ZG Controllers of Z2g0 and Z2g1 Types for Tracking Control of IPC Mathematical Model

Abstract Recently, the Zhang dynamics (ZD) and the gradient dynamics (GD) have been used for solving online problems, but they are usually investigated separately. In this paper, we firstly illustrate the ZD method and the GD method by employing them separately to solve the time-varying matrix inversion problem. Then, to solve the tracking-control problem of the mathematical model of the inverted pendulum on a cart (IPC) system, the ZD-based (i.e., z2g0) controller and the ZD-GD combined (i.e., z2g1) controller are designed. These two types of controllers with greatly simplified design procedure can achieve good performance in terms of tiny tracking error and quick response. The simulation results further substantiate the feasibility and superiority of the z2g0 controller and the smoother z2g1 controller for the output tracking of the mathematical model of the IPC system.