Limitations on minimum tracking energy for SISO plants

This paper discusses the fundamental limitations imposed by the intrinsic characteristic of plants. The plant is stable of unstable. The performance is about minimum tracking energy for tacking error asymptotically approaching zero. Using a time-domain integral of the square of the input as a performance index, we derive relations that represent fundamental limits on the achievable performance for single-input single-output systems. The relations depend on the unstable poles and right half plane zeros of the plant under study, and the stable and minimum part of part is also related. When the plant is unstable, the two-free-of-controller is addressed, too. The limitations are significant references for the controller designs. A numerical example shows the design limitation.