Robust controller design for a non‐colocated spring‐mass system via mixed 𝓁/∞ optimization

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Abstract
A successful controller design paradigm must take into account both model uncertainty and performance specifications. Model uncertainty can be addressed using the ℋ︁∞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. We recently proposed design procedures to explicitly incorporate time‐domain specifications into the ℋ︁∞framework. In this paper we apply these design procedures to the simple mass‐spring system used as a benchmark in the 1990–1992 ACC, with the goal of minimizing the peak control effort while satisfying disturbance rejection, settling time, tracking and robustness specifications. The results show that there exist a severe trade‐off between peak control action and robustness to unstructured model uncertainty.

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