Iterative Nonlinear Control of a Semibatch Reactor. Stability Analysis

This paper presents the application of Iterative Nonlinear Model Predictive Control, INMPC, to a semibatch chemical reactor. The proposed control approach is derived from a model-based predictive control formulation which takes advantage of the repetitive nature of batch processes. The proposed controller combines the good qualities of Model Predictive Control (MPC) with the possibility of learning from past batches, that is the base of Iterative Control. It uses a nonlinear model and a quadratic objective function that is optimized in order to obtain the control law. A stability proof with unitary control horizon is given for nonlinear plants that are affine in control and have linear output map. The controller shows capabilities to learn the optimal trajectory after a few iterations, giving a better fit than a linear non-iterative MPC controller. The controller has applications in repetitive disturbance rejection, because they do not modify the model for control purposes. In this application, some experiments with a disturbance in inlet water temperature has been performed, getting good results.Ministerio de Ciencia y Tecnología DPI2004-07444-C04-0

Application of iterative nonlinear model predictive control to a batch pilot reactor

IFAC WORLD CONGRESS (16) (16.2005.PRAGA, REPÚBLICA CHECA)The aim of this article is to present the Iterative Model Predictive Controller, inmpc, as a good candidate to control chemical batch reactors. The proposed control approach is derived from a model-based predictive control formulation which takes advantage of the repetitive nature of batch processes. The proposed controller combines the good qualities of Model Predictive Control (mpc) with the possibility of learning from past batches, that is the base of Iterative Control. It uses a nonlinear model and a quadratic objective function that is optimized in order to obtain the control law. The controller is tested on a batch pilot reactor, and a comparison with an Iterative Learning Controller (ilc) is made. Under input constraints and for this nonlinear plant, a fast convergence rate is obtained with the proposed controller, showing good operational results. Although the controller is designed for discrete-time systems, it is a necessary condition that the continuous-time model does not present blow-up characteristics. The batch pilot reactor emulates an exothermal chemical reaction by means of electrical heating

Measurements, Models, Systems and Design

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In-phase and anti-phase synchronization in noisy Hodgkin-Huxley neurons

We numerically investigate the influence of intrinsic channel noise on the dynamical response of delay-coupling in neuronal systems. The stochastic dynamics of the spiking is modeled within a stochastic modification of the standard Hodgkin-Huxley model wherein the delay-coupling accounts for the finite propagation time of an action potential along the neuronal axon. We quantify this delay-coupling of the Pyragas-type in terms of the difference between corresponding presynaptic and postsynaptic membrane potentials. For an elementary neuronal network consisting of two coupled neurons we detect characteristic stochastic synchronization patterns which exhibit multiple phase-flip bifurcations: The phase-flip bifurcations occur in form of alternate transitions from an in-phase spiking activity towards an anti-phase spiking activity. Interestingly, these phase-flips remain robust in strong channel noise and in turn cause a striking stabilization of the spiking frequency

A MRAS-based Learning Feed-forward Controller

Inspired by learning feed–forward control structures, this paper considers the adaptation of the parameters of a model–reference based learning feed–forward controller that realizes an inverse model of the process. The actual process response is determined by a setpoint generator. For linear systems it can be proved that the controlled system is asymptotically stable in the sense of Liapunov. Compared with more standard model reference configurations this system has a superior performance. It is fast, robust and relatively insensitive for noisy measurements. Simulations with an arbitrary second–order process and with a model of a typical fourth–ordermechatronics process demonstrate this

A mapping approach to synchronization in the "Zajfman trap": stability conditions and the synchronization mechanism

We present a two particle model to explain the mechanism that stabilizes a bunch of positively charged ions in an "ion trap resonator" [Pedersen etal, Phys. Rev. Lett. 87 (2001) 055001]. The model decomposes the motion of the two ions into two mappings for the free motion in different parts of the trap and one for a compressing momentum kick. The ions' interaction is modelled by a time delay, which then changes the balance between adjacent momentum kicks. Through these mappings we identify the microscopic process that is responsible for synchronization and give the conditions for that regime.Comment: 12 pages, 9 figures; submitted to Phys Rev