Gain Scheduled Automatic Flight Control Systems Design for a Light Commercial Helicopter Model

Transcription

1 Erkan Abdulhaitbilal, Elbrous M. Jafarov Gain Scheduled Autoatic Flight Control Systes Design for a Light Coercial Helicopter Model Erkan ADULHAMITILAL and Elbrous M. JAFAROV Faculty of Aeronautics and Astronautics Istanbul Technical University Turkey abdulhaitbilal@gail.co, cafer@itu.edu.tr Abstract: - In this paper, nonlinear rigid body dynaics for rotorcraft atheatical odel is studied. A linearization of helicopter flight dynaics is evaluated. Autoatic Flight Control Syste (AFCS) with gain scheduled LQ optial control is designed based on look-up tables. Stability analyses are perfored and results are illustrated graphically for open and closed-loop systes. As seen fro results, LQ optial control syste pushes eigenvalues to left side of iaginary axis without excessive control inputs to aintain stability of naturally unstable rotorcraft dynaics. Proposed AFCS is tested by nonlinear flight dynaics odel in Matlab- Siulink environent. Siulation results illustrate effectiveness of evaluated ethod and techniques. Key-Words: - helicopter, flight dynaics, nonlinear odel, siulation, 1 Introduction Autoatic Flight Control Systes (AFCSs) are electro-hydro echanical systes that provide inputs to the control surfaces or eleents to assist the pilot in aneuvering and handling the aircraft in desired flight conditions. The AFCSs provide both oscillation daping (dynaic stability) and aintain desired flight attitude, speed and heading (static stability). Major coponents of the AFCSs are stick, collective and pedals position sensors, servo acceleroeters, flight control panel, flight coputer, rate gyros, air data and speed transducers, etc. In control theory, gain scheduling is an approach to control of non-linear systes that uses a set of linear controllers, which provides satisfactory control for a different operating point of the syste. Scheduling variables are used to deterine the operating region of the syste and to enable the appropriate linear controller. In aircrafts, AFCSs have altitude and Mach nuber (or forward speed) as scheduling variables with different linear controller paraeters available as look-up tables for various cobinations of those two variables. A full nonlinear atheatical odel of helicopter dynaics of prototyped helicopter with tri, perforance and linearization analyses, huan pilot analysis, and AFCS design is studied in [1]. Design handbook of the flexible rotor used in the prototype helicopter is given in [2]. Siilarly full nonlinear rotorcraft dynaics odel of Sikorsky UH-6A is studied in [3]. On the other hand, gain scheduled control syste for the odeled prototype helicopter is evaluated in [4]. Siilarly reconfigurable control for a tande helicopter is investigated in [5]. Autoatic flight control systes and flight dynaic are studied in [6-7]. Optial control theory is evaluated in [8]. Gain scheduling theory and applications are studied in [9]. Helicopter flight dynaics and theory is researched in [1-12]. Soe rotorcraft control systes such as state feedback and robust control are designed in [13-16]. Fuzzy and classical control approaches are applied to the proble in [17-18]. The significance of this paper is evaluation of the proble fro beginning to the end which eans odeling the rotorcraft dynaics, calculation of corresponding stability and control derivatives, design of control syste for a flight envelope and siulation of control syste with nonlinear flight dynaics. In this paper, we will first study nonlinear rotorcraft equation of otion. Rotor dynaics and aerodynaics is not evaluated, but referred fro [1] because these are hard to study in this paper. Then, we will linearize rotorcraft flight dynaics near a tri condition and propose a gain scheduled LQ optial control law to be integrated in AFCS. We are going to perfor all siulations with Matlab- Siulink on nonlinear flight dynaics odel given at the end of the paper. ISSN: Issue 12, Volue 6, Deceber 211

