JOLRNAL OF SCIENCE* TECHNOLOGV * No 838-2011 A RESEARCH ON DESIGNING A TRACKING EQUIPMENT FOR VTOL AIRCRAFT NGHIEN CUU THIET KE THIET B\ QUAN SAT CHO MAY BAY VTOL Pham Huu Due Due University for Economic and Technical Industries ABSTRACT Research on designing tracking equipment tg satisfy the autopilot for vertical take-off and landing (VTOL) aircraft has been done by more and more scientists in the world Mathematical model of VTOL aircraft is a non-linear multiple input-multiple output (MIMO) type, so VTOL aircraft is a complex tracking and control object This paper proposed a new solution using the output feedback method to design a tracking equipment to satisfy the autopilot of a VTOL aircraft for Its both longitudinal motion and the lateral motion model Simulation results shew that the output signals of tracking equipment follow closely with the constant command input signals being observed in both models mentioned above, thus confirmed the effectiveness and feasibility of this solution Key words: VTOL aircraft, closed-loop, eigenvalue, MIMO, regular, tracking TOM TAT Nghien cwu thiit ki thiit bi quan sit phuc vu yeu ciu lil tw ddng ditng cho loai miy bay cit cinh vi h^ dnh theo chiiu thing dirng (VTOL) da vi dang dwgc nhiiu nhi khoa hgc trin thi gidi quan tim Md ti toin hgc cua miy bay VTOL li dang nhiiu vio-nhiiu phi tuyin phwc t^p, dd miy bay VTOL li doi twgng khd quan sit, diiu khiin Bai bio di xuit mdt giii phip mdi dd li U'ng dpng phwong phip phin hdi diu di thiit ki thiit bi quan sit phuc vu yeu ciu lii tt/ ddng cho ci hai d$ng md hinh li: md hinh cic chuyin ddng dgc vi md hinh cic chuyin ddng ben cua miy bay VTOL Kit qui md phdng cho thiy cic tin hieu d diu thiit bi quan sit da bim sit theo dwgc dc tin hiiu dit cin quan sit d diu vig ciia d hai md hinh ndi tren, dd khing dinh tinh hiiu qui vi thi cita giii phip niy VTOL aircraft in both manual pilot and autopilot mode I INTRODUCTION VTOL aircraft is used in many countries in the world because they have many advantages in take-off, landing Jet-fighters of VTOL aircraft type used on aircraft carriers are able to take off and landing on veiy short flights (about 100-200 metres) Mathematical description of VTOL aircraft is a nonlinear multiple input-multiple output (MIMO) type, so there are many difficulties in the observation and control process Although different methods of observation and control for nonlinear MIMO system have alreadv existed, this paper proposes a new solution that applies output feedback method to design tracking equipment vvhich helps a pilot observe input signals of VTOL aircraft This solution is applied lo both models of VTOL aircraft motions the longitudinal motions and the lateral motions, fhis tracking equipment helps the pilot observes and control all signals on a II OUTPUT SYSTE.M FEEDBACK TRACKING The state and output equation of a MIMO plant [1] are • = ^.v -I- Bu (1) • = Cx (2) where the dimension of ^4 is (nxn), B is (/; X m) C is (^ X n), _v is (^ X I), and the rank of is m These equations are often available or mav' be transformed to the partitioned form r , ' -V, UJ A\ Al A> Al y =[c, 97 Cj } -I- (3) ^1 x (4) X JOLR.NAL OF SCIENCE* TECHNOLOGV * No 838-2011 '• +.(5?^ z K.2 ^>6^ ' gl + y Kl Mi 1> 1 1 B \6 > ^ y X C + A I Fig Output feedback tracking system containing a proportional plus integral PI controller 3.Detennine the transmission zeros thai comprise set S of the closed-loop eigenvalues There are detennined from where x, is (m x 1) B, is (//(x m) and has rank m, C, is (m x m) and has rank m, and the remaining elements in these equations have appropriate dimensions [/l/,_,-.4„-h,4,,C,"'C,J = The design method for the tracker presented in this paper requires that the number of controlled outputs v must be equal to the number of controls u Thus, f = m A high-gain controller implements a proportional plus integral Pl control law (Fig.l) u = g[K^e + K,z\ The transmission zeros must be located in the LH plane or the design cannot proceed In the case of a controllable and observable plant the transmission zeros can also be computed from the determinant of the system matrix which is defined by (5) (6) The design procedure is based on the requirement that all of the closed-loop eigenvalues must be located in the left \\a\f(LH) plane so that the system is stable In addition, non-interacting or decoupled control is desirable This means that each output tracts its respective command input; that is, i ( follow r(t) Also, the amplitudes of any transients due to other