Quantitative analysis

Abstract

As shown in the previous chapters, several different control schemes for integral processes with dead time resulted in the same disturbance response. Moreover, it has already been shown that such a response is sub-ideal [73, 160]. In this chapter, the achievable specifications of this disturbance response and the robust stability regions of the system are quantitatively analysed. The control parameter is quantitatively determined with compromise between the disturbance response and the robustness. Four specifications—(normalised) maximal dynamic error, maximal decay rate, (normalised) control action bound, and approximate recovery time— are given to characterise the step-disturbance response. It shows that any attempt to obtain a (normalised) dynamic error less than Lm is impossible, and a sufficient condition on the (relative) gain-uncertainty bound is √3/2.