H∞ loop shaping design with time domain constraints: application of fuzzy logic

The H_∞ loop shaping design method is an effective way to design robust controllers. One of the main limitations in the design of H_∞ loop shaping controllers is that the design method is based on frequency domain specifications that do not precisely represent the underlying time domain performance requirements. Even if the time response constraints were not present, the approach is based on trial and error selection of the frequency dependent weights that are used in the design. Selection of these functions becomes more difficult if time response constraints must be satisfied. This paper presents a systematic way of selecting the loop parameters for the frequency-dependent weights and develops a fuzzy algorithm that selects these parameters so that the resulting H_∞ loop shaping controller yields a closed loop system that satisfies the time response constraints for a single-input single-output system