Design for Feedback Systems With Plant Input Amplitude and Rate Saturation

In this paper, a method of compensation for feedback systems subject to simultaneous plant input amplitude and rate saturation is presented. It applies to uncertain, stable plants of a type greater than or equal to 1. Founded on Horowitz’s original idea for amplitude saturation compensation (Horowitz, I., 1983, Int. J. Control, 38(1), pp. 169–197) and extensions developed in (Wu, W., and Jayasuriya, S., 1999, Proceedings of American Control Conference, San Diego, CA, pp. 3046–3050; Wu, W., and Jayasuriya, S., 2001, ASME J. Dyn. Syst., Meas., Control, 123(2), pp. 225–232; Wu, W., 2000, Ph.D. dissertation, Texas A&M University), a synthesis method that explicitly takes into account input amplitude and rate saturation is further developed. In the case of simultaneous amplitude and rate saturation, approaches developed separately for amplitude alone, and rate alone saturation (Wu, W., 2000, Ph.D. dissertation, Texas A&M University), respectively, are integrated into one method, and results in a 4DOF(degrees of freedom) feedback system with two extra compensators to deal with two saturation nonlinearities. Design constraints for saturation compensation are developed and expressed as frequency domain bounds. Synthesis of the two additional compensators follows from loop shaping methods, such as QFT. This approach guarantees input/output stability for the class of plants considered. Examples are given to illustrate the application of this approach.

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Design of Feedback Systems With Plant Input Rate Saturation via QFT Approach

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.2232693 ◽

2005 ◽

Vol 128 (3) ◽

pp. 701-705 ◽

Cited By ~ 1

Author(s):

Wei Wu ◽

Suhada Jayasuriya

Keyword(s):

Input Rate ◽

Response Behavior ◽

Feedback Systems ◽

Describing Function ◽

Robust Performance ◽

Original Design ◽

Design Constraints ◽

Input Amplitude ◽

Output Stability ◽

Synthesis Approach

In this paper, a synthesis approach for input rate saturation compensation of feedback systems is presented. Uncertain, stable plants of type greater than or equal to 1 are considered. Based on Horowitz’s original design for input amplitude saturation (Horowitz, I., 1983) and extensions developed in (Wu, W., and Jayasuriya, S., 1999; Wu, W., and Jayasuriya, S., 2001; Wu, W., 2000) an independent loop around the rate saturating element is introduced for saturation compensation by means of the third DOF (degree of freedom) saturation compensator, H(s). First, the structure of the additional loop transmission is constructed to generate the desired response behavior on a systems recovery from saturation. Second, robust stability and robust performance under the addition of H(s) are investigated. The circle criterion, describing function, and nonovershooting conditions are utilized to generate design constraints. In the end, all design constraints involving saturation compensation are expressed as frequency domain bounds, and the synthesis of saturation compensator H(s) follows from loop shaping methods such as QFT. The proposed approach guarantees input/output stability under saturation for the plant class considered.

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