DEVELOPMENT OF A DYNAMIC OUTPUT-FEEDBACK REGULATOR FOR STABILIZATION AND TRACKING OF NON-SQUARE MULTI-INPUT MULTI-OUTPUT SYSTEMS
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ABSTRACT
This research work is aimed at the development of an observer-based dynamic output feedback controller for stabilization and tracking of nonlinear systems. The developed controller is designed after the immersion-invariance and internal model principle (IMP) frameworks and targets non-square systems such as rotational-translational actuator (RTAC), cart-driven inverted pendulum (CIP) and quadrotor unmanned aerial vehicle (UAV). However non-square multiple-input multiple-output (MIMO) systems such as the UAV represented the principal system of choice for their structural properties. Non-square MIMO systems are systems that have more inputs than outputs (over-actuated) or vice-versa (under-actuated) and reflect the structures of many real world systems. The developed immersion invariance error feedback control law(IIEFCL) is used to solve stabilization and robust tracking problems of non-square MIMO non-linear systems. The output feedback internal model based observer is developed and tested with the RTAC, CIP and UAV while the immersion invariance stabilizing controller is developed and tested on the RTAC system. The output feedback controller showed good stability response on the selected models while the immersion invariance method displayed a good transient phase stability and tracking results with the addition of a robust state feedback feature to the underlying controller. The obtained settling times for the output feedback stabilization results were 2.7s, 1.113s and 0.6435s respectively for the three systems. The immersion-invariance control law acting as a robustifier to another controller produced zero percent overshoot and tracking error. The results showed attainment of desired stability and tracking and also quick convergence, disturbance rejection and handling of transient oscillations such as finite time escape or transient instability phenomena, from which many nonlinear systems do not recover after they occur. The IIEFCL was developed for the Quadrotor UAV and the results obtained were compared with some other standard nonlinear controllers that have been used in QUAV control. The metric for comparison was the integral of the squared control input (ISCI) signal. Results obtained compared favourably with existing nonlinear control laws. The IIEFCL showed the most improvement of 92.92% improvement over the backstepping control law, it had a 72.92% improvement over the feedback linearization control law and the least improvement was with respect to the sliding mode control law where only 66.225% improvement was recorded. Simulations were made using Matlab/Simulink and embedded C++ tools.
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