Abstract
To setup a universal proper user toolbox from previous individual research publications, this study generalises the algorithms for the U-model dynamic inversion based on the realisation of U-model from polynomial and state-space described continuous-time (CT) systems and presents the corresponding U-control system design in a systematic procedure. Then, it selects four CT dynamic plants plus a wind energy conversion system for simulation case studies in Matlab/Simulink to test/demonstrate the proposed U-model-based design procedure and dynamic inversion algorithms. This work can be treated as a U-control system design user manual in some sense.
Highlights
Linear control system design approaches can be divided into state-space model-based [1] and polynomial model-based, which have been well studied and are widely used
Compared with the linear polynomial model, nonlinear polynomial models, such as the Nonlinear Autoregressive Moving Average with eXogenous inputs (NARMAX) [2] model, have been used widely in applications and academic research publications [3]; there is no systematic routine to convert it into an equivalent statespace model
There are three methodologies for the nonlinear plant-model-based control system design, two widely used and one less-attended. e first approach is using linear expressions to describe the nonlinear state-space models by feedback linearization approach [4, 5] and designing this linear-expression corresponding control systems by linear state-space approaches, which has been well studied in [1]. This case-by-case method requires certain skills in selecting the appropriate coordinate system and solving the equations requires extraeffort. This state-space linearization approach cannot be directly applied for nonlinear polynomial models. e second method is to use a time-varying linear model to fit the polynomial model, for example, state-dependent parameter (SDP) transformation [6, 7] method can use specified poles to transform a nonlinear closed-loop control system model to a linear transfer function expression
Summary
Linear control system design approaches can be divided into state-space model-based [1] and polynomial model-based, which have been well studied and are widely used. E nonlinear polynomial model can be converted into a time-varying linear state-space model by the second method; there are obstacles for using this method because this design and transform procedure is not unique, that is, personal and subjective for selection of SDP models. E U-model-based design method can be recognised as converting nonlinear models to time-varying parameter models associated with controller output u, that is, linear control-oriented model structure [10,11,12,13]. (1) Generalise dynamic inversion algorithms for continuous-time U-model (2) Generalise U-model-based design procedure for continuous-time dynamic plants in forms of linear/ nonlinear and polynomial/state space (3) Showcases for bench tests and illustration of applications (4) An industrial backgrounded study: U-control of a wind energy conversion system.
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