On the design of robust servomechanisms for minimum phase nonlinear systems

Abstract

We consider a single‐input single‐output nonlinear system which has a well‐defined normal form with asymptotically stable zero dynamics. We study the design of a robust output feedback controller that incorporates a linear servo compensator to achieve asymptotic tracking and disturbance rejection. We determine the least amount of precise information about the plant that is needed to design the controller. Such design will be robust to plant parameters and uncertainties which are not used in the design calculations. We also study robustness of the design to errors in determining the linear servo compensator. Such errors could arise from approximating a general continuous nonlinear function by a polynomial one, or from errors in determining the frequencies of the exogenous signals. We give regional as well as semiglobal results. Copyright © 2000 John Wiley & Sons, Ltd.

Time- vs. Frequency-domain Identification of Parametric Radiation Force Models for Marine Structures at Zero Speed

“…One of the fundamental properties of passive systems is that the negative feedback interconnection of passive systems is passive; and thus, stable under observability conditions (Khalil, 2000). Figure 1 shows a block diagram representation of the Cummins Equation in the frequency domain in terms of the parametric modelK(s) and the transfer function matrix G ′ (s) given in (36).…”

“…The above it is an informal account of the concept, the reader should refer, for example, to Khalil (2000) for a formal discussion. Damaren (2000) was the first to discuss the passivity of the radiation force components due to memory effects.…”

Nonlinear Discrete-Time Robust Output Regulation Problem

“…Here both the class of reference inputs and the class of the disturbances are generated by autonomous differential equations. For continuous-time systems, the problem has been extensively studied since 1970s for linear systems ( Davison (1976), Francis and Wonham (1976), Francis (1977) et al) and since 1990s for nonlinear systems (Isidori and Byrnes (1990), Huang and Rugh (1990), Huang and Rugh (1992), Huang and Lin (1993a), Huang and Lin (1994a), Khalil (1994), Byrnes et al (1997), Khalil (2000), and Huang (2001), to name just a few). Recently, a new framework for studying the robust output regulation problem was proposed in Huang and Chen (2004).…”

The global output regulation problem: An incremental stability approach

“…Most of the semiglobal results make use of certain types of high-gain controllers or observers, see e.g. (Khalil, 2000). Only a few global results exist and are mostly limited to systems which are linear in the unmeasured variables (Serrani and Isidori, 2000;Ding, 2001).…”