Control of Piston Position in Inviscid Gas by Bilateral Boundary Actuation

We design backstepping control to stabilize a piston moving freely in a cylinder filled with inviscid gas, under the actuation of gas injected at both extremities. The piston problem has been widely studied in engineering processes such as combustion engines, but boundary control of such a system is highly nontrivial. The gas dynamics are modeled by two sets of coupled first-order hyperbolic partial differential equations (PDEs), and each domain is separated by the piston's position, dynamics of which are represented by a second order ordinary differential equation (ODE). The control objective is to stabilize both the gas states (pressure and velocity) and the piston to a given setpoint. We design the state feedback controller based on a delay compensation technique using the backstepping method. With Lyapunov analysis on the moving boundary problem, we show local stability of the system in H¹ norm. The performance of the controller is studied by numerical simulations, which illustrate the efficient stabilization of the piston position and velocity.