On mixed H2=H∞ controller design for systems with time delay
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This study discusses mixed H2=H∞ controller design problem for uncertain Linear Time-Invariant (LTI) systems with a time delay. More precisely, the goal is to find an internally stabilizing controller that minimizes the H2 performance measure subject to robust stability condition which bounds the H∞ norm of the weighted closed loop transfer function. Two different methods are used to find the optimal H2 controller. The first method is inspired from the H∞ control design to reduce the two block problem into one block. Second method, however is the implementation of the Mirkin's formula. These methods are compared and their pros and cons are discussed. The key point in the optimal controller is that, it is in Smith predictor form that includes an internal feedback in the form of an Finite Impulse Response (FIR) filter. These types of controllers are easy to implement and programmed in physical systems. A case study is considered to show the exact way to controller design. The simulation results and the effects of delay term on the performance measure are also provided.