Simple Robust Normalized PI Control for Controlled Objects with One-order Modelling Error

TL;DR: A large mission on safety and a small mission on analytic solutions are introduced after indicating the some problems in discussing robust PI control systems and the countermeasure for safeness of that is introduced.

Abstract: In this section, the small gain theorem is introduced as a background theory of this chapter. Then, a large mission on safety and a small mission on analytic solutions are introduced after indicating the some problems in discussing robust PI control systems. Moreover, the way how it came to be possible to obtain the analytic solution of PI control adjustment for the concrete robust control problems with uncertain modeling error which is impossible using the space theory for MIMO systems, is shown for a SISO system. The worst lines of closed loop gain margin were shown in a parameter plane. Finally, risk, merit and demerit of the robust control is discussed and the countermeasure for safeness of that is introduced. And some theme, eg., in the lag time system, the MIMO system and a class of non-linear system for expansion of the approach of this chapter is introduced. Many researchers have studied on many kinds of robust system recently. The basic robust stability concept is based on the small gain theorem (Zbou K. with Doyle F. C. and Glover K., 1996). The theorem insists that a closed loop system is internal (robust) stable sufficiently and necessary if the H∞ norm of the nominal closed loop transfer function is smaller than the inverse of H∞ norm of the any uncertainty of feedback elements. (Fig. 1) Moreover, the expansion of the theorem claims that a closed loop system is stable sufficiently if the product of H∞ norms of open loop transfer functions is smaller than 1 when the forward and the feedback transfer functions are both stable.