An adaptive control scheme for hyperbolic partial differential equation system (drilling system) with unknown coefficient
Divisions of PAS
<jats:title>Abstract</jats:title> <jats:p> The adaptive boundary stabilization is investigated for a class of systems described by second-order hyperbolic PDEs with unknown coefficient. The proposed control scheme only utilizes measurement on top boundary and assume anti-damping dynamics on the opposite boundary which is the main feature of our work. To cope with the lack of full state measurements, we introduce Riemann variables which allow us reformulate the second-order in time hyperbolic PDE as a system with linear input-delay dynamics. Then, the infinite-dimensional time-delay tools are employed to design the controller. Simulation results which applied on mathematical model of drilling system are given to demonstrate the effectiveness of the proposed control approach.</jats:p>
CORON (2007), D ANDREA NOVEL and A strict Lyapunov function for boundary control of hyperbolic systems of conservation laws on Automatic Control, IEEE Trans, 52, 2. ; BRESCH (2010), Delay - adaptive predictor feedback for systems with unknown long actuator delay on Automatic Control, IEEE Trans, 55, 2106. ; KOBAYASHI (2001), Stabilization of infinite - dimensional second - order systems by adaptive PI controllers Mathematical Methods in the Applied, Sciences, 24, 513. ; PIETRI (2014), Output - feedback adaptive control of wave PDE with boundary anti - damping, Automatica, 50, 1407, doi.org/10.1016/j.automatica.2014.02.040 ; ZHI ZHANG (2010), and Sliding mode control of rotary drilling system with stick slip oscillation Workshop on Intelligent Systems and Applications China, Int, 1. ; BRESCH (2009), Adaptive trajectory tracking despite unknown input delay and plant parameters, Automatica, 45, 2074, doi.org/10.1016/j.automatica.2009.04.027 ; CASTILLO (2012), Dynamic boundary stabilization of hyperbolic systems st IEEE Conf on Decision and Control Maui USA, Proc, 51. ; SHIRINABADI (2011), Lyapunov stability analysis of special class of PDE systemsControl nd Int on Instrumentation and Automation, Conf, 648.