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Transient response control via characteristic ratio assignment

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3 Author(s)
Y. C. Kim ; Sch. of Electr. & Electron. Eng., Chungbuk Nat. Univ., Cheongju, South Korea ; L. H. Keel ; S. P. Bhattacharyya

This note develops an approach to directly control the transient response of linear time-invariant control systems. We begin by considering all-pole transfer functions of order n for which we introduce a set of parameters αi, i=1,...n called the characteristic ratios. We also introduce a generalized time constant τ. We prove that α1 and τ can be used to characterize the system overshoot to a step input and the speed of response, respectively. By independently adjusting α1 and τ in all-pole systems, arbitrarily small or no overshoot as well as arbitrarily fast speed of response can be achieved. These formulas are used to develop a procedure to design feedback controllers with feedforward or two parameter output feedback type for achieving time response specifications. For a minimum phase plant we show that arbitrary transient response specifications, namely one with independently specified overshoot and specified rise time or speed of response can be exactly attained.

Published in:

IEEE Transactions on Automatic Control  (Volume:48 ,  Issue: 12 )