Abstract
Nonlinear rational systems/models, also known as total nonlinear dynamic systems/models, in an expression of a ratio of two polynomials, have roots in describing general engineering plants and chemical reaction processes. The major challenge issue in the control of such a system is the control input embedded in its denominator polynomials. With extensive searching, it could not find any systematic approach in designing this class of control systems directly from its model structure. This study expands the U-model-based approach to establish a platform for the first layer of feedback control and the second layer of adaptive control of the nonlinear rational systems, which, in principle, separates control system design (without involving a plant model) and controller output determination (with solving inversion of the plant U-model). This procedure makes it possible to achieve closed-loop control of nonlinear systems with linear performance (transient response and steady-state accuracy). For the conditions using the approach, this study presents the associated stability and convergence analyses. Simulation studies are performed to show off the characteristics of the developed procedure in numerical tests and to give the general guidelines for applications.
Highlights
This section justifies the reasons for designing controllers for rational models by introducing model expression and representations, achieved results in model identification, and a critical review of controller-designing approaches.1.1
The major properties of the rational model (1) are summarised below: It is defined as a total nonlinear model [2] as it covers many different linear and nonlinear models as its subsets (such as NARMAX models [3] and intelligent models for neurofuzzy systems [4])
Rational systems have been observed in general engineering, chemical processes, physics, biological reactions, and econometrics; for example, rational models are a class of mechanistic models in describing catalytic reactions in chemical kinetics [5, 6]; metabolic, signal, and genetic networks in systems biology [1]; and movement of satellites in Earth orbit [1]
Summary
The studied nonlinear rational model has no such explicit expression for input u to be designed, and this immediately reveals that the methodologies rooted in the approach, useful references, are not directly applicable in designing control of nonlinear rational systems. The U-model systematically converts smooth (polynomial and extended including transcendental functions) models, derived from principles or identified from measurements, into a type of U-based model to equivalently describe plant input-output relationship, so that it establishes a general platform to facilitate control system design and dynamic inversion. It is expanded by including a rational model and transcendental functions as its subsets to lay a basis for applying linear control system design techniques.
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