A Simplified Methodology for the Synthesis of Adaptive Flight Control Systems

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1 A Simplified Methodology for the Synthei of Adaptive Flight Control Sytem J.ROUSHANIAN, F.NADJAFI Department of Mechanical Engineering KNT Univerity of Technology 3Mirdamad St. Tehran IRAN Abtract- A implified approach for the deign of an efficient alternative to adaptive flight control ytem baed on combination of invariance theory and high gain feedback ha been developed. The derivation of the algorithm i preented. The application of thi method to deign adaptive control of launch vehicle attitude i demontrated. The feaibility and advantage of the propoed tructure are dicued. Key- Word: Adaptive-euivalent ytem, Invariance, Attitude control, Launch Vehicle, Flight imulation. Introduction The problem of elf adjuting the parameter of controller in order to tabilize the dynamic characteritic of a feedback control ytem, when drift variation in the aircraft parameter occur, wa the origin of adaptive flight control ytem. Attitude control of launch vehicle i till claic example of adaptation theory. Variou definition from the adaptive ytem have been preented. In thi paper definition of Y.Z. Typkin will be conidered []: tructure or / and parameter to maintain the index of Adaptive characteritic may be found in other cla of nonadaptive ytem conidering above definition. Thee ytem are referred a alternative to adaptive or adaptive-euivalent (in Ruian literature) [],[3]. Therefore we can conider ally two clae of flight control ytem with adaptive characteritic:. Adaptive flight control ytem: The firt development of uch an adaptive flight control ytem eem to be the MIT propoal [4]. Uppermot, the model reference adaptive ytem (MRAS) wa one of the main approache to adaptive flight control. [4],[5],[6],[7][8][9]. There are eentially three baic approache for the analyi and deign of MRAS [],[3],[7],[9]: -Deign method baed on local parameter optimization -Deign method baed on tability theory -Deign method related to etimation theory Although the adaptive algorithm improve IP of control ytem but they are eldom ued in launch vehicle or miile attitude control ytem becaue of complexity in realization and high cot.. Adaptive-euivalent flight control ytem The main approache in thi cla are: [], [3]: -Parametric invariant compenation ytem (a referred in Ruian literature). -High-gain feedback control ytem -Variable tructure ytem -Self ocillating ytem -Model reference control ytem Structure, deign method, and implementation apect of uch ytem are dicued in [],[3],[]. In thi paper a new tructure and deign method, belong to cla of adaptive-euivalent ytem for the flight control with appropriate adaptive characteritic preented. The main advantage of the propoed method i imple realization. Adaptive-euivalent approach In order to eliminate diadvantage of parametric invariant compenation and high-gain ytem, a pecial combination of them developed.. parametric invariant compenation ytem General block diagram of parametric invariant compenation ytem (PICS) i repreented in figure. In thi ytem the IP remain relatively contant by appropriate election of controller tranfer function:, ),..., n. Some method for electing the unknown tranfer function

2 are preented in [3][9]. Contraint and complexity in deign and implementation of PICS dicued in detail [3]. x G C ( ) G C ( ) W Where: W = G G ( ) ; A P G A (), () -Actuator and plant tranfer function; G P - Figure Block diagram of PICS. High gain feedback control ytem High gain feedback control ytem (HGFC) i another approach to tabilize IP with variation in plant dynamic [],[3]. Block diagram of uch ytem i illutrated in figure. The main diadvantage of high gain ytem i tability atifaction, epecially in the preence of nonlinear characteritic in the ytem (a actuator aturation). x - K 3 Adaptive euivalent propoal To reach an adaptive performance with imple tructure and realization, it i propoed to ue a combination of PICS and HGFC approache. Such a combination eliminate diadvantage of each one. G C3 G C 4 G C ( ) G ( C ) K W Figure. Block diagram of HGFC 3. Formulation of deign method In order to achie ve more implified tructure than x + y + G C K W N G C y y PICS and improve tability characteritic of HGFC a particular combination of them i propoed in fig 3. There are two loop in thi tructure. The tranfer function of inner loop i: K W Φ = () I + K W G It i fairly eay to ee that when K we obtain: Φ () I G The cloe-loop tranfer function of the ytem will be: G C Φ (3) G + G C Variation in plant and actuator dynamic ( δ W ( ) ) have been eliminated in the ytem tranfer function. Therefor by appropriate deign of controller tranfer function, ) and gain K one may be achieve deirable IP, in the preence of parametric perturbation. The above tructure ha three degree of freedom. Thi opportunity make eay deign procedure. One may find different method to elect the gain K and unknown tranfer function, ) in the theory of automatic control. In thi work we ued the method of tandard coefficient [],[]. Thi method recommend pecial configuration of coefficient for any cla of ytem tranfer function. The implicity and capability of the propoed tructure to achieve adaptive characteritic are illutrated in the practical example of launch vehicle (LV) attitude control ytem deign. 3. Deign example The performance of adaptive-euivalent ytem deigned by the method dicued in the previou ection can be illutrated by applying it to a launch vehicle control ytem. The plant for thi example i a longitudinal dynamic of a launch vehicle in pitch channel. The block diagram of a typical claic attitude control ytem i hown in figure 4. However the ytem i time varying and a tranfer function can not be defined in the uual fahion. Thu, the frozen pole approximation i ued. It conider that the coefficient have contant value during a certain interval of time and are eual to thoe correponding to a particular intant. In thi way a tranfer function can be obtained. Figure 3.Block diagram of combined tructure

