Output-Feedback Control of an Extended Class of Sandwiched Hyperbolic PDE-ODE Systems
Ji Wang, Miroslav Krstić
Abstract
Motivated by an engineering application in brake control of cable mining elevators, where the dynamics consist of a brake, a shock absorber, a time-varying-length cable, and a cage, we address a theoretical problem of control of a particular class of coupled hyperbolic PDEs sandwiched between a nonlinear ODE on the actuated side and a linear ODE on the opposite side, with a PDE domain that is time-varying. A state-feedback controller entering a single ODE state is designed to exponentially stabilize the overall system through several backstepping transformations. An observer which only uses the boundary values at the actuated side is constructed to recover all the states of the overall system, based on which a “collocated” type output-feedback control system is proposed. The global exponential stability of the closed-loop system, boundedness, and exponential convergence of the controller, are proved via Lyapunov analysis. The performance is investigated via numerical simulation.