ZG controllers handling VIP system with nonzero link mass, large friction coefficient and different initial pendulum angle

The vehicular inverted pendulum (VIP) system is one of the most important issues in dynamics and control theory, and has been widely used as a benchmark for testing control algorithms. However, the tracking control and swing-up control of the VIP system have often been investigated separately. In this paper, by combining the Zhang dynamics (ZD) method and the traditional gradient dynamics (GD) method, two Zhang-gradient (ZG) controllers of z2g0 type and z2g1 type are constructed. Note that z2g1 controller can conquer the singularity problem encountered by z2g0 controller and other conventional controllers, thus achieving the tracking control and swing-up control of VIP system simultaneously. The numerical-experimental results substantiate the feasibility and effectiveness of z2g0 and z2g1 controllers for tracking control of the VIP system. Particularly, numerical-experimental results illustrate that the z2g1 controller can achieve tracking control and swing-up control simultaneously with suitable control input. Thus, the z2g1 controller is more suitable for handling the VIP system with nonzero link mass.