大學(xué)精確制導(dǎo)與控制研究所，西安 710072）

基于綜合識別的高速飛行器自適應(yīng)控制方法*

王立祺，周 軍，林 鵬

（西北工業(yè)大學(xué)精確制導(dǎo)與控制研究所，西安 710072）

針對高速飛行器的傳統(tǒng)自適應(yīng)控制方法中控制器參數(shù)獲取時間長，辨識存在收斂性的問題，設(shè)計了一種基于綜合識別方法的新型自校正控制方案。首先，由在線直接可測量構(gòu)成特征模型的特征狀態(tài)量，并以特征模型作為參考模型來設(shè)計控制器；其次，通過獲得的特征狀態(tài)量來在線調(diào)配對象系統(tǒng)的零極點，輸出達到期望性能所需要的控制參數(shù)。仿真結(jié)果表明：該方法能較理想地實現(xiàn)在線自適應(yīng)控制，保證系統(tǒng)良好的魯棒性和快速性，同時在工程上易于實現(xiàn)。

高速飛行器，綜合識別，特征狀態(tài)量，在線控制，自適應(yīng)控制

Introduction

The research for control system of High Speed Vehicle（HSV）has some challenges，such as time-varying parameters，fast response，strong robustness and effective control etc［1］.The traditional adaptive method of HSV is self-tuning control.It online identify typical characteristic parameters of the plant，then automatically adjust the control quantity with result obtained. The application of adaptive controller［2-3］has been widely used due to identifying the parameters of process automatically，regulating the quantity of controller automatically，and having adaptability for variable coefficients.But how to accomplish quickly online identification for HSV is a new challenge.To a fast time-varying process，control system must response quickly and need short sample period.Online identification can not guarantee the real time operation，so it restrict the applica-tion of adaptive control strategy to be used in the attitude control system`s design.The paper［4］propose an adaptive control method base on characteristic model.it have built a characteristic model［5］on 6-DOF dynamic model of hypersonic vehicle on glide phase，then design a inner-outer loop adaptive controller base on characteristic model respectively.The paper［6］design a feed forward compensated adaptive controller based on both parameter identification for the state equation and Pole-assignment for maneuvering reentry vehicles control problem on the condition of large scale fight envelope and hardly aerodynamic couple.Though those methods all have a nice simulation result for the control strategy of hypersonic vehicle，the control parameters all need online identification.For HSV's control system within a plant of high-order time-varying property and controller of complex construct，it increase both time and magnitude of calculation due to system identification.Furthermore it`s harmful to the control system of HSV which has high time-sensitivity.

In this paper，an attitude control method based on integrated identification strategy was proposed.The characteristic state variables were consist of measurable quantity which can be online measured directly without iteration，and the reference model of self-tuning controller are derived by characteristic state variables.Then quantity of controller was calculated by adjusting the plant`s pole-zero to achieve the ideal performance.The simulation results improve the effectiveness of this method.

1 Dynamic Model and Characteristic Model

Refer to the database of NASA Langley research center［7］，the originalmodelofthis paper is Winged-Coned model.Meanwhile we focus on the attitude control system's design in glide phase of HSV.

Fig.1 The figure of HSV

Base on"Principle of Solidification"，the dynamic and kinematics equations of variable-mass system are considered as form of constant mass rigid body.Then motion equations are derived as follow：

For the attitude control system，angle of attack（AOA），side slip angle and flight path angle are often considered to be the control quantities of pitch，yaw and roll path respectively.In order to design and analysis control system，the differential equations of these control quantities should be derived.The characteristic model would be derived in pitch path for example.There are steps：

Step1：Build the angular motion equation of vehicle.Refer to the definition of attitude angular between different coordinate systems and the equivalence relationship of rotational angular velocity，two vector equations can be derived：

where T，F(xiàn)，H，V，B represent translational coordinate system，launch coordinate system，ballistic coordinate system，velocity coordinate system and body system respectively.C represents transformation matrix.ω represents rotational angular velocity between two coordinate system，is the derivative of angular velocity in the mapping coordinate system.

Substituting equation（5）and（6）into equation（4），the control-oriented differential equation of pitch path can be obtained：

Step2：Make the Earth's rate of rotation dissociated from attitude equation obtain：

Step3：Consider long-period motion parameters as constant on glide phase，neglect high derivative，the equation（8）can be written as

Step4：Note that in the longitudinal motion，the quantity of lateral motion can be considered too small to be neglected.Obtain：

Step5：Build nominal motion equation，combine with equation（2），Substitute the expanded formula of moment and neglect the component of aerodynamic nonlinear

Where fzis the disturbing force of pitch path.

2 The approach of integrated identification

From the characteristic model（equation（12）），we define characteristic state variables of longitudinal motion as follow：

Where ap2is the ratio of stabilizing moment to AOA and it represents the ability of producing angular acceleration due to per unit AOA.bpis the ratio of manipulate moment to rudder deflection，and it represent the ability of producing angular acceleration due to per unit rudder deflection.

So，the characteristic model can be written in the form：

In order to applying the characteristic model to control law's design process，the procurability problem of characteristic state quantities must be resolved firstly. Consider the time-varying character of characteristic state quantities，the traditional method of parameter identification have some problems such as mass data calculation，parameters for lag，initial value issue and identifiability of close-loop.If the transient characteristic of system which consist of characteristic state quantities can't be timely response to the controller，the approach of integrated identification would lost its advantage.

