Robust l1 design of a multivariable PI controller using a real-coded genetic algorithm

This paper considers the use of a real-coded genetic algorithm (RCGA) in the design of a robust PI controller under the framework of multiplier theory (essentially mixed structured singular value theory (MSSV)) and l(1) theory. Using the Popov-Tsypkin multiplier, the robust control design is formulated as an l(1) optimization problem. The solution to this problem is described using an RCGA to obtain the optimal proportional and integral gains. This approach is illustrated in the design of a robust PI controller for a linear model of a jet engine. The controller is shown to exhibit good tracking performance and disturbance rejection in the presence of model uncertainty.