inputs must be verv small The design process consist of the following steps: Because decoupling of the outputs are selected and used in C.B.K =Y^ B -i] -n-h c:" (81 The values -gcr^ -gcr, comprise the fast eigenvalue set -gaw The aircraft motions are illustrated in Fig.2 To guarantee a coherent use of the controls available, the actual controls used in the analysis are defined as follows: S3 is an equal deflection angle of the thrust at cveiy fan in the longitudinal direction; 6T is an increase of the total thrust, i.e an equivalent increase of the thrust at eveiy enaine; ('>T, is an e.xchanae csf thrust between v = [.v,,z,, , , i , , z , , ,9,] ; u = [S9 SJ SJ,,,]' 99 ; r = [ V, i , , ] ' JOLRNAL OF S C I E N C E * TECHNOLOGV , where units: x^ and _, (ft); 5,(rad); x^ and i, (fts): 5jrads): ST (ST = lif Sf = Sf = -9057.5 lb and ST, = -9385.1 lb ) Sf.,(Sf^,=\ 'if ST, =ST,=-9051.5 (57; =18115 lb) A =5; ^=i; B \h and the constant command inputs: '•=[i., ^, •9 J =[0.5 0.1 0.7]' K 0 0 0 0 •21.211 -10.989 2.976 4.595 1265 2.864 0.194 -2.685 0 0 ;C= 0 0 0 0 0 ' = [}',- !>.,] ; Perform simulations on Matlab software [5] from the step I to the step which were presented in part IL vve can find the following results The matrix >o ».>B - :ui i and the matrix " = [.^s ¥„ y^, (dashed line), respectively Thus the task set for B/controller has been satisfied IV CONCLUSION Simulation resuhs showed that the output signals of both the longitudinal motions and the lateral motions model were followed closely with the constant command inputs r It has been proven that the solution applying the output feedback methods to design tracking equipment 100 JOLRNAL OF SCIENCE* TECHNOLOGV * No 838-2011 for VTOL aircraft, is really effective The advantages of this solution are as follows: tracking equipment is not too complex, easy to manufacture and its cost is not high Moreover, nowadays, many countries in the world are improving their military potential in their sea So military scientists in the world are studying to advance the automation level of VTOL jetfighters because of they have good combat efficiency on aircraft carriers This shows that this solution is capable of application in the fields of aviation and especially in military one Fig The deflection angle of the Fig.4 The increase of Ihe total thrust al every fan 59 thrust ST Fig The exchange of thrust between the front and aft fans ST,, Fig The conslani command Fig The constant command Fig.S The constant command input i^, (dashed line), Ihe output inpul i^, (dashed line), the output input 9^ (dashed line), Ihe output signal X, (solid line) signal z^ (solid line) ^j^^^i ff^ (solid liney Fig.9 The deflection angle oflhe thrust al both aft fans Sa,, Fig 10 The exchange of thrust between the aft fans ST,, Fig.l The lateral deflection angle of Ihe thrust al the front fan Sa, Fig 12.The constant command Fig 13 The conslani command Fig 14 The conslani command input y ,Jdashed line), the oittpul input ^^ (dashed line), the output input if/^Jdashed line), the signal V, (solid line) signal^ (solid line/ output signal i//^ (solid line) REFERENCES John J.D'Azzo, Constantine H Houpis; Linear Control System Analysis and Design; McGrawHill, Inc, 1995 Marc Bodson, Michael Athans; Multivariable Control of VTOL Aircraft for Shipboard Landing; l niversitv of Califomia, Berkeley, California 1985 M S Triantafyllou, M.Athans; Real Time Estimation of the Heaving and Pitching Motions of a Ship Using a Kalman Filter; Proc Oceans '81 Massachusetts, 1981 \1 S.friantafvllou et al; Real Time Estimation of Ship Motions Using Kalman Filtering Techniques; I E E E J.of Oceanic Engineering, \ o l O E - No.I, pp.9-20, (1983) http://wvvvv.mathworks.coni, Matlab the Language of Technical Computing; 1996 Author's address: Pham Huu Due Due - Tel: (^84)913.238.632 - Email: phdduc.uneti®moet.edu.vn Universitv for Economic and Technical Industries, 101 ... respectively, in the alternate fonns as: A'',=[CB]''X Fig.2 VTOL aircraft motions (10) 3.L Perform simulations on the longitudinal motions model of VTOL aircraft It is not necessary to detennine the transformation... that the output y follows closely with the constant command input r for two following models of VTOL aircraft: the longitudinal motions and the lateral motions one form, it can be achieved by... matrices ('' and B can be used directly in Eq (10) to compute A'', The longitudinal motions model of VTOL aircraft is represented by the state and output equations as in Eqs (1) and (2), where: A simple