2 Erkan Abdulhaitbilal, Elbrous M. Jafarov 2 Proble Forulation In this paper, we have considered a prototype helicopter designed and anufactured by Rotorcraft Design and Excellence Centre (ROTAM) - Istanbul Technical University (ITU) [1]. The rotorcraft has four flexible blades with Hanson s rotor hub odel [2]. Tail rotor is designed as conventional one and epennages are fixed. The helicopter is equipped with a turbo-shaft engine which produces 65 SHP (shaft horsepower). A picture of the rotorcraft fro anufacturing phase is given in Figure 1 and soe paraeters for atheatical odel are illustrated in Table 1. Table 1 Soe helicopter paraeters [1] Main Rotor lade nuber Radius Rotor angular velocity.. lade twist. Rotor solidity. STA L.. WL. Tail Rotor lade nuber Radius Rotor angular velocity... Rotor solidity. STA L.. WL. Vertical Fin Area Incidence... STA L.. WL. Horizontal Stabilizer Area Incidence STA L.. WL... Fuselage Gross Weigh.. STA L.. WL rp deg - - rp - 2 deg 2 deg kg Figure 1 Prototyped Helicopter Autoatic Flight Control Syste (AFCS) proposed with this study consists of speed hold, height hold, and heading hold properties. Scheatic view of AFCS panel on the board is shown in Figure 2. The panel includes a aster switch to turn on/off the syste. Speed, height and heading hold switches as well have on and off options. When the aster switch is engaged, AFCS supplies short-ter attitude and attitude rate stabilization to assist the pilot. For use in hands-free flight pilot ust switched on speed hold, height hold, and heading hold switches. The rotorcraft will keep current flying speed just after turning speed hold switch on. eside, height hold switch should be turned on to hold current flight altitude. If speed hold is on when height hold is turned on then control algorith that runs for speed hold is cancelled and a new control law is replaced both for speed an altitude hold ode. And finally, turning heading switch on will keep rotorcraft heading angle at current flying yaw angle. Figure 2 Scheatic view of flight control panel We should first define nonlinear flight dynaics of the rotorcraft to design a control law for ISSN: Issue 12, Volue 6, Deceber 211

3 Erkan Abdulhaitbilal, Elbrous M. Jafarov stabilization. Then we can easily linearize nonlinear dynaics near any tri point. Hence a LQ optial control law, as we desire, can be structured. The rigid-body equation of otion of the rotorcraft is as [1,3,6,11]: u X s 1 v Y g c s w Z c c r q u r p v q p w p L r q p 1 1 q I M I r p I q r N q p r 1 s t c t p c s q s sc c sc r (1) (2) (3) where X, Y, Z are the acting total forces in (N); L, M, N are the acting total oents in (N); u, v, w are the body velocities in (/s); p, q, r are the body angular rates in (rad/s);,, are the body attitude angles in (rad); c = cos, s = sin, t = tan, sc = sec; is the ass in (kg) and I is the inertia atrix as: I I I I I I I I I I xx xy xz xy yy yz xz yz zz (4) Expansion of X, Y, Z, L, M, N for a single rotor helicopter is studied in [1,3,1,11,12]. We pass this stage because evaluating rotorcraft forces and oents are wide area of study. We will use only results that we have obtained. Design procedure of AFCS is based on linear quadratic optial control proble. At this stage, nonlinear flight dynaics will be linearized and control law will be designed on linear flight dynaic odel. To guarantee the stability at any flight speed and altitude control gains will be scheduled for flight speed and altitude by flight coputer fro data tables. We would like to point that siulations of AFCS will be perfored on nonlinear flight dynaics odel. The linear for of above equation of otions (1)- (3) describing rigid body otion of helicopter is of the for: x A x (5) where x is the perturbations fro tri of the states variables of longitudinal otion: u, w, q, and lateral otion: v, p, r ; δ is the deviation fro tri control positions of longitudinal otion c, 1s and lateral otion 1c, p. The eleents of the A and atrices consist of inertial and gravitational ters that can be obtained analytically fro the equation of otion (1)-(3) and partial derivatives fored fro aerodynaics forces and oents. The force and oent derivatives can be obtained by considering both position and negative perturbation fro tri as [1,9]: X u X u X ( u u ) X ( u u ) 2u (6) Noralized stability and control derivatives for longitudinal otion are x i =X i /, z i =Z i /, i =M i /I yy, where i = u, w, q, δ c, δ 1s. For lateral otion stability and control derivatives are noralized as y j =Y j /, l j =(I zz L j +I xz N j )/I c, n j =(I xz L j +I zz N j )/I c, 2 where j = v, p, r, δ 1c, δ p and Ic I xxi zz I xz. These derivatives are calculated for considered helicopter in [1] for any tri conditions. At the end of the paper in Table 2 we give soe stability and control derivatives for prototype helicopter odel at different flight speeds and altitudes. Also, corresponding stability and control derivatives that appear in this paper can be easily calculated fro nonlinear flight dynaics odel for any tri conditions in the bounds of to 7 /s forward speed and to 1, ft of flight altitude with steps size of 5 /s of forward speed and 2,5 ft of altitude. 2.1 Speed Hold Proble For speed hold proble now consider linearized the set of equation witch are enough to describe longitudinal flight dynaics of the helicopter [6]: u x u x w z w q g cos u w q x C x c 1s 1s w z u z w z u q g sin u w q z z C c 1s 1s (7) (8) ISSN: Issue 12, Volue 6, Deceber 211

