Robust controller design for the benchmark problem using mixed L∞/H∞ optimization

A successful controller design paradigm must take into account both model uncertainty and performance specifications. Model uncertainty can be addresed using the H_∞ robust control framework. However, this framework cannot accommodate the realistic case where in addition to robustness considerations, the system is subject to time domain specifications although some progress has been recently made in this direction [1-2]. We recently proposed a design procedure to explicitly incorporate time-domain specifications into the H_∞ framework [3]. In this paper we apply this design procedure to the simple flexible structure used as a benchmark in the 1990-1992 ACC, with the goal of minimizing the peak control effort due to disturbances while satisfying settling time and robustness specifications. The results show that there exist a severe trade-off between peak control action, settling time and robustness to model uncertainty.