Fig2 Process of integrated identification method

The integrated identification method is based on measuring characteristic state quantities by sensors aboard.The main idea of this paper is to use the sensor to get the information from high order system replacing the parameter identification method based on principle of statistics，and to enhance the online rapidity of get ting characteristic state quantities by increase number and sort of sensor.The process of this approach is illustrated in Figure（2）.The key steps of integrated identi fication method are showed：

Step2：The quantities measured are used in the follow equation：

When the sampling period is sufficiently small，it is assumed that quantitiesp2，pcan be neglect.So the estimating expression of trim coefficient can be derived：

Step4：Calculate the remaining characteristic state quantities：

So that，all characteristic state quantities have been obtained.

3 Controller design based on integrated identification

The approach of integrated identification identify characteristic state quantities，then obtain characteristic.The output of control quantity by adjusting the desired plant's pole-zero point is used to achieve the ideal performance.The frame of controller is show in figure（3）.

Fig 3 The structure of self-tuning controller

When characteristic state quantities，ap1，ap2，bpof plant have been obtained，the characteristic model can be written in form as：

While，the equal two order characteristic equation of plant is：

Simultaneous equations（19）and（20）obtain the characteristic gain K0，the characteristic frequency ω0and the characteristic damping ξ0.

The PD feedback corrector is taken into the control system，Assume the transfer function is

Where Kpis proportional gain coefficient，Kdis differential gain coefficient.The closed-loop transferfunction of corrective circuit can be described as：

Assume the desired frequency，desired damping of nominal plant is ωqand ξqrespectively，obtain

The closed-loop gain of feedback system is

So，the balance coefficient of gain is

In actual attitudecontrolsystem，the angular velocityfeedbackisoftenchosebecausethefeedbackofdifferential amplify noise.Where Kp，Kd，Kgare according to e quations（23），（24）and（26）foradjustingrespectively.

4 Numerical Simulation

To testify the effectiveness of this method，we de signed self-tuning control simulation scheme for the Winged-Cone model，and tested trajectory simulation on the platform of Matlab/Simulink.

Initial height，velocity and AOA are 34 km，4 000 m/s and α0=0°respectively.The desired frequency is 10 Hz，damping is 0.707.Simulation time is 500 s.The conditions of simulation is no bias of aerodynamic coefficient，50%bias of aerodynamic coefficient and negative 50%bias of aerodynamic respectively.From the results of simulation，real AOA of vehicle track the command accurately in various simulation conditions，and control system designed show the good adaptive performance.

Fig 4 Curve of Height and Velocity

Fig 5 Curve of AOA

Fig 6 Curve of Rudder

5 Conclusions

For the problem of long time to calculate the quantity for controller and the convergence issue of identification，we presented an approach of adaptive control based on integrated identification.It's a valuable explore to study the online control of HSV，and apply a realizable path to implementing adaptive control method. Characteristic state variables were consist of measurable quantities which can be measured directly online，and the reference model of the self-tuning controller were derived by characteristic state variables quickly by avoiding iteration and convergence issue.This method can retain the control characteristic of nominal plant by parameter self-tuning inner circuit，furthermore，the logic of inner circuit is simple，physical signification is clear and it`s implemented easily.

［1］Wu H X.Review on the Control of Hypersonic Flight Vehicles［J］.Advance in Mechanics，2009，39（6）：330-333.

［2］Kuipers M，Ioannou P，F(xiàn)idan B.Robust Adaptive Multiple Model Controller Design for Airbreathing Hypersonic Vehicle Model［C］//.AIAA Guidance，Navigation and Control Conf. 2008：7142-7163.

［3］Lei Y，Cao C，Cliff E，et al.Design of an l1 Adaptive Controller for Airbreathing Hypersonic Vehicle model in the presence of unmodeled dynamic［C］//AIAA Guidance，Navigation and Control Conf.2007：6527-6541.

［4］Meng B，Wu H X.Adaptive Control Based on Characteristic Model for A Hypersonic Flight Vehicle［C］//Proceedings of the 26th Chinese Control Conference.Zhang jia jie，Hunan，China，2007：720-724.

［5］Wu H X，Hu J，Xie Y C.Adaptive Control Based on the Characteristic Model［M］.Beijing：China Science and Technology Press，2009.

［6］Wang X H.Design of Adaptive Flight Control System for Maneuvering Reentry Vehicles［J］.Journal of Astronautics，2002，23（1）：80-85.

［7］Shaughnessy J D，Pinckney S Z，MCMinn J D，et al.Hypersonic Vehicle Simulation Model：Winged-Cone Configuration［R］.NSAS TM-102610，19，2007.

Adaptive Control for High Speed Vehicle Based on Integrated Identification

WANG Li-qi，ZHOU Jun，LIN Peng
（Institute of Precision Guidance and Control，Northwestern Polytechnical University，Xi'an 710072，China）

For the problem that high speed vehicle`s traditional adaptive control method have long time to calculate control parameters and identification convergence，a novel Self-Tuning control method based on integrated identification is proposed.Firstly，online measurable quantities constituted characteristic state variables of characteristic model which is used to be the reference model to design controller.Then，control quantity that satisfied the desired performance is calculated by adjusting the plant`s pole-zero with characteristic state variables obtained.Finally，simulation results provide the capability of online adaptive controllerand enhance the robustness and rapidity ofsystem. Furthermore，it can be implemented easily in engineering.

high speed vehicle，integrated identification，characteristic state variables，online control，adaptive control

V448

A

1002-0640（2014）10-0108-05

2013-08-05

2013-10-15

教育部高等學(xué)校博士基金資助項目（20106102120008）

王立祺（1985- ），男，安徽省涇縣人，博士。研究方向：先進控制理論與應(yīng)用。