4 Erkan Abdulhaitbilal, Elbrous M. Jafarov q u w q (9) u w q C c 1s 1s q (1) The state space for is: x ( t) A x ( t) ( t) SH SH SH SH SH y ( t) C x ( t) SH SH SH (11) where the state vector is x SH (t)=[u w q ] T, the control vector is SH (t)=[ c 1s ] T, C SH is unit atrix, and A SH SH xu xw xq w g cos zu zw zq u g sin u w q 1 x x C 1s z z C 1s C 1s (12) (13) The stability of longitudinal flight dynaics can be deterined by calculation of the eigenvalues of the syste atrix (A SH ). Eigenvalues are illustrated in Figure 3 for considered flight envelope. There are any roots at rights side of iaginary axis which eans that open-loop longitudinal dynaics are unstable. 2.2 Height Hold Proble For height/altitude hold syste linear height dynaics as given below are included to the linear longitudinal dynaics described in previous subsection by (12)-(13) as [6]: h w u (14) Therefore, the state vector can be rewritten as x SH (t)=[u w q h] T. Then, syste and control distribution atrices can be fored as: xu xw xq w g c zu zw zq u g s ASH u w q 1 1 u (15) x z 1s 1s SH C 1s C C x z (16) The eigenvalues of height hold dynaics are given in Figure 3. As seen fro the figure so any eigenvalues are the right side of iaginary axis and the worst situation is that soe of the have greater values which ean that those odes cannot be stabilized by a huan pilot. Figure 3 Eigenvalues of open-loop longitudinal helicopter flight dynaics. 2.3 Heading Hold Proble Heading of rotorcraft is deterined by lateral flight dynaics. The set of equation which describes lateral flight dynaics are [6]: v y v y u r y w p v r p + g c c y y 1c 1c v p r 1c 1c p p p p (17) p l v l p l r l l (18) r n v n p n r n n (19) v p r 1c 1c p p p c tr (2) c sc r (21) The state space for is: x ( t) A x ( t) ( t) HH HH HH HH HH y ( t) C x ( t) HH HH HH (22) ISSN: Issue 12, Volue 6, Deceber 211

