Minimax design of robust controllers for flexible systems

The design of robust time-delay and saturating controllers based on the range of expected variation of uncertain parameters from their nominal values is investigated. 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. By the adoption of the residual energy as the cost function, the optimization problem formulation is simple because it requires only one equation that is used both as the cost function and constraint. 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 the two-mass-spring benchmark problem.