This paper presents the position and trajectory tracking control scheme for the ball and plate system (BPS) using the double feedback loop structure (a loop within a loop) for effective control of the system. The inner loop was designed using linear algebraic method by solving a set of Diophantine equations. The outer inner loop was designed using sensitivity approach. Simulation results showed that the plate was stabilized at 0.3546 seconds, and the ball was able to settle at 1.7087 seconds, when given a circular trajectory of radius 0.4 m with an angular frequency of 1.57 rad/sec, with a trajectory tracking error of 0.0095 m, which shows that the controllers have adaptability, strong robustness and control performance for the ball and plate system.