5 Erkan Abdulhaitbilal, Elbrous M. Jafarov where the state vector is x SH (t)=[v p r ] T, the control vector is HH (t)=[ 1c p ] T, and yv y p w g c c yr u l v l p l r AHH 1 c t (23) n v n p n r c sc y y 1c P l l 1c P HH (24) n n 1c P iprove ission reliability and enhance safety of flight. 3.1 LQ Optial Control Law Consider that helicopter flight dynaics are described with linear set of equations like (15)-(16) or (23)-(24). To achieve an optial condition a perforance easure to be iniized should be defined [8]: 1 T T J x ( t) Q( t) x( t) ( t) R( t) ( t) dt 2 (25) where Q is a real syetric positive sei-definite atrix, R is a real syetric positive definite atrix, x and are states and control vectors, respectively. In the design process, it is assued that the states and controls are not bounded. However, control inputs are bounded due to physical liitation of the swash plate echanis and also states of the syste are bounded because of aerodynaic rules and perforance of power-plant. Here, the ai is to aintain the state vector close to the origin without an excessive expenditure of control effort. So, the optial control law is linear and it is fored as a cobination of the syste as [8]: * 1 T * * ( t) R Fx ( t) Kx ( t) (26) Figure 4 Eigenvalues of open-loop lateral helicopter flight dynaics. The stability of lateral dynaics syste can be obtained by calculation of the eigenvalues of the syste atrix A HH. Eigenvalues are illustrated in Figure 4 for considered flight envelope. There are any roots at rights side of iaginary axis which eans that open-loop longitudinal dynaics are unstable. 3 Design of Autoatic Flight Control Syste (AFCS) Typically, SAS, autopilot and flight director systes and odes of operations are luped together and referred to as an Autoatic Flight Control Syste (AFCS). There can be various cobinations of single and dual AFCS installations available for a particular helicopter odel. In this paper we have considered single ode. The LQ optial control law for AFCS is designed to reduce pilot workload, where F is the solution of following Algebraic Riccati Equation (ARE): (27) T 1 A F FA Q FR F And the optial cost of perforance index can be calculated fro: J =.5x T ()Kx(). The stability of the closed-loop syste can be deterined by calculation of the eigenvalues of the closed-loop syste atrix A R -1 T F or (A K) according to the optial control law (26). 3.2 Gain Scheduled LQ Optial Law Gain scheduling siply eans changing values of control atrix according to predefined conditions. In this paper, the control law is calculated for each tri points considered in flight envelope. In other words, the control atrix K is deterined fro forward speed and flight altitudes as: * * ( h, u, t) K ( h, u) x ( t) (28) In this paper we have obtained surfaces for each gain of control atrix K. ISSN: Issue 12, Volue 6, Deceber 211

6 Erkan Abdulhaitbilal, Elbrous M. Jafarov Figure 5 lock schee of proposed AFCS 3.3 Gain Scheduled Speed Hold AFCS The proposed LQ optial control law for speed hold AFCS is considered as: 3.4 Gain Scheduled Height Hold AFCS Siilarly to previous control law height hold is fored as: * c * SH SH 1s K ( h, u) x ( t) (29) * c * AH AH 1s K ( h, u) x ( t) (3) where K SH,ij (h,u) is the scheduled control atrix which eleents are selected fro Figure 9. In flight coputer these plots are coded as look-up tables. The eigenvalues of Speed Hold AFCS are illustrated in Figure 6. As seen fro figure closed-loop eigenvalues are at left side of iaginary axis which eans the syste is stable. After speed hold is turned on, reference value is selected to be current forward flight speed. Therefore, longitudinal dynaics of the rotorcraft is stabilized near selected forward speed by selection of proper gains fro look-up tables in (3) and therefore hands free flight is achieved. where K AH,ij (h,u) is the scheduled control atrix which eleents are selected for Figure 1. Switching height hold on selects reference values to be current forward speed and altitude. If speed hold is on when height hold is switched on then control law for longitudinal otion is replaced with height hold control algorith (31). Therefore, longitudinal dynaics of the rotorcraft is stabilized near selected forward speed and flight altitude. The eigenvalues of Speed Hold AFCS are illustrated in Figure 7. O, the stability of the closed-loop syste is graphically shown. All real parts of eigenvalues of height hold syste are negative signed with enough daping values. Figure 6 Eigenvalues of closed-loop speed hold syste Figure 7 Eigenvalues of closed-loop height hold syste. ISSN: Issue 12, Volue 6, Deceber 211

