Synthesis of approximately spatially round control systems

This paper deals with the synthesis of robust multi-variable controllers in the frequency domain. The notion of an approximately spatially round (ASR) system is introduced in this work to re-formulate conventional performance requirements such as disturbance rejection, tracking, sensor noise propagation, and robustness. A number of performance bounds are derived for both general controller structure as well as for PID type controllers. The method of Adaptive Potential Field Method (APFM) is then introduced to utilize these bounds for synthesizing ASR controllers. It is shown that by combining ASR with APFM, both theoretical and numerical advantages can be obtained. Finally, two examples: the Rosenbrock problem and an aircraft control system, have been considered. In both cases, it is shown that the ASR closed loop system exhibits balanced output response as well as the achievement of frequency domain performance specifications.