An adaptive control scheme for hyperbolic partial differential equation system (drilling system) with unknown coefficient

• Main Authors: Farahani Hamed Shirinabadi, Talebi Heidar Ali, Baghermenhaj Mohammad
• Format: Article
• Language: English
• Published: Polish Academy of Sciences 2017-03-01
• Series: Archives of Control Sciences
• Subjects: drilling systems; adaptive control; hyperbolic partial differential equation; wave equation; boundary control
• Online Access: http://www.degruyter.com/view/j/acsc.2017.27.issue-1/acsc-2017-0004/acsc-2017-0004.xml?format=INT

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.