7 Erkan Abdulhaitbilal, Elbrous M. Jafarov 3.5 Gain Scheduled Heading Hold AFCS The proposed LQ optial control law for heading hold AFCS is considered siilarly to previous ones as: * 1c * HH HH p K ( h, u) x ( t) (31) where K HH,ij (h,u) is the scheduled control atrix which eleents are selected fro Figure 11. In flight coputer these plots are coded as look-up tables. The eigenvalues of Heading Hold AFCS are illustrated in Figure 8. As seen, all eigenvalues of closed-loop syste for bounded flight condition are pushed to the left side of iaginary axis. This pilot illustrates graphically the stability of the syste. Figure 8 Eigenvalues of closed-loop heading hold syste. 4 Siulations After design of AFCS we need to test its perforance and tie responses. For this purpose we have considered nonlinear rotorcraft dynaics odel of prototype helicopter given in [1]. The atheatical odel is built in Matlab-Siulink environent and top view of its block diagra is given in Figure 12. Tie responses of pure rotorcraft dynaics or disabled (off ode) of AFCS are shown in figure 13. As seen fro the figure the unstable nature of rotorcraft pushes state variables away fro steady state situation after 4 seconds. This tie is sufficient for the pilot to take a control action to stabilize the rotorcraft. To iprove ission reliability, enhance safety of flight without excessive control inputs and reduce pilot workload AFCS is enabled for different operating cases and aneuvers. Tie responses of aneuvers rejecting 5 /s (9.72 knots) vertical and sideward winds with 5 seconds duration at sea level and 3 /s (58.32 knots) forward flight speed are given in Figure 14 and 15, respectively. In this case, only aster switch of AFCS is on. The disturbance wind effects are rejected with high daping pitch and roll rates for both cases. However rotorcraft odel is losing 3 of altitude and pushed 25 to sideward for each aneuver. Forward speed correction aneuver at sea level and 3 /s (58.32 knots) forward flight speed is given in Figure 16. The optial control algorith eliinates 3 /s forward speed error in a couple of seconds with high daping attitude rates where only aster switch of AFCS is on. On the other hand, attitude angles reach steady state in 15 seconds with a confortable aneuver. Tie responses for total 7.1 /s (13.8 knots) crosswind rejection at sea level and 3 /s (58.32 knots) forward flight speed when AFCS aster, speed hold, height hold, and heading hold switches are engaged are given in Figure 17. The distributive crosswind with 5 seconds duration is eliinated in 15 seconds. LQ optial control algorith provides high daping roll, pitch and yaw rates. ut roll angle sees to exhibit daped oscillation for a while during stabilization because of the 7.1 /s crosswind. For this disturbance rejection aneuver only collective inputs appears to provide a little bit high control values in arrange of 15 degrees to keep rotorcraft at desired flight altitude, where the rest control inputs changes in 2-3 degrees. 5 Conclusion In this paper, we have introduced nonlinear rigid body dynaics for rotorcraft atheatical odel. Then we have linearized helicopter flight dynaics to design a gain scheduled LQ optial control syste to reduce pilot workload, iprove ission reliability and enhance safety of flight without excessive control inputs. We have designed our AFCS to stabilize helicopter flight dynaics and aintain desired flight speed, altitude and heading as gain scheduled where gains of feedback atrix are selected with flight speed and altitude fro look-up tables coded in flight coputer. Stability analyze is perfored graphically by plotting eigenvalues both for open and closed-loop systes in considered flight envelope which bounds are to 7 /s forward speed and to 1, ft of flight altitude. Proposed LQ optial control law ISSN: Issue 12, Volue 6, Deceber 211

