Sigma‐Delta Modulated Digital Control for Random Lagrange System Driven by DC Motors

ABSTRACT In this paper, the digital control problem of trajectory tracking is investigated for a random Lagrange system. Firstly, for a general random differential equation, it is shown that the “equivalent output” signal of the sigma‐delta modulation can almost match the input signal generated by a continuous feedback controller. Then, considering the random Lagrange system driven by DC motors, a continuous bounded controller is systematically synthesized by the vectorial backstepping technique and random quadratic programming. On this basis, a digital controller is designed via sigma‐delta modulation, which enables the tracking error of the closed‐loop system can be as small as possible by adjusting the parameters. Finally, a simulation experiment of a 3‐link robotic arm is given.