Abstract
This paper is concerned with the problem to design a state feedback law which provides the closed-loop system with lower sensitivity property. Gain curves are defined by taking dB-values of singular values of the return difference matrix on imaginary axis in complex plane, and gain band is defined as the band which consists of area between the largest gain curve and the smallest gain curve. It is shown that in order to achieve lower sensitivity property, the smallest gain curve should be at higher position and then the gain band should be nallower. It is well known that the state feedback is obtained by solving the pole assignment problem. There are two kinds of free parameters, i.e., (1) poles to be assigned and (2) directions of eigenvector of the closed-loop system, whose specifications give the unique solution of the problem It is shown that the arithmatic mean of gain curves, which is called mean gain curve, depends upon the first freedom only and therefore the distribution of gain curves around mean gain curve depends upon the second freedom after fixing the first freedom. Based on the facts, the visual method is proposed to adjust the first freedom, observing the effects of poles to the mean gain surface defined by extending mean gain curve in the direction of real axis. Using this method, the mean gain curve should be lifted. After fixing the first freedom, the method is proposed to adjust the second freedom, using quasi-Newton method so that nallower gain band is achieved. As the results, the closed loop system with lower sensitivity property can be obtained.
