Abstract
In this work, a new adaptive controller is designed for substrate control of a fed-batch bioreactor in the presence of input saturation and unknown varying control gain with unknown upper and lower bounds. The output measurement noise and the unknown varying nature of reaction rate and biomass concentration and water volume are also handled. The design is based on dead zone quadratic forms. The designed controller ensures the convergence of the modified tracking error and the boundedness of the updated parameters. As the first distinctive feature, a new robust adaptive auxiliary system is proposed in order to tackle input saturation and control gain uncertainty. As the second distinctive feature, the modified tracking error converges to a compact region whose bound is user-defined, in contrast to related studies where the convergence region depends on upper bounds of either external disturbances, system states, model parameters or terms and model parameter values. Simulations confirm the properties of the closed loop behavior.
Highlights
The modified tracking error converges to a compact set whose width is user-defined, so that model coefficients, and bounds of either external disturbances, system states, model terms, and model coefficients are not required to be known. This is in contrast to current adaptive control designs for input saturation, where the width of the convergence region depends on the aforementioned bounds
A no feeding phase can be used before the feeding phase, featuring substrate consumption and biomass growth, being the feeding phase initiated when the substrate concentration has decreased until a critical value [4,34]
There are several input saturation events after of updated parameters, such that proper convergence of the signal z is achieved despite during which: (i) z > C, e > C (Figure 4b,f); (ii) the constrained signal υ satura this uncertainty; the effect of input saturation is tackled by means of the auxiliary system, its lower bound (Figure 4c,e); (iii) the updated parameters increase as z > C, wi such that convergence of the signal z is achieved; discontinuous signals are used in neither upper bound (Figure 4d)
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. The control gain is considered as accurately known in the control design, and the convergence region of the modified tracking error depends on the bounds of: external disturbances, system states, and model coefficients. A Lyapunov-based adaptive controller is developed for a fed-batch bioreactor in the presence of input saturation, unknown varying model parameters, output measurement noise, and unknown varying control gain, with unknown upper and lower bounds. The modified tracking error converges to a compact set whose width is user-defined, so that model coefficients, and bounds of either external disturbances, system states, model terms, and model coefficients are not required to be known This is in contrast to current adaptive control designs for input saturation (see [25,29,30]), where the width of the convergence region depends on the aforementioned bounds.
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