A multi-system optimization approach to coupling in robust design and control.

Abstract

The design and control of an engineering system often present themselves as two coupled problems. Based on evaluations of the coupling strength between design and control, the integrated design and control system optimization problem can be simplified by solving separate design and control optimization problems. Previous work on coupling definitions have relied on mathematical models that do not incorporate uncertainty. Ignoring uncertainty precludes an explicit study of the relationship between system robustness and the coupling measure. In addition, previous investigations on coupling have been limited to links between two nominal systems (i.e., systems with no uncertainty) rather than multiple nominal systems. To study the impact of uncertainty, a general approach that combines robust design with robust control and investigates the coupling between them is presented. Sequential and iterative solution strategies are proposed and compared to an all-in-one strategy for solving the combined robust design and robust control problem, using a DC motor as an illustrative example. An investigation of the coupling between nominal design and robust control is then presented. An explicit measure of coupling between the design and robust control optimization problems is introduced using concepts from nonsmooth optimization theory. Varying system parameters then leads to establishing a relationship between coupling and robustness that can be utilized to aid the designer in assessing the parameters' influence on coupling and robustness. These ideas are then applied to study the effect of level of uncertainty, unsprung mass, and tire stiffness parameters on coupling between design and robust control of a vehicle suspension system. We show that the coupling between design and robust control tends to increase as the applied level of uncertainty increases. In addition, demanding more robustness for a vehicle suspension with harsh ride characteristics increases coupling compared to suspensions with soft ride characteristics. By assuming nominal systems, these coupling concepts are then extended to more than two nominal systems and integrated with decomposition-based optimization strategies. An explicit measure of coupling strength among interconnected subproblems in a decomposed optimization problem is introduced, along with a systematic way for calculating it. The strength measure is then used to suspend weak couplings and, thus, improve decomposition-based optimization strategies, such as the model coordination method. These original contributions show that achieving highly robust optimal systems requires combined robust design and control strategies.