On undershoot in scalar discrete-time systems

We identify a class of asymptotically stable, strictly proper, non-minimum-phase, scalar discrete time systems whose step response is shown to exhibit undershoot a given number of times. The conditions governing this correspondence can be verified by inspection and have a simple expression in terms of the zero/pole locations of the underlying system. Both qualitative and quantitative aspects of the undershooting phenomenon are discussed, and a simple but non-trivial example is used to gain further insight into the main result of this paper.

[1]  Nobuaki Kobayashi,et al.  Design of non-undershooting multivariable servo systems using dynamic compensators , 1986 .

[2]  James R. Leigh.  Applied Digital Control , 1985 .

[3]  M. Dahleh,et al.  Design techniques for transient response control , 1989 .

[4]  Oscar D. Crisalle,et al.  Influence of zero locations on the number of step-response extrema , 1993, Autom..

[5]  Mathukumalli Vidyasagar,et al.  On undershoot and nonminimum phase zeros , 1986 .

[6]  Stephen P. Boyd,et al.  Linear controller design: limits of performance , 1991 .

[7]  Yves Piguet,et al.  On compensation of nonminimum-phase zeros , 1995, Autom..

[8]  S. Bhattacharyya,et al.  A technique for choosing zero locations for minimal overshoot , 1989, Proceedings of the 28th IEEE Conference on Decision and Control,.

[9]  M. Sain,et al.  Qualitative features of discrete-time system responses , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[10]  Mathukumalli Vidyasagar,et al.  Design of non-overshooting feedback control systems , 1990, 29th IEEE Conference on Decision and Control.

[11]  Mathukumalli Vidyasagar,et al.  Control system design via infinite linear programming , 1992 .

[12]  Delabarra Ba,et al.  On Undershoot in SISO Systems , 1994 .

[13]  Manfred Morari,et al.  Digital controllers for SISO systems: a review and a new algorithm , 1985 .

[14]  Rick H. Middleton,et al.  Trade-offs in linear control system design , 1991, Autom..

[15]  Mario El-Khoury.  Influence des zéros d"une fonction de transfert sur le comportement dynamique d"un système linéaire et application au réglage polynomial , 1991 .

[16]  Bernardo A. León de la Barra.  Sufficient conditions for monotonic discrete time step responses , 1994 .

[17]  G. Goodwin,et al.  Open unit disk zeros of scalar stable discrete time transfer functions: Implications for feedback design , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.

[18]  Oscar D. Crisalle,et al.  Discrete Transfer-function Zeros and Step-response Extrema , 1993 .

[19]  I. Eliahu Jury.  The effect of pole and zero locations on the transient response of sampled-data systems , 1955, Transactions of the American Institute of Electrical Engineers, Part II: Applications and Industry.