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Algebraic Inequality (algebraic + inequality)

Distribution by Scientific Domains

Engineering	60%
Chemistry	40%

Selected Abstracts

A new method for mixed H2/H, control with regional pole constraints

OPTIMAL CONTROL APPLICATIONS AND METHODS, Issue 3 2003
Jenq-Lang Wu
Abstract In this paper, the problem of state feedback mixed H2/H, control with regional pole constraints is studied. The constraint region is represented by several algebraic inequalities. This constrained optimization problem cannot be solved via the LMI approach. Based on the barrier method, we instead solve an auxiliary minimization problem to get an approximate solution. We shall show that the obtained minimal solution of the auxiliary minimization problem can be arbitrarily close to the infimal solution of the original problem. An example is provided to illustrate the benefits of the approach. Copyright © 2003 John Wiley & Sons, Ltd. [source]

Experimental validation of a high-gain observer for composition estimation in an ethanol,water distillation column

ASIA-PACIFIC JOURNAL OF CHEMICAL ENGINEERING, Issue 6 2009
A. C. Téllez-Anguiano
Abstract In this paper a high-gain observer used to estimate the product compositions in a distillation column for a non-ideal mixture (ethanol,water) through the tray temperature measurements is presented. The design of this observer is based on a simplified mathematical model. One of the main advantages of this observer is its constant gain, therefore its tuning depends only on choosing a few constant parameters satisfying some simple algebraic inequalities. The effectiveness of the proposed method is demonstrated through on-line experiments in a distillation pilot plant. Copyright © 2009 Curtin University of Technology and John Wiley & Sons, Ltd. [source]

Feedback stabilization of bifurcations in multivariable nonlinear systems,Part II: Hopf bifurcations

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 4 2007
Yong Wang
Abstract In this paper we derive necessary and sufficient conditions of stabilizability for multi-input nonlinear systems possessing a Hopf bifurcation with the critical mode being linearly uncontrollable, under the non-degeneracy assumption that stability can be determined by the third order term in the normal form of the dynamics on the centre manifold. Stabilizability is defined as the existence of a sufficiently smooth state feedback such that the Hopf bifurcation of the closed-loop system is supercritical, which is equivalent to local asymptotic stability of the system at the bifurcation point. We prove that under the non-degeneracy conditions, stabilizability is equivalent to the existence of solutions to a third order algebraic inequality of the feedback gains. Explicit conditions for the existence of solutions to the algebraic inequality are derived, and the stabilizing feedback laws are constructed. Part of the sufficient conditions are equivalent to the rank conditions of an augmented matrix which is a generalization of the Popov,Belevitch,Hautus (PBH) rank test of controllability for linear time invariant (LTI) systems. We also apply our theory to feedback control of rotating stall in axial compression systems using bleed valve as actuators. Copyright © 2006 John Wiley & Sons, Ltd. [source]

Recursive estimation in constrained nonlinear dynamical systems

AICHE JOURNAL, Issue 3 2005
Pramod Vachhani
In any modern chemical plant or refinery, process operation and the quality of product depend on the reliability of data used for process monitoring and control. The task of improving the quality of data to be consistent with material and energy balances is called reconciliation. Because chemical processes often operate dynamically in nonlinear regimes, techniques such as extended-Kalman filter (EKF) and nonlinear dynamic data reconciliation (NDDR) have been developed for reconciliation. There are various issues that arise with the use of either of these techniques. EKF cannot handle inequality or equality constraints, whereas the NDDR has high computational cost. Therefore, a more efficient and robust method is required for reconciling process measurements and estimating parameters involved in nonlinear dynamic processes. Two solution techniques are presented: recursive nonlinear dynamic data reconciliation (RNDDR) and a combined predictor,corrector optimization (CPCO) method for efficient state and parameter estimation in nonlinear systems. The proposed approaches combine the efficiency of EKF and the ability of NDDR to handle algebraic inequality and equality constraints. Moreover, the CPCO technique allows deterministic parameter variation, thus relaxing another restriction of EKF where the parameter changes are modeled through a discrete stochastic equation. The proposed techniques are compared against the EKF and the NDDR formulations through simulation studies on a continuous stirred tank reactor and a polymerization reactor. In general, the RNDDR performs as well as the two traditional approaches, whereas the CPCO formulation provides more accurate results than RNDDR at a marginal increase in computational cost. © 2005 American Institute of Chemical Engineers AIChE J, 51: 946,959, 2005 [source]