Abstract
It has been known that the high-gain feedback is very effective to reduce the parameter sencitivity, the effect of disturbances and so on. But the analyses of high-gain feedback systems are numerically stiff because of different magnitudes of their coefficients. In this study we remove this stiffness with singular perturbation method.
We consider regulators with high-gain feedback. In general it is not clear that we can get a highly accurate regulator when a scalar gain tends to infinity. Moreover the systems are sometimes unstable and even if the systems are stable, the responses often have remarkable peeks. Thus it is important to decide a class of systems such that a high-gain feedback is permitted.
First we show the conditions of gain matrices under which the regulator is stable and has arbitrary accuracy. Next we get a class of systems for which we can design the highly accurate regulator. Such systems are following:
i) A dimension of input is greater than or equals to that of output.
ii) They have minimum phase.
iii) CB has full rank.
In addition authors present the procedure to design a highly accurate regulator by showing the algorithm for HRP (High-gain Regulator Problem) and demonstrate it for a example.