3 C The variation in dynamic of the Launch vehicle i expreed by tranfer function in three different of power-flight motion. (A in tab. ) N Table Powered flight Dynamic of LV in the tart Dynamic of LV in the maximum head 3 Dynamic of LV in upper atmopheric flight Tranfer function G P () Dynamic of actuator and rate gyro may be neglected in the firt tep of ynthei. Therefore: W GP (4) Effect of uch fat-repone element have been conidered in the modeling tage after deign. Uing the propoed deign methodology, block diagram of longitudinal attitude control ytem would be a illutrated in figure 5. C + - Control Law Actuator Rate Gyro Figure 4. Pitch Channel control ytem Launch Vehicle G C ( ) W ( ) K G Figure 5.Block diagram of the propoed attitude control ytem Where: C i command pitch rate, -actual pitch rate of launch vehicle. Let u chooe controller tranfer function and ome coefficient a follow: K( T + ) ( ) = ; ) = ; τ + (5) K = 7 ; τ =. Selection of, ) tructure i baed on following criteria: -Structure of tranfer function G ( C ) elected a it generally ued in claic autopilot (for pitch channel). The integrator term of ( ) eliminate teady tate G C error of the ytem. The coefficient K and T will be determined uing method of tandard coefficient. -Structure of tranfer function ( ) elected o that G inner loop tranfer function, for high gain K fulfill maximum implicity. -The upper limit in electing gain K i tability margin of ytem in preence of actuator nonlinear characteritic. The gain K obtained in reult of imulation. The coefficient τ elected o that: G If we take inner gain ( K ) enough high, then the tranfer function of the inner loop would be: Φ (6) i G There for cloe loop tranfer function of the ytem i given by : KΤ + K W (7) + KΤ + K Method of tandard coefficient recommend following coefficient for obtaining tranfer function:.5p + p W ST = (8) +.5p + p Where p i a parameter, which determine velocity of the ytem repone. Therefor we find two imple algebraic euation: KT.5 =, K = (8) For p=3 we have: K = 9 ; T =. 8 (9) Now all the parameter are determined. 3.3 Simulation reult In thi tep we have imulated propoed attitude control ytem (fig.5) conidering the entire main element a actuator and rate gyro. The reult of imulation are repreented in figure 6-. In figure 6,7, 8 tep repone of the launch vehicle control ytem correponding to three 3

4 different flight (tab.) deigned by claic control theory are illutrated. Thee figure how different behavior of claic attitude control ytem during powered-flight phae. Figure 6.repone of claic ytem at tart [deg/].5 In figure 9,, the tep repone of the attitude control ytem deigned by preented methodology at the ame flight, are illutrated. [deg/].5 Figure9. repone of adaptive-euivalent at the tart.5 In the figure 9,,tep repone of propoed attitude control ytem are demontrated time[] time[] 4 [deg/] Figure7.repone of claic ytem at max-head [deg/].5.5 Figure. repone of adaptive-euivalent at max-head time[] time[] 4 [deg/] Figure 8.repone of claic ytem at the end of powered-flight [deg/].5.5 Figure. Repone of adaptive-euivalent at end of powered-flight time[] time[] 4 4

5 In all the cae, the adaptive characteritic of combined method are obviouly demontrated. The tability reuirement have been atified by uch tructure. 4 Concluion A general procedure ha been developed for deigning a new adaptive-euivalent control ytem uing a combined approach. The experimental reult obtained by the imulation of a launch vehicle attitude control problem have hown the feaibility and advantage of thi type of adaptive-euivalent tructure. Further tudie will be concerned with the development of optimization of the parameter of the controller tranfer function. Reference [] Y.Z.Typkin, Adaptation and le arning in automatic ytem, Mocow,Naouka,97.(In ruian). [] K.J.Atrom, B.Wittenmark Adaptive control, 995. [3]N.I.Cokolov, V.Uo. Rotkovcki, N.B.Coodzilovki, Adaptive flight control,mahinotroenie, 988. (In Ruian). Mocow, [7] W. C. Leite Filho L.Hu, Adaptive control of Miile attitude, IFAC conference, 987. [8] Landau I. D, Adaptive control, model reference approach, 979. [9] Landau I.D, A urvey of model reference adaptive techniue-theory and application, Automatica, Vol., 975. [] B.N.Petrov. Adaptive flight control ytem, Mahinotroenie, Mocow, 97, (In Ruian). [] V.A Biekerki, E.P.Popov, Theory of automatic ytem regulation, Naouka,,Mocow,98 (In Ruian). [] Uo.P.Dobrolenli, V.I.Ivanova, Automatic control of rocket, Oborongiz, Mocow,967. (In ruian). [4] Whitker H.P.,Yamron J.,Kezer A. Deign of model-reference adaptive control ytem for aircraft. Report of Maachuett Intitute of Technology, 959, No R-34 P [5] Goett.T.D., Corli.L.D.A uadratic performance index for a VTOL aircraft prefilter model reference attitude control ytem. TN D- 63,97,NASA. [6] Landau I. D., Courtil B, Adaptive model following ytem for flight control and imulation, Journal of Aircraft, Vol.9, No9,

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