Sinusoidal control strategy applied to continuous stirred-tank reactors: Asymptotic and exponential convergence

The main goal of this proposal is to present a class of nonlinear controllers for regulation and set point changes in continuous chemical reactors. The proposed control law has in its mathematical structure a proportional term of the regulation error to provide closed-loop stability and a sinusoidal term, which can compensate for the nonlinearities of the plant. The closed-loop stability of the plant is demonstrated via Lyapunov analysis, which reveals an asymptotic convergence of the control output to the required set points. Furthermore, the analysis of the regulation error's dynamic under the considered assumptions leads us to conclude that exponential stability is also reached. The controller is implemented via numerical experiments in two examples to generalize the applicability of the proposed approach by considering continuous stirred-tank reactors models. The first case considers autocatalytic chemical oscillatory reactions that induce chaotic behaviour. For the second case, a process of acetone, butanol, and ethanol (ABE) fermentation through Clostridium acetobutylicum is considered. The proposed strategy shows an adequate performance because it can reach the required set point without long time settings and overshoot. A comparison with a smooth sliding-mode and a standard proportional-integral (PI) controller indicates the advantages of the proposed control approach.