Capabilities and limitations of multirate control schemes

✍ Scribed by Kevin L. Moore; S.P. Bhattacharyya; Mohammed Dahleh

• Publisher: Elsevier Science
• Year: 1993
• Tongue: English
• Weight: 799 KB
• Volume: 29
• Category: Article
• ISSN: 0005-1098
• DOI: 10.1016/0005-1098(93)90098-e

✦ Synopsis

Multirate sampling techniques can be used to provide arbitrary pole and zero assignment with respect to the output sample times in digital control systems. However, these techniques lead to a degradation in the intersample behavior of the system.

Key Wor~--Digital control; zeros; transfer functions; sampled-data systems, multirate control.

AbarKt--A fundamental obstacle in control system design is the presence of plant zeros. Recently it has been suggested that in digital control systems such problems may be overcome by using multirate sampling. In this paper we describe the capabilities of such multirate control schemes with regard to pole and zero assignment. We also point out a limitation of the approach due to degradation in the intersample behavior. In Mita and Chida (1988, Proc. 27th Conf. on Dec. and Control, pp. 1883-1888) it is shown that with a two-delay input control scheme it is possible to assign all the poles and zeros of the closed-loop system using state feedback. In this paper we generalize this result to the case of N-delay input control using dynamic compensators. In an N-delay input control scheme the input to the continuous system is changed N times more often than the output is sampled. Using such a scheme we show how to design output feedback controllers for SISO systems that ensure arbitrary placement of all the poles and zeros of the closed-loop system. Corresponding results for the MIMO regulator and the SISO servomechanism are given. We also show that a hidden cost associated with the use of N-delay input control is a degradation in the intersample behavior. We demonstrate this via simulation and present an analysis which explains why this degradation arises.