Backstepping Boundary Control for First-Order Hyperbolic PDEs on Inverted Pendulum Stabilization with Constant Input Delay

Abstract

In this paper, a problem of inverted pendulum stabilization considering constant input delay has been investigated. A state feedback controller using a back-stepping method has been designed, it was recently created for parabolic PDEs, moreover the unstable PDE is characterized by integral transformation and boundary feedback. A time-delay system which is unstable is morphed into a stable system which further converges to zero in a finite period of time. In back-stepping controller it needs all the past input, and using this method the infinite dimensional delayed system can be represented by a cascade ODE-PDE equation, where the boundary of the PDE is defined by the constant delay. These ideas makes the input delay problem more interesting to handle. Moreover, we compare the optimal state feedback based stabilizing controller (LQR) with and without back-stepping approach for stabilization of inverted pendulum on cart, and finally, the results are depicted in a MATLAB environment