Longitudinal automatic control ytem for a light eight aircraft Critian VIDAN*,, Silviu Ionut BADEA *Correponding author Military echnical Academy, Faculty of Mechatronic and Integrated Armament Sytem, M Department of Aircraft Integrated Sytem and Mechanic, 39-49 George Coşbuc Avenue, Sector 5, Bucharet 54, Romania, vidan.critian@yahoo.com*, badea.ilviu_ionut@yahoo.com DOI:.3/66-8.6.8.4.3 Received: 5 September 6/ Accepted: 5 October 6/ Publihed: December 6 Copyright 6, INCAS. hi i an open acce article under the CC BY-NC-ND licene http://creativecommon.org/licene/by-nc-nd/4./ International Conference of Aeropace Science AEROSPAIAL 6 6-7 October 6, Bucharet, Romania, held at INCAS, B-dul Iuliu Maniu, ector 6 Section 5 Sytem, Subytem and Control in Aeronautic Abtract: hi paper preent the deign of an automatic control ytem for longitudinal axi of a light eight aircraft. o achieve thi goal it i important to tart from the mathematical model in longitudinal plane and then to determine the teady-tate parameter for a given velocity and altitude. Uing MALAB Softare the mathematical model in longitudinal plane a linearized and the ytem tranfer function ere obtained. o determine the automatic control deign e analyzed the tability of the linearized model for each input. After the tability problem a olved, uing MALAB- Simulink Softare e deigned the control ytem architecture and e conidered that the objective for a table flight a to continuouly adjut the pitch angle θ through control of elevator and velocity through control of the throttle. Finally, e analyzed the performance of the deigned longitudinal control ytem and the reult highlighted in graph outline that the purpoe for hich it a deigned a fulfilled. Key Word: control, ytem, MALAB, Simulink, longitudinal, aircraft. INRODUCION Light eight aircraft flying around the orld and the number or licened pilot on thi category of aircraft i increaing from year to year. Flight afety of thee aircraft depend on kill and experience of the pilot but it i more important to have a flight tabilization ytem autopilot on board. Autopilot do not replace a human operator, but ait them in controlling the vehicle, alloing them to focu on broader apect of operation, uch a monitoring the trajectory, eather and ytem [. hi ork i focued on the modelling of longitudinal automatic control ytem hich i able to enure rapid damping of ocillation due to the effect of the diturbance or the elevator command and to maintaining contant peed and teering angle. o create a link ith the real orld of lighteight aircraft e choe an aircraft ith the folloing characteritic: eight i equal to kg, moment of inertia about a lateral axi i INCAS BULLEIN, Volume 8, Iue 4/ 6, pp. 57 64 ISSN 66 8
Critian VIDAN, Silviu Ionut BADEA 58 equal to kg.m, the ing reference urface i equal to m and the ing reference length i equal to m. Without ind tunnel teting of the caled model or flight tet e ue analytical prediction to determine aerodynamic coefficient and that a quite complicated.. MAEMAICAL MODEL OF E AIRCRAF IN LONGIUDINAL PLANE he evolution of a lighteight aircraft in longitudinal plane, ithout roll and ya movement can be decribed a a ytem of differential equation of the folloing form: q co v S Cx v g in m m in v S Cz g co m m v v b S C vb S C q m v b S C mq J y J y J y h vin q m p In calculating the aerodynamic force and moment e ued aerodynamic dimenionle coefficient C, C, C, C, C hich ere etimated by analytical prediction. x z m m q m hee aerodynamic coefficient are referred to a tability derivative becaue their value determine the tatic and dynamic tability of the aircraft [. he value of aerodynamic coefficient are diplayed in the table belo: C x C z able. Aerodynamic coefficient C C m mq.5.5 5 5.5 It i oberved that the ytem of differential equation of motion i trongly nonlinear, being impoibly to be integrated analytically. he four firt order differential equation decribe the evolution of four tate variable, hich are grouped in the tate vector, X: C m X V q A value of interet that characterize the evolution of the aircraft, e ill conider all tate parameter, plu angle of incidence, hich are grouped into the ytem output vector, Y : Y V 3 A input in the ytem e have the elevator and throttle command hich add ind a external perturbation. All thee input are grouped into the ytem input vector, U: INCAS BULLEIN, Volume 8, Iue 4/ 6
59 Longitudinal automatic control ytem for a light eight aircraft c U 4 With previou pecification, the aircraft can be repreented a hon in Figure. Fig. Sytem State-Space Repreentation 3. MAEMAICAL MODEL LINIARIZAION Before linearizing the mathematical model it i important to determine the teady-tate condition. herefore, the teady-tate condition of a dynamic ytem are characterized by zero value of derivative of the differential equation of motion a follo: v m/,, h 5m 5 Uing differential equation ytem e achieved to the folloing flight parameter value in teady-tate condition: V S K 5 Cx.6.5 643[ N 6 mg 9.8.99[ rad V SC z 646.6.5 7.99[ rad After etablihing the teady-tate condition e moved to the linearization of the mathematical model. he parameter that define the evolution of aircraft V,,, q can be expreed by declination V,,, q, compared to the value correponding to the teady tate condition V,,, q =: V V V X X X 9 q q Compared to the value of teady-tate condition, input vector ill be expreed imilarly: 8 INCAS BULLEIN, Volume 8, Iue 4/ 6
Critian VIDAN, Silviu Ionut BADEA 6 INCAS BULLEIN, Volume 8, Iue 4/ 6 U U U c c c he angle of incidence may be defined a declination from the teady-tate value: Subjecting the differential equation ytem to teady-tate condition and uing the declination V,,, q, then procceing the reult and uing MALAB Softare for calculating the three matrice of the liniarized ytem, e get the folloing:.95[ 6.35[ 6.35[.9733[.9733[.6[.97[ 9.683[.66[ m A.4575[ 48.975[.65[.54[ 9.99[ m m B 3 C 4 Baed on tate-pace model, the input-output model of the aircraft, hich i defined by tranfer matrix, F can be obtained: 4 B A I C q pq q p p p V V V F 5 In the above relation, the term xy repreent the tranfer function from input x to output y. he tranfer matrix contain 5 imilar tranfer function from each of the three input to each of the three output. he aircraft can be repreented input-output on longitudinal plane a hon in figure, taking into account the relation for the tranfer function of the angular velocity and the angle of incidence.
