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 l₁ theory. Using the Popov-Tsypkin multiplier, the robust control design is formulated as an l₁ 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.