In this paper, we propose an LMI-Loop shaping method where simultaneous controller design for multiple specifications is possible. First, we present a design of a reduced-order controller design for an frequency weighted problem. The problem is an extention of the robust stabilization problem which has been used for an
H∞-Loop Shaping method. It can be solved with coprime factorization representation and LMI optimization. Second, we show that the design can be applied to some
H∞ 2 block problems. Since the controller parameters are embedded in the same way and they are common for all LMI's (multiple LMI's can be regarded as a single large LMI), the control design can be done simultaneously for the multiple specifications. Last, we apply the design method to a vibration control system for a boom of truck-mounted concrete pump.
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