FINAL PROJECT

Short Period Oscillation Control of an Unmanned Aerial Vehicle

DIGITAL FEEDBACK CONTROL SYSTEMSAER E 576

ADRIN ISSAI ARASU LShort Period Oscillation Control of an Unmanned Aerial Vehicle

INTRODUCTION

Unmanned Aerial Vehicles (UAVs) have contributed significantly in many areas like combat, reconnaissance, and civil and commercial applications. Though UAVs have wide range of applications, its poor reliability and control, reduced autonomy and operator workload requirements of current unmanned vehicles present a roadblock to their success. Main objective of this project is to minimize the maximum amplitude in short period oscillation and settling time of the system. Furthermore, effects of controller on short period oscillations control are analyzed.Short period oscillations are heavily damped oscillations that last for a period of few seconds. The motion is a rapid pitching of the aircraft about the center of gravity. The oscillation is essentially an angle of attack variation with speed and altitude of the aircraft being constant. A disturbed flight consists of short period oscillations, and long period oscillations called Phugoid mode. It is a difficult task to resolve and isolate the short period mode, which is of importance in this project. Short period oscillation transfer function is derived from longitudinal equations of motion with some approximations to simplify the problem and to eliminate the Phugoid mode.

NOMENCLATURE

M - Mach numberm - mass of the aircraft = 11611.965 KgU - Velocity of the aircraft along X-axis = 182.62 m/sIy - Moment of Inertia = 3.5x106 Kg/m2- Angle of attacke- Elevator deflectionc- Chord of the airfoil = 6.1 mS- 200 m2Q- Dynamic Pressure (Altitude = 55,000 ft) = 1000 kg/msCxu - variation of drag and thrust with u = -2CD = -0.088Cx - variation of drag and lift along X-axis = 0.392Cz - variation of drag and lift along X-axis = -1.13Cz - Downwash lag on lift of tail = -4.46Czq - effect of pitch rate on lift = -3.94Czu - variation of normal force with u = -1.48Cmq - Damping in pitch = -11.4Cm - Static Longitudinal Stability = -0.619Cm - Downwash lag on moment = -3.27TRANSFER FUNCTIONTransfer functions for this system are derived from longitudinal equations of motion of an aircraft. Longitudinal equations of motion are based on three very important assumptions. Mass of the aircraft is assumed to be constant. Aircraft is considered to be rigid. i.e. Aeroelastic deformations are neglected. Quasisteady flow All derivatives with respect to rate of change of velocities are neglected except for those with respect to downwash velocity w.

The longitudinal equations of motion is given as follows

Substituting the values in the above equation yields

(10.6s+0.088)u(s) 0.392(s)+0.74(s) = 01.48u(s) + (10.61887s+4.46)(s)+0.5434s(s) = 0(0.0546s+0.619)(s)+(2.868s2+0.19)(s) = 0

The characteristic equation of the system is given by

S4+0.4472s3+0.2847s2+0.03s+0.0002365 = 0(s2+0.008s+0.000627)( s2+0.4392s+0.2489) = 0

The equation is of the form (s2+pnps+np2) (s2+snss+ns2) = 0

Therefore, for short period oscillation,n = 0.498898 0.5 rad/s= 0.44016And for Phugoid mode,n = 0.02504 rad/s= 0.0159

SHORT PERIOD APPROXIMATION

As the short period approximation occurs at a constant speed, u=0. So the equation reduces to

The characteristic equation becomess2+0.508s+0.8474 = 0

The block diagram of the system is given below

DISCRETE SYSTEM CHARACTERISTICS

The root locus plot for the open loop system is given by

The bode plot and step response of the system is shown in the fig. above. The settling time for the plant is approximately 20s. The discrete transfer function for the system sampled at T = 1s is given by

0.4565 z2 + 0.1383 z - 0.2875 ---------------------------------- z3 - 1.983 z2 + 1.584 z - 0.6017

Closed loop discrete transfer function is given by

0.1969 z3 0.6084 z2 + 0.2971 z - 0.123 .z4 + (0.1969k-2.983) z3- (3.567-0.6084k) z2 + (0.2971k-2.186) z + (0.123k+0.6017)

The range of k is found using Jurys stability test

Q(1) (-1)n Q(1) Ia0I an

The range of K is

The step response for partially stable gain K = 1.519 is given above. The settling time for the system is approximately 35s. It is higher when compared to the open loop configuration.

PHASE LAG COMPENSATOR

A phase lag compensator is designed for the system. Phase margin is chosen to be 42.75. The transfer function of the controller is given by

The step response of the system with phase lag compensator is not convincing as the oscillation amplitude is lower and the settling time is approximately 25s.

PHASE LEAD COMPENSATOR A phase lead compensator is designed for the system. The transfer function of the controller is given by

The step response of the system with phase lead compensator is not better compared to phase lag compensator. The oscillation amplitude is higher and the settling time is approximately 40s.

CONCLUSION

From the results, it can be concluded that phase lag compensator is better than other controllers considered in this project. It is evident from lower settling time and minimum oscillation amplitude. Some valuable information and data about longitudinal stability control for Global Hawk (UAV) were not available. So, approximate values were chosen which might have had some effects in the results. In future, this project can be extended for accurate analysis of stability control.

REFERENCES Modeling and Control of Unmanned Aerial Vehicles Current Status and Future Directions by George Vachtsevanos, Ben Ludington, Johan Reimann, Georgia Institute of Technology Panos Antsaklis, Notre Dame University Kimon Valavanis, University of South Florida An Intelligent Approach to Coordinated Control of Multiple Unmanned Aerial Vehicles, by Vachtsevanos, G., Tang, L. and Reimann, J. Analysis of Short-period Longitudinal Oscillations of an Aircraft - Interpretation of Flight Tests By S. NEUMARK, Techn.Sc.D., A.F.R.Ae.8.