8 Erkan Abdulhaitbilal, Elbrous M. Jafarov have pushed eigenvalues to the left side of iaginary axis for all design conditions. Proposed control laws are designed on linear flight dynaics however they are evaluated in nonlinear flight dynaics atheatical odel of the prototype helicopter. Siulation results illustrate effectiveness of evaluated ethod and techniques. References: [1] E. Abdulhaitbilal, ITU-Light Coercial Helicopter flight dynaics, stability analysis, and interconnected control systes design, ITU-Library, Istanbul, 21. [2] T. F. Hanson, A Designer Friendly Handbook of Helicopter Rotors, ideasalacarte.co, [3] J.J. Howlett, UH-6A lack Hawk Engineering Siulation Progra: Volue I Matheatical Model, NASA CR 16639, [4] E. Abdulhaitbilal, E.M. Jafarov, and L. Güvenç, Gain Scheduled LQ Optial Control of a Paraetric Light Coercial Helicopter Model at Sea Level. Proceedings of ACMOS'7, 9th WSEAS International Conference on Autoatic Control, Modeling and Siulation, June 27-29, 27, Istanbul, Turkey, [5] C.Y. Huang, R. Celi, I-C. Shih, Reconfigurable flight control systes for a tande helicopter, Journal of Aerican Helicopter Society, vol. 44, pp [6] D. McLean, Autoatic Flight Control Systes, Prentice Hall, London, 199. [7].L. Stevens, F.L. Lewis, Aircraft Control and Siulation, John Wiley & Sons, Inc., [8] D.E. Kirk, Optial Control Theory, Prentice Hall, New Jersey, 197. [9] K.J. Aströ,. Wittenark, Adaptive Control, Addison-Wesley, New Jersey, [1] W. Johnson, Helicopter Theory. Dover Publications Inc, New York, [11] R.W. Prouty, Helicopter Perforance, Stability, and Control. Krieger Publishing, Florida, [12] A.R.S. rawell, G.T. Sutton Done, D. alford, rawell s Helicopter Dynaics, 2nd Edition, AIAA, Virginia, 21 [13] M.D. Takahashi, Rotor-state feedback in the design of flight control laws for a hovering helicopter, Journal of Aerican Helicopter Society, vol. 39, pp [14] R.M. McKilip Jr., T.A. Perri, Helicopter flight control syste design and evaluation using controller inversion techniques, Journal of Aerican Helicopter Society, vol. 37, pp [15] J.N. Rozak, A. Ray, Robust ultivariable control of rotorcraft in forward flight, Journal of Aerican Helicopter Society, vol. 42, pp [16] I. Postlethwaite, A. Serlas, D.J. Walker, A.W. Gubbels, S.W. aillie, M.E. Strange, J. Howitt, H control of the NRC ell 25 fly-by-wire helicopter, Journal of Aerican Helicopter Society, vol. 44, pp [17] Y. Isik, Pitch rate daping of an aircraft by fuzzy and classical PD control, WSEAS Transactions on Systes and Control 5 (7), 21, pp [18] J.-M. Lin, P.-K. Chang, Ziegler-Nichols PID controller based intelligent fuzzy control of a SPM syste design, WSEAS Transactions on Systes and Control 5 (1), 21, pp Table 2 Soe stability and control derivatives of prototype helicopter Uo h T GW /s ft 288K 227kg Φ θ ψ θc θ1s θ1c θp U V Q V P R dc d1s d1c dp X Z M Y L N /s ft 288K 227kg ISSN: Issue 12, Volue 6, Deceber 211

9 Erkan Abdulhaitbilal, Elbrous M. Jafarov /s ft 288K 227kg /s ft 288K 227kg /s 1ft 288K 227kg /s 1ft 288K 227kg /s 1ft 288K 227kg /s 1ft 288K 227kg ISSN: Issue 12, Volue 6, Deceber 211

