Minimax design of robust controllers for flexible systems

The focus of this paper is on the design of robust controllers based on the range of expected variation of uncertain parameters from their nominal values. A minimax optimization problem is formulated with the objective of minimizing the maximum value of the cost function over the range of the uncertain parameter. To expedite the optimization process, equations are derived for the gradient of the cost and constraint functions with respect to the parameters of the controller. The proposed technique is illustrated on two examples. The first is a spring-mass-dashpot and the second is a two-mass-spring benchmark problem.