E. Picó-Marco

Sliding mode scheme for adaptive specific growth rate control in biotechnological fed-batch processes

This paper addresses the control of biomass growth rate in fed-batch bioreactors. The main difficulty when designing controllers for these processes is the lack of accurate on-line knowledge of the controlled variable as well as the strong parameter and model uncertainties. A completely novel approach to the control design is introduced in this paper which allows us to overcome these problems. In fact, the proposed controller, which is applicable to a large class of fermentation processes, requires minimal knowledge of the process parameters and only uses on-line measurement of volume and biomass concentration. First, a reference model is proposed and a goal manifold in the state space is derived where the control objective is satisfied. A partial state feedback law is then proved to be an invariant control for the goal manifold. Then, the feedback gain is dynamically adjusted via a discontinuous action that enforces a sliding regime such that all state trajectories are steered towards the goal manifold. This sliding mode controller presents very attractive robustness properties. The performance of the controller is evaluated through numerical analysis and experimental results.

Stability preserving maps for finite-time convergence: Super-twisting sliding-mode algorithm

The super-twisting algorithm (STA) has become the prototype of second-order sliding mode algorithm. It achieves finite time convergence by means of a continuous action, without using information about derivatives of the sliding constraint. Thus, chattering associated to traditional sliding-mode observers and controllers is reduced. The stability and finite-time convergence analysis have been jointly addressed from different points of view, most of them based on the use of scaling symmetries (homogeneity), or non-smooth Lyapunov functions. Departing from these approaches, in this contribution we decouple the stability analysis problem from that of finite-time convergence. A nonlinear change of coordinates and a time-scaling are used. In the new coordinates and time-space, the transformed system is stabilized using any appropriate standard design method. Conditions under which the combination of the nonlinear coordinates transformation and the time-scaling is a stability preserving map are given. Provided convergence in the transformed space is faster than O(1/@t)-where @t is the transformed time-convergence of the original system takes place in finite-time. The method is illustrated by designing a generalized super-twisting observer able to cope with a broad class of perturbations.

A Closed-loop Exponential Feeding Law for Multi-substrate Fermentation Processes

This article addresses the computation of invariant and stabilizing control laws for dual-substrate fed-batch fermentors. The design is based on two commonly used model structures. It will be shown how to derive partial state feedbacks, using only biomass and volume as measures, that keep the substrates at a desired concentration provided the model is good enough and does not change with time. In the paper an analysis of invariance and a study of global stability within the framework of partial stability is provided.

ADAPTIVE SLIDING MODE CONTROL OF FED-BATCH PROCESSES USING SPECIFIC GROWTH RATE ESTIMATION FEEDBACK

Abstract Regulation of the biomass specific growth rate is an important goal in many fermentation fed-batch processes. Inspired in an invariant control law, we propose in this paper a controller with the structure of a partial state feedback with gain dependent on the output error. Further, to make the desired state trajectory effectively invariant despite modeling errors and parameter variations, the feedback gain is continuously adapted by means of a sliding mode algorithm. The stability properties of the closed–loop process are investigated in detail.

Robust Adaptive Specific Growth Rate Control in Biotechnological Fed-Batch Processes

Abstract In this paper, the problem of robust specific growth rate control in biological reactions in fed-batch mode is dealt with. It is assumed that only part of the state is measurable on-line, namely biomass and volume. Moreover, no estimation of the specific growth rate is used, and the only required knowledge about the process is an upper bound of the kinetic functions, and whether it is monotonous or not.