10 Erkan Abdulhaitbilal, Elbrous M. Jafarov Figure 9 Gain scheduling surfaces of speed hold feedback atrix gain, K SH (h,u). ISSN: Issue 12, Volue 6, Deceber 211

11 Erkan Abdulhaitbilal, Elbrous M. Jafarov ISSN: Issue 12, Volue 6, Deceber 211

12 Erkan Abdulhaitbilal, Elbrous M. Jafarov Figure 1 Gain scheduling surfaces of height hold feedback atrix gain, K AH (h,u). ISSN: Issue 12, Volue 6, Deceber 211

13 Erkan Abdulhaitbilal, Elbrous M. Jafarov Figure 11 Gain scheduling surfaces of heading hold feedback atrix gain, K HH (h,u) u(t) Display 2 x(t) p,q,r u,v,w X X Control Error Control FlightHeight X Control FlightHeight Oega FM Helicopter Aerodinaik Model (MR -TR -HS-VF-F-E) FM 6DoF X phi,theta,psi x_e,y_e,z_e Flight Altitude e e e e e e e-6 Oega Arrius 2T1 Turboeca Display 4 FM Display 1 Total F &M e e e Display Display 3 Figure 12 lock diagra of nonlinear flight dynaics of prototyped helicopter ISSN: Issue 12, Volue 6, Deceber 211

14 Erkan Abdulhaitbilal, Elbrous M. Jafarov Figure 13 Tie responses of nonlinear odel for a tri condition (h = ft, u = 3/s): AFCS is off. Figure 14 Rejection of vertical wind (h = ft, u = 3/s): AFCS is on. ISSN: Issue 12, Volue 6, Deceber 211

15 Erkan Abdulhaitbilal, Elbrous M. Jafarov Figure 15 Rejection of side wind (h = ft, u = 3/s): AFCS is on. Figure 16 Forward speed correction anoeuvre (h = ft, u = 3/s): AFCS is on. ISSN: Issue 12, Volue 6, Deceber 211

16 Erkan Abdulhaitbilal, Elbrous M. Jafarov Figure 17 Rejection of vertical and side wind (h = ft, u = 3/s): AFCS is on, speed hold is on, height hold is on, and heading hold is on. Erkan Abdulhaitbilal was born in alchik, ulgaria in He received.sc., M.Sc., and Ph.D. degrees in Aeronautics and Astronautics Engineering fro Istanbul Technical University (ITU), Turkey, in 22, 25, and 21, respectively. He worked as a research engineer in stability and control group of Rotorcraft Research and Excellence Center of ITU under Project DPT-HAGU fro 23 to 29. He is now with Altinay Robot Technologies and works as a research engineer in electrical car departent, 211. Dr. Abdulhaitbilal is the author of ore than 2 international conference papers and research reports. His research interests include autoatic control, variable structure control, flight dynaics and control, robot control. Elbrous M. Jafarov was born in province Gokche (west Azerbaijan) in He received his M.Sc. degree in Autoation and Control Engineering fro Azerbaijan State Oil Acadey (aku) in The Ph.D. and D.Sc. (Eng) degrees were received fro NIPINefteKhiAutoat- TsNIIKAutoation (Moscow) and Institute of Cybernetics of Azerbaijan Science Acadey; and Institute of Control Sciences (Moscow)-MIEM-LETI in Control Engineering in 1973 and 1982, respectively. He was the Head of Variable Structure Process Control Laboratory fro 1969 to 1984, the Chairan of the Autoation and Robotic Systes Departent at the Az. TU during He has been a professor in Istanbul Technical University since His research and teaching interests include control theory, sliding ode control, tie-delay systes, robot control, robust control, optial control. ISSN: Issue 12, Volue 6, Deceber 211