Fuzzy Impulsive Control of High Order Interpolative Lowpass Sigma Delta Modulators

In this paper, high order interpolative sigma delta modulators (SDMs) in audio applications are considered. For these SDMs, limit cycle and divergent behaviors may be observed, especially when the inputs are overloaded. A novel fuzzy impulsive control strategy is proposed. The control law is to minimize the difference between the uncontrolled trajectory and the control trajectory, suppress the occurrence of limit cycles, and maintain the local stability of the SDMs. Examples of high order lowpass interpolative SDMs are given to illustrate the effectiveness of the proposed control strategy.