Improving Transient Responses with Compensation Law

In the synthesis of tracking control systems, the compensation signal, which is applied in the finite-horizon time, is effective for improving the performance of controlled system. In this paper, a design method of finite-horizon compensation signal and optimal internal state of controller is discussed for stabilized systems. By characterizing the singular-value problem for correspondingly defined Hankel operator, it is shown that the internal state and the compensation signal, which attains favorable transient, is constructively given based on the combination of singular vectors. The strength and the limitation of applying the compensation signal are illustrated with numerical examples.