Transient response control via characteristic ratio assignment

Fixed, low-order controller design with time response specifications using non-convex optimization

“…Theorem 1 ( [9]). Consider two all pole transfer functions of the same degree T K 1 and T K 2 (s), of which the generalized time constants are τ 1 and τ 2 , respectively.…”

“…First we need to generate a reference transfer function that meets the given time response specifications. A possible method based on the K-polynomial [9] is presented in Appendix A. Once we have a reference transfer function, condition (i) in the problem statement can be formulated as the problem of minimizing the squared error function.…”

“…As a result, an objective function is defined. In Appendix A, we will give a brief summary of how one can generate a target transfer function satisfying the given time response by using the K-polynomial [9]. However, the LSE solution above can not guarantee closed-loop stability because it does not give an exactly matched characteristic polynomial due to the order of the controller less than l − 1 (where l is the order of the plant).…”

A new approach for transient response control via characteristic ratio assignment method

“…However, because of the fixed CR set, CDM does not allow many degrees of freedom for adjusting the controller. In the Characteristic Ratio Assignment(CRA) method [1], to control the system overshoot, the use of Butterworth polynomial is proposed because it is the maximally flat function, i.e., the frequency response has as many flat characteristics at a low frequency range as possible. This choice is a compromise with the result given by Chestnut [13], who concluded that a lower (or no) resonant peak and a more gradual attenuation slope in the high frequency region are necessary to achieve a smaller or no overshoot.…”

“…In this section, we propose a polynomial that can be employed to control the system overshoot with an effect comparable to that shown in [1].…”