Transient response control via characteristic ratio assignment

This paper develops an approach to directly control the transient response of linear time-invariant systems. We begin by considering all pole transfer functions of order n for which a set of parameters α_i, i=1, .... n are introduced, called the characteristic ratios, with α₁=: α being the principal characteristic ratio. We also introduce a generalized time constant τ for such systems. We prove that the principal characteristic ratio and generalized time constant, namely the two parameters α and τ can be used to independently characterize or control the system overshoot to a step input and the speed of response, respectively. These formulas are used to develop a procedure to design a state feedback plus feedforward controller for a minimum phase plant that provides "good" transient response, namely one with specified overshoot and specified rise time or speed of response.