Optimal design of robust quantitative feedback controllers using random optimization techniques

Quantitative design of robust control systems proposes a transparent and practical controller design methodology for uncertain single-input single-output and multivariable plants. There are several steps involved in the design of such controllers. The main steps involved in the design are template generation, loop shaping and pre-filter design. In the case of multivariable uncertain plants, manipulation of tolerance bounds within the available freedom, for both sequential and non-sequential designs, consideration of template size of next step in sequential design, and the appropriate selection of the nominal transfer function matrices in the equivalent disturbance attenuation design are also crucial steps. In all the quantitative designs, a time-consuming trial-and-error procedure is adapted and a successful compromise between various design requirements is very much dependent on the designer experience and expertise. In this paper, these steps are reformulated in terms of different cost functions, and it is shown that the optimization of these cost functions leads to an optimal design of quantitative controllers, for both single input single output and multivariable plants. This proposes a nonlinear constrained optimization problem that can be easily solved using any of the random optimization techniques. Simulation results are used to show the effectiveness of the proposed method.