Control of a class of nonlinear cascade systems with input-dependent saturations

Abstract

International audienceIn the present paper, we propose a control strategy for the stabilization of a class of nonlinear cascade systems with input-dependent saturation. The saturation constraint considered is a constraint of order: the control input of one subsystem has to be smaller than the control input of the preceding subsystem of the cascade structure. This class of systems include interconnected reactors device such as multi-stage continuous fermentors. The control law is designed on the basis of a specific Lyapunov function previously introduced by R.Antonelli and A.Astolfi in [1]. It guarantees the stability of the closed-loop system, the convergence of the state variable to the set-point and the fulfillment of the saturation constraint all along the trajectories of the closed-loop system. The approach is applied, in numerical simulation, to a concrete example of a series of interconnected continuous bioreactors

Antiwindup Input–Output Linearization Strategy for the Control of a Multistage Continuous Fermenter With Input Constraints

“…In order to make the control law more robust to this uncertainty, an adaptive control law could be proposed that would adjust on line the value of the initial sugar concentration. An other interesting perspective would be to test and compare other control strategies that have been recently proposed in [18], [19]. Finally, the next objective for the control of the MSCF will be to control both the sugar concentration and the CO2 production rate in each of the reactor.…”

“…• Application to the MSCF The input-output linearization, already presented in section V-A, is obtained with the change of variables (10) that is of the form (18)…”