Abstract
A very important application of feedback is servo-tracking, or the ability of a closed-loop system to track a given class of reference input signals, while rejecting a given class of external disturbances, in the sense that the asymptotic tracking error must be zero, in the presence of plant uncertainty. This problem has been studied extensively in the literature, especially for linear-time-invariant systems. In the asymptotic tracking problem, no particular attention is given to initial tracking errors, though they remain bounded by virtue of closed-loop system stability. The focus of the present study is servo-tracking in the context of the ability to follow a desired output, within a prespecified error bound, over its entire duration; that is, to obtain a closed-loop system which has the ability to track a reference input vector while rejecting a class of external disturbances, to the extent required by the error bound. This type of tracking is referred to as tracking in the sense of spheres. It has been shown in the literature that a solution to this tracking problem may be obtained by a quantitative pole placement (QPP) approach. In particular, a nonlinear observer-based state feedback controller will guarantee the desired tracking performance, provided state feedback gains can be found such that a specific induced norm of a linear closed-loop operator can be made sufficiently small. In this dissertation a systematic procedure is given for solving the QPP problem when the induced norm is the L[infinity] - norm. In particular, a Lure type system is considered with the input and output spheres measured with respect to the L[infinity] - norm, and an algorithm is developed on the basis of minimizing the H[infinity] - norm of a linear and closed-loop operator for solving the QPP problem. Relevant design criteria are derived by first embedding the problem in the L[infinity] - function space, leading to an H[infinity] - minimization problem which is followed by an exponential weighting technique for estimating the tracking error bounds in terms of L[infinity] - norms. The approach to this problem is based on fixed-point techniques and the multivariable circle criterion. The controller gains satisfying the design criteria and the QPP are obtained by solving two Riccati equations.
Hwang, Cheng-Neng (1990). Controller synthesis for input-output tracking in Luŕe type uncertain nonlinear systems. Texas A&M University. Texas A&M University. Libraries. Available electronically from
https : / /hdl .handle .net /1969 .1 /DISSERTATIONS -1118174.