Robust sliding mode‐based extremum‐seeking controller for reaction systems via uncertainty estimation approach

Abstract

Summary This paper deals with the design of a robust sliding mode‐based extremum‐seeking controller aimed at the online optimization of a class of uncertain reaction systems. The design methodology is based on an input–output linearizing method with variable‐structure feedback, such that the closed‐loop system converges to a neighborhood of the optimal set point with sliding mode motion. In contrast with previous extremum‐seeking control algorithms, the control scheme includes a dynamic modelling‐error estimator to compensate for unknown terms related with model uncertainties and unmeasured disturbances. The proposed online optimization scheme does not make use of a dither signal or a gradient‐based optimization algorithm. Practical stabilizability for the closed‐loop system around to the unknown optimal set point is analyzed. Numerical experiments for two nonlinear processes illustrate the effectiveness of the proposed robust control scheme. Copyright © 2017 John Wiley & Sons, Ltd.

Numerical optimization‐based extremum seeking control of a class of constrained nonlinear systems via finite‐time state transition

“…By selecting the asymptotic bound (−2, 2) for the function 𝜑, we design the reference output trajectory y * according to (16) as…”

“…Therefore, it finds applications in many engineering fields, spanning from power optimization, 1 robotic motion control, 2 source seeking 3,4 . To date, various ESC methods have been proposed by, for example, incorporating dither signals and averaging methods, 5‐7 sliding mode control, 8,9 sample‐data optimization, 10,11 adaptation‐based methods, 12,13 and numerical optimization methods 14‐16 . It is well known that the first two techniques require a fine tuning of some dither signal, whereas the latter three methods naturally entail dither‐free and chattering‐free behaviors.…”

“…3,4 To date, various ESC methods have been proposed by, for example, incorporating dither signals and averaging methods, [5][6][7] sliding mode control, 8,9 sample-data optimization, 10,11 adaptation-based methods, 12,13 and numerical optimization methods. [14][15][16] It is well known that the first two techniques require a fine tuning of some dither signal, whereas the latter three methods naturally entail dither-free and chattering-free behaviors. A short overview of ESC related works will be given in the following, with emphasis on ESC with constraints and numerical optimization-based ESC, aspects which are the focus of our work.…”

Ekstremum Arama Temelli Hata Tahmini ile Esnek Bağlantılı Robot Kolunun Çıkış Geri Besleme Kontrolü

“…In (Dochain et al 2011), an extended state observer-based regulator is designed, and conjugate gradient based extremum seeking is achieved. In (Lara et al 2017), extremum seeking sliding-mode controller is designed for input-output linearized model with an uncertainty function.…”

Model-Free Extremum Seeking Control of Bioprocesses: A Review with a Worked Example

“…In the same spirit, Vargas et al [57] tackle the problem of biomass productivity optimization in bacteria cultures, presenting overflow metabolism using a two-level controller with super-twisting observers as process output estimators. Further, an input-output linearizing sliding-mode control is derived for well-defined relative degree systems with minimum phase in [58,59].…”