Regional Pole Placement Design Based Stabilization for Cart Inverted Pendulum System

Abstract

The inverted pendulum has been considered as a benchmark control problem due to its nonlinearity and stabilization around the unstable equilibrium point. To achieve stabilization, it is well known that all the closed loop system poles should lie in left half of s-plane. In present work, different approaches have taken to shift the system poles to left half of the plane. At first Linear Quadratic Regulator (LQR) is used, where the desired pole locations can be achieved by suitably selecting weight matrix of cost function. With this guaranteed cost control scheme, one does not have to bother about specifying closed-loop poles. Next, a two loop PID is designed based on pole matching conditions. Where the closed loop with unknown controller coefficient characteristic equation is compared with desired characteristics, to find out the controller gains. In both the methods, one has to deal with point wise pole placing, which can be tricky sometimes. With the recent development of LMIs tool, regional pole placement is well suited to achieve the goal. At last, a regional pole placement controller is synthesized, where desired specifications are transformed into LMI regions. In present case, a conical sector of left half plane is taken so that stabilisation with better transient performance can be achieved