Miguel A. Barron

Robust PI2 controller for continuous bioreactors

Abstract An estimation algorithm related to the kinetics terms of the main uncertainties present in a continuous stirred tank bioreactor, is developed. This algorithm is based on a proportional–integral reduced order uncertainty observer. With the estimate generated of the uncertain term, an input–output linearizing feedback control is designed which provides robust regulation model uncertainties, noisy measurements and sustained disturbances. This control strategy could be represented as PI 2 controller where new tuning rules of the controller gains are given in terms of the estimation and closed-loop time constants. The performance of the estimation algorithm and the corresponding closed-loop behaviour of the system are compared to a standard PI controller and they are illustrated by means of numerical simulations.

Sliding mode observer-based control for a class of bioreactors

Abstract A robust control algorithm which uses partial state feedback is designed for a class of biochemical processes in the presence of modeling uncertainties. To design the controller, the model uncertainty and the nonmeasurable state are combined into a new state variable. A sliding mode state observer is used to obtain on-line estimates of this new state. A practical stabilizer is obtained by combining the observer with an input–output linearizing controller. The practical convergence of the observer and the controller are proved. The performance of the sliding mode observer and the closed-loop behavior is illustrated through numerical simulations.

Model-based control of mold level in a continuous steel caster under model uncertainties

Abstract In tackling the problem of liquid steel level regulation in the mold of a continuous steel caster, the values of some system parameters, such as the clogging degree and the discharge coefficients of nozzles, are seldom precisely known. The discrete control laws developed in this work employ on-line estimated values of these parameters, to produce a stable regulation of mold and tundish levels for an industrial-type two-strand continuous slab caster. The estimation procedure is delayed by one time step (the sampling time) in order to become realizable; when the sampling time is small enough, the discrete control scheme gives stability and convergence properties that are analogous to those of an ideal control scheme with accurate knowledge of the parameter values.

Dynamic behavior of a continuous stirred bioreactor under control input saturation

A continuous stirred bioreactor with open-loop periodic behavior is analyzed under closed-loop conditions, using the dilution rate as control input. In the absence of control input bounds, the limiting substrate concentration converges to set point. When stringent bounds on control input are imposed, it becomes permanently saturated; then a limit cycle is generated, and the substrate concentration oscillates around an equilibrium point induced by saturation (EPIS). Suitable conditions are developed to avoid the presence of this closed-loop limit cycle. When the above conditions are satisfied, numerical simulations show that the substrate concentration in the closed-loop bioreactor has no permanent oscillations, the EPIS disappears and the limiting substrate concentration converges again to set point, in spite of the control input bounds.

A discrete approach to the control and synchronization of a class of chaotic oscillators

This work deals with the control and synchronization of chaotic systems. In the first part of the work, a general discrete-time strategy is developed to control a class of second-order uncertain nonlinear systems. The proposed strategy is based on an iterative procedure, borrowed from contraction map methodologies, and provides estimates of unmeasured states and modeling errors. Nonidentical chaotic systems can be synchronized by means of the proposed strategy. By assuming that the exact model of the oscillators is not known and that position is the only state available for measurements, the robust synchronization scheme comprises a recursive feedback-control law. Computer simulations are provided to illustrate the operation of the designed synchronization scheme.

Linearizing control of a binary distillation column based on a neuro-estimator

Abstract In this work, the LV-control problem in binary distillation columns is addressed. With least prior knowledge, a linear reference model with unknown terms is obtained. The time variations of the unknown terms are estimated using two on-line trained perceptrons. These estimates are subsequently used to design a feedback linearizing-like controller. The closed-loop behavior is analyzed through numerical examples. The resulting controller shows robustness against external disturbances and set-point changes.

Control of a fluid catalytic cracking unit based on proportional-integral reduced order observers

Abstract The fluid catalytic cracking (FCC) unit is one of the most complex interactive processes in the refining industry, and is difficult to operate and control. This work deals with the regulative control law design for stabilization of the reactor and regenerator temperatures, considering that the kinetics terms are poorly known. The proposed control law makes use of on-line estimates of the input/output modeling errors, obtained from a proportional-integral reduced order observer. The structure of the proposed controller is similar to a proportional-double integral compensator (PI 2 ) such that a new parameterization of the controllers gains is given in terms of the closed-loop and estimation time constants. The performance of the control scheme proposed here is analyzed via numerical simulations.

Successful bounded control for a chemical reactor with non-linear oscillatory consecutive reactions

Abstract The closed-loop dynamic behavior of a chemical reactor with two consecutive and oscillatory exothermic reactions is analyzed. When bounds are imposed on the control input, equilibrium points induced by saturation (EPIS) are generated. In this case, the reactor dynamic trajectories are deviated towards the EPIS and their convergence to the set-point is no longer guaranteed. By means of bifurcation analysis, necessary and sufficient conditions are derived to obtain quasi-optimal regulatory control and to avoid the presence of EPIS. Simulation studies proved the advantages of implementing these conditions, giving smooth responses with no oscillation.

Influence of the Slag Density on the Splashing Process in a Steelmaking Converter

The way in which slag density influences the slag splashing phenomenon in an oxygen steelmaking converter is numerically analyzed in this work. Several values of the density of the slag are considered, and their effect on the global mass balance and slag average volume fraction on the sidewalls of the converter is studied using isothermal, two-dimensional transient computational fluid dynamics simulations. Diameter of the slag drops is determined from the slag density and the impact velocity of the nitrogen jet. Besides, the effect of the nitrogen jet Mach number on the slag splashing is simulated and discussed. A qualitative comparison between the computer simulations and results from the literature is made.

Numerical Analysis of Oscillation Death in Coupled Self-Excited Elastic Beams

The emergence of the oscillation death phenomenon in a ring of four coupled self-excited elastic beams is numerically explored in this work. The beams are mathematically represented through partial differential equations which are solved by means of the finite differences method. A coupling scheme based on shared boundary conditions at the roots of the beams is assumed, and as initial conditions, zero velocity of the first beam and three normal vibration modes of a linear elastic beam are employed. The influence of the self-exciting constant on the ring dynamics is analyzed. It is observed that oscillation death arises as result of the singularity of the coupling matrix.