APPLICATION OF POPOV CONTROLLER SYNTHESIS TO BENCHMARK PROBLEMS WITH REAL PARAMETER UNCERTAINTY

A new approach to robust control design with real parameter uncertainty has been developed using the analysis criteria from absolute stability theory. Both time and frequency domain stability conditions have been investigated, and the results demonstrate that the analysis tests include information about both the phase and structure of the unknown parameters. This paper uses these analysis results to investigate the synthesis of robust controllers. The control design algorithm uses state space optimization techniques to minimize an overbound of the H-2 permormance objective that is developed using the Popov stability criterion. In this technique, the optimal compensator and multiplier coefficients are designed simultaneously, which avoids the D-K iteration of mu synthesis. The procedure is applied to the two and four mass benchmark problems. These examples illustrate that good guaranteed robust performance can be achieved using this Popov controller synthesis (or combined H-2/mixed mu) algorithm.