SAMPLED-DATA BACKSTEPPING CONTROLLER FOR GYROSCOPE WITH CONTROL DESIGN BASED ON APPROXIMATE DISCRETE-TIME MODEL

Abstract

This thesis describes sampled-data control of gyroscope based on approximate discrete-time model. Discrete-time backstepping technique is used to design the control law in discrete-time. The control law is based on state feedback. Four degrees of freedom of the gyroscope constitute the four states which are used in the feedback control law. The approximate discrete-time model of the gyroscope is computed from its continuous-time model using Euler method. To apply backstepping technique, the model is converted to the chained form which is more suitable form for the application of backstepping. The discrete-time controller is designed to stabilize the approximate discrete-time model of the plant using the discrete backstepping technique. Two torques are used as input to control the four degrees of freedom of the gyroscope which is an under actuated system. It is ensured that different degrees of freedom of the gyroscope track their desired trajectories respectively. This thesis explains the detailed derivation of the controller design stage and provides the numerical simulation as well as the experimental results of the controller implementation on the physical system. The performance of the discrete-time controller based on approximate discrete-time model is compared to that of the continuous-time controller based on the continuous-time model of the gyroscope. Different phenomenon like phase portraits and domain of attraction (DOA) are compared for both the continuous-time and sampled data controllers. Finally, the conclusion of the thesis is drawn and some future suggestions related to the thesis work are given which include some improvement techniques that can further enhance the tracking performance for the different degrees of freedom of the gyroscope.