Cart Velocity Tracking of General IPC Model Using ZG Control Compared with Cart Path Tracking

As a typical model, the inverted pendulum on a cart (IPC) has nonlinear, unstable and non-minimum-phase characteristics and is investigated widely for tracking control problem solving. In this paper, we investigate a more general IPC model, in which the link of the pendulum has nonzero mass. Due to device velocity constrained, it is important and meaningful to investigate and analyze the velocity tracking control. To achieve velocity tracking control purposes, the presented ZG controllers consist of controllers of z1g0 and z1g1 types, named by the numbers of times of using Zhang dynamics (ZD) and gradient dynamics (GD) methods. Computer simulations and numerical experiments substantiate the feasibility and effectiveness of the ZG controllers for the velocity tracking control of the general IPC model. Furthermore, the superiority [in conquering the singularity problem (i.e., Division-by-zero problem)] of z1g1 controller for velocity tracking control of the general IPC model is well substantiated via comparative simulation and numerical experiment results. At last, the ZG controllers for cart velocity tracking are compared with those for cart path tracking.