Time-Optimal Control of a Class of Unstable Third-Order Plants

✍ Scribed by M. Malek-Zavarei

• Publisher: Elsevier Science
• Year: 1980
• Tongue: English
• Weight: 530 KB
• Volume: 309
• Category: Article
• ISSN: 0016-0032
• DOI: 10.1016/0016-0032(80)90078-2

✦ Synopsis

A class of unstable relay-controlled plants possessing one pole at the origin and two non-zero distinct real poles is studied. Cases corresponding to one or both non-zero poles in the right half-plane are considered. In each case a controller which simultaneously reduces the error and its first and second derivatives to zero in minimum time is designed. Also the class of admissible inputs is found which, after a minimum transient time, can be followed without any ewor. Through some linear transformations, it is shown that the equations of the switch curve and the switch surface can be made independent of the plant's constant gain and dependent only on the ratio of the non-zero pole values. It is established that in both regulating and tracking modes the ewor and its first and second derivatives can be reduced to zero with at most two switching reversals of the control provided that the initial values of error and/or its derivatives fall in a "controllable region".