Trajectory tracking control for unconstrained objects based on supervisory fuzzy scheme

A steel ball on the hard plate is an unconstrained object. This paper presents visual servo control for a ball on a flat plate to balance set-point or to track its desired trajectory. Firstly, the dynamic model of the ball and plate system was established by Lagrangian equation. After that a supervisory fuzzy scheme was proposed. It was composed of two layers. The low layer defined a SIRM fuzzy rule and an importance degree for each input item, which had direct control function. The high layer performed supervisory task for ball's velocity and acceleration. When the ball was close to halt, or at high velocity, the supervisory fuzzy controller could overcome disturbance that was subject to environment change as static friction etc. We applied this controller to ball and plate system setup named BPVS-JLU I developed in author's laboratory. The experiment results show that the proposed algorithm had good static and dynamic performance. The steady-state tracking error is less, and transitory process time is short than conventional fuzzy controller. Therefore, the control scheme is proposed feasible. The acquired conclusion can be used to investigate similar nonlinear under-actuated dynamics system.