6 Longitudinal automatic control ytem for a light eight aircraft Fig. Simplified Input-Output Repreentation [3 4. LONGIUDINAL AUOMAIC CONROL SYSEM DESIGN ranfer function previouly obtained ho that the mathematical model of the aircraft i near the limit of tability or may even be untable. Stabilization can be made afe by the negative reaction cheme deigned to enure a table maintenance of the tangent of trajectory angle, to reduce tate ocillation of the ytem, and to enure diturbance rejection and maintaining the correct flight path to influence vertical current [5. In order to deign the control ytem architecture e conidered that the objective for a table flight i to continuouly adjut the pitch angle θ through control of elevator and velocity through control of the throttle. In the tructure belo, the controller i repreented by the tranfer function R : Fig. 3 Simplified Controller Architecture o enure the accuracy of the ramp input ignal and rejection of diturbance, the controller ill have a imple pole in origin. Conequently, e choe a PI controller, for hich the tranfer function i of the form [5: R KR / i KR 6 i INCAS BULLEIN, Volume 8, Iue 4/ 6
Critian VIDAN, Silviu Ionut BADEA 6 Controller coefficient, amplification contant K R and time contant i of the integrator ere obtained by Ziegler-Nichol method a through relationhip: becaue KR.45 K i.8 KR.456.9 3. i.8.483.3864 M K A / i.483 6.9 he coefficient K and time contant, ere obtained conidering that the previou controller architecture ued a purely proportional regulator. Actually, K mean the maximum contant gain controller to hich the ytem reache the tability limit and the value of hich i equal to the reerve amplitude. repreent the ocillation time period hen the ytem goe to the tability limit. he tranfer function of the controller a determined uing thee value: 7 8 9 3.. 63 R Belo i given the tep repone of the ytem to thi channel for the controller deign, compared to the direct repone. [4 Fig. 4 Step Repone of the Sytem to Pitch Channel he characteritic of the tep repone can be oberved much better. he ytem repond acurately, in very hort period of time, ith lo overhoot. Fugoid ocillating mode phenomena are eliminated. INCAS BULLEIN, Volume 8, Iue 4/ 6
63 Longitudinal automatic control ytem for a light eight aircraft 5. PERFORMANCE ANALYSIS OF LONGIUDINAL CONROLLER he control architecture of the complete ytem ill be: Fig. 5 Control Architecture of the Complete Sytem [3 o obtain a control architecture model of the complete ytem in the MALAB oftare, in order to implement a feedback loop, then the feedback loop ill ha to proce the tate vector uing a tranfer matrix that enure the election of the component. he formal tructure of the complete ytem configuration for the automatic control ill be the folloing: Fig. 6 Formal Structure of Complete Sytem Configuration Since the MALAB Simulink module [6 allo the repreentation ytem of nonlinear differential equation and imulate their evolution, the parameter aner obtained after the linearization of the mathematical model i more accurate. Fig. 7 Velocity Variation INCAS BULLEIN, Volume 8, Iue 4/ 6
Critian VIDAN, Silviu Ionut BADEA 64 Fig. 8 Incidence Angle Variation Fig. 9 Angular Velocity Variation Fig. Pitch Angle Variation It can be noticed that the control ytem i able to enure rapid damping of ocillation due to the effect of the diturbance or the elevator command and to maintain contant peed and teering angle. 6. CONCLUSIONS We deigned a longitudinal automatic control ytem that ha good performance for external diturbance and it i able to maintain a good tability on the pitch axi. Alo, e analyzed the performance of the deigned longitudinal control ytem and the reult highlighted in graph outline that the purpoe for hich it a deigned a fulfilled. A a future ork e intend to achieve a imilar controller for the lateral channel and to combine it ith the already made longitudinal channel automatic ytem in order to deign a controller enabling a full control of any light eight aircraft. REFERENCES [ * * * Automated Flight Control - faa.gov. Federal Aviation Adminitration. Retrieved February 4. [ R. W. Beard,. W. McLain, Small Unmanned Aircraft. heory and Practice, Princeton Univerity,. [3 V. Nuțu, eoria Sitemelor Automate, Editura Academiei ehnice Militare, Bucureti. [4 J. D. Barton, Fundamental of Small Unmanned Aircraft Flight, John opkin APL echnical Diget, Vol. 3, Nr.,. [5 K. P. Valavani, G. J. Vachtevano, he handbook of Unmanned Aircraft Vehicle, Springer Reference 4. [6 * * * http://.mathork.com/ INCAS BULLEIN, Volume 8, Iue 4/ 6