Online Identification Of Aircraft Parameters Using State-space Model

Online identification of aircraft parameters is playing an increasingly important role in designing modern flight control systems,and in recent years,has become one of the major research topics related to aircraft designing.The flight control system is generally designed based on pre-established mathematical models that consider the uncertainty of parameters to improve the robustness of the control system.However,because modeling errors are inevitably present,some parameters are especially prone to flight condition changes,aircraft configuration changes,failures,or battle damage.Some changes in these parameters cannot be detected or are sometimes unexpected,thus hindering the performance of flight control systems and compromising the flight safety.Through the online identification system,one can obtain parameters that are more accurate,track changes in parameters,detect faults,correspondingly adjust the control system online,and maintain the stability and the expected performance of the system to ensure flight safety.Therefore,online identification of aircraft parameters is significant for these applications.However,it is very difficult to identify useful information from the data containing noise and interference.In addition,online identification algorithms are also limited by computational time and complexity.Based on the state-space model and using the grey-box identification method,this paper presents a systematic study on the online identification of the model parameters.The aircraft dynamics model and parameter identification model are the basis of the online identification research;although these two models differ from each other,they are closely related.We create a continuous/discrete hybrid system identification model frame by combining the continuous-time state-space model and the discrete observation model.The continuous-time state-space model used to describe the aircraft system gives all parameters clear physical meanings,which is very necessary and convenient for aircraft design optimization and flight control system design.However,it complicates the process of online parameter identification.In this case,the parameters that need to be identified are the elements of the state transition matrix and input control matrix from a linear state-space model,corresponding respectively to the stability derivative and control derivative of the aircraft.However,the identification algorithm requires all state variables to be measurable and the differential term on the left side of the state equation to be acquired accurately;this is often difficult to attain in practice.This work focuses on online parameter identification in the descriptive framework of the state-space model.In consideration of different system dimension,input types,noise,parameters and states,we designed and implemented a variety of effective online identification algorithms based on both time and frequency domains.This meets the requirements for online applications in terms of recognition rate,accuracy,and algorithm efficiency.For online identification in the time domain,first the parametric model of the aircraft was given.The grey-box identification algorithm was divided into three categories: the equation error method,output error method,and filtering error method;based on the continuous state-space model,the basic identification algorithm,recursive least squares(RLS)was given.For the equation error identification method,as the left entry of the regression equation(corresponding to the differential term in the state equation)could not be directly observed,an RLS identification algorithm with Kalman filter state estimation(KF + RLS)was proposed.To resolve the issue of inapplicability of the Kalman state filter when parameters are unknown,the non-linear identification algorithm of extended Kalman filter(EKF)based on augmented state was proposed,and the joint estimation of states and parameters was realized.Furthermore,to overcome the limitation of having prior knowledge about the noise parameters for using the Kalman filter,we use the nonlinear identification algorithm of Extended Forgetting Factor RLS(EFRLS)for augmented parameters to realize the joint estimation of states and parameters under the condition of no prior knowledge about noise.For online identification in the frequency-domain,the paper presents a deep study on the Fourier transform regression(FTR)identification method which has advantages to process noise and reduce computation effort,additionally,has no need to be stimulated continuously as traditional frequency method.By recursive Fourier transform(RFT),the time domain data was converted into the frequency domain data online,resulting in the frequency-domain linear regression model of aircraft parameter identification.Then parameter identification could be implemented using the batch least squares algorithm.This paper presents three least-square formulae in frequency domain and contains a comparative analysis of these three formulae.To improve the stability of the algorithm,matrix inversion was performed by using the singular value decomposition(SVD)method.For frequency-domain identification of a multi-input multi-output(MIMO)system,an orthogonal multi-sine excitation signal design method was proposed;this method is capable of exciting multiple input channels simultaneously,to improve the identification efficiency and reduce flight test time and cost.The impact of a typical input's length on the identification results was analyzed,and useful conclusions were obtained.Finally,an analysis was conducted to compare the performance of the time-domain and frequency-domain online identification methods,which served as a reference for selecting the algorithm.In addition,these online identification methods have been validated by double-computer simulation.The online identification of time-variant parameters is a challenging problem,the principal literature deals with slowly changed parameters.However,the parameters of an aircraft may be changed suddenly by failure.To resolve the time-varying parameter identification problem,the forgetting factor/fading factor was introduced to the time-domain and frequency-domain identification algorithms,so that each algorithm had the capability of tracking and identifying time-varying parameters.Based on the concept of the adaptive Kalman filter,the fading factor was introduced to the extended Kalman filter identification algorithm of augmented parameters for joint estimation of quick changed parameters and states.Improvement in the time-varying parameter tracking performance and stability was achieved.Online identification algorithm simulation was carried out for all of the above algorithms,and satisfactory results were obtained.