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Impact of Process Design on the Multiplicity Behavior of a Jacketed Exothermic CSTR
, 1995
"... Much of the previous research on exothermic reactor operation has been based on the classic twostate continuous stirred tank reactor (CSTR) model. An implicit assumption of this model is that the cooling jacket temperature dynamics are negligible. In this case the cooling jacket temperature is the ..."
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Cited by 9 (8 self)
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Much of the previous research on exothermic reactor operation has been based on the classic twostate continuous stirred tank reactor (CSTR) model. An implicit assumption of this model is that the cooling jacket temperature dynamics are negligible. In this case the cooling jacket temperature is the manipulated input (instead of the cooling jacket flowrate) for feedback control of reactor temperature. We show that the addition of a cooling jacket energy balance results in much more complex behavior than a simple lag effect. We also show that a stabilizing innerloop cascade controller is assumed in the twostate CSTR model, because the threestate CSTR model (incorporating cooling jacket temperature dynamics) may be openloop unstable when the twostate model is openloop stable. The influence of design parameters on the multiplicity behavior of a threestate CSTR model is considered in this paper. We use singularity theory to study the effect of process parameters (such as the cooling ...
Flat systems, equivalence and trajectory generation
, 2003
"... Flat systems, an important subclass of nonlinear control systems introduced via differentialalgebraic methods, are defined in a differential geometric framework. We utilize the infinite dimensional geometry developed by Vinogradov and coworkers: a control system is a diffiety, or more precisely, an ..."
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Cited by 9 (3 self)
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Flat systems, an important subclass of nonlinear control systems introduced via differentialalgebraic methods, are defined in a differential geometric framework. We utilize the infinite dimensional geometry developed by Vinogradov and coworkers: a control system is a diffiety, or more precisely, an ordinary diffiety, i.e. a smooth infinitedimensional manifold equipped with a privileged vector field. After recalling the definition of aLieBäcklund mapping, we say that two systems are equivalent if they are related by a LieBäcklund isomorphism. Flat systems are those systems which are equivalent to a controllable linear one. The interest of such an abstract setting relies mainly on the fact that the above system equivalence is interpreted in terms of endogenous dynamic feedback. The presentation is as elementary as possible and illustrated by the VTOL aircraft.
SymmetryPreserving Observers
"... Abstract—This paper presents the theory of invariant observers, i.e, symmetrypreserving observers. We consider an observer to consist of a copy of the system and a correction term, and we propose a constructive method (based on the Cartan movingframe method) to find all the symmetrypreserving cor ..."
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Cited by 3 (2 self)
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Abstract—This paper presents the theory of invariant observers, i.e, symmetrypreserving observers. We consider an observer to consist of a copy of the system and a correction term, and we propose a constructive method (based on the Cartan movingframe method) to find all the symmetrypreserving correction terms. The construction relies on an invariant frame (a classical notion) and on an invariant outputerror, a less standard notion precisely defined here. Using the theory we build three nonlinear observers for three examples of engineering interest: a nonholonomic car, a chemical reactor, and an inertial navigation system. For each example, the design is based on physical symmetries and the convergence analysis relies on the use of invariant stateerrors, a symmetrypreserving way to define the estimation error. Index Terms—Inertial navigation, moving frame, nonlinear observer, symmetries. I.
Invariant asymptotic observers
, 2006
"... This paper presents three nonlinear asymptotic observers corresponding to three examples of engineering interest: a chemical reactor, a nonholonomic car, and an inertial navigation system. For each example, the design is based on physical symmetries. This motivates the theoretical development of i ..."
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Cited by 2 (0 self)
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This paper presents three nonlinear asymptotic observers corresponding to three examples of engineering interest: a chemical reactor, a nonholonomic car, and an inertial navigation system. For each example, the design is based on physical symmetries. This motivates the theoretical development of invariant observers, i.e, symmetrypreserving observers. We consider an observer to consist in a copy of the system equation and a correction term, and we give a constructive method (based on the Cartan movingframe method) to find all the symmetrypreserving correction terms. They rely on an invariant frame (a classical notion) and on an invariant outputerror, a less standard notion precisely defined here. For each example, the convergence analysis relies also on symmetries consideration with a key use of invariant stateerrors. For the nonholonomic car and the inertial navigation system, the invariant stateerrors is shown to obey an autonomous differential equation independent of the system trajectory. This allows us to prove exponential convergence, with almost global stability for the nonholonomic car and with semiglobal stability for the inertial navigation system. Simulations including noise and bias show the practical interest of such invariant asymptotic observers for the inertial navigation system.
Robust feedback stabilization of chemical reactors
 78; y f = 140, y r = 448:4, u = 140, v = 141:5, d =1during the
, 1997
"... Abstract—This paper deals with the temperature stabilization of a large class of continuously stirred tank chemical reactors. We design state feedback controllers, and we show their ability to globally stabilize the temperature at an arbitrary set point in spite of uncertainties on the kinetics. Fur ..."
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Abstract—This paper deals with the temperature stabilization of a large class of continuously stirred tank chemical reactors. We design state feedback controllers, and we show their ability to globally stabilize the temperature at an arbitrary set point in spite of uncertainties on the kinetics. Furthermore, it is also shown that these controllers can handle input constraints along the closedloop trajectories in some instances. For the implementation purpose, we design a robust state observer for the case of partial state measurement, and we prove that its incorporation in the feedback loops does not impair the nominal stabilization properties of the controllers. Index Terms—Chemical reactors, robust feedback stabilization, robust observer, temperature control. I.
On Invariant Observers
"... Summary. A definition of invariant observer and compatible output function is proposed and motivated. For systems admitting a Lie symmetrygroup G of dimension less or equal to the state dimension and with a Gcompatible output, an explicit procedure based on the moving frame method is proposed to c ..."
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Cited by 1 (1 self)
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Summary. A definition of invariant observer and compatible output function is proposed and motivated. For systems admitting a Lie symmetrygroup G of dimension less or equal to the state dimension and with a Gcompatible output, an explicit procedure based on the moving frame method is proposed to construct such invariant observers. It relies on an invariant frame and a complete set of invariant estimation errors. Two examples of engineering interest are considered: an exothermic chemical reactor and an inertial navigation problem. For both examples we show how invariance and the proposed construction can be a useful guide to design nonlinear convergent observers, although the part of the design procedure which achieves asymptotic stability is not systematic and must take into account the specific nonlinearities of the case under study.
Global Optimization with NonAnalytical Constraints
"... This paper presents an approach for the global optimization of constrained nonlinear programming problems in which some of the constraints are nonanalytical (nonfactorable), defined by a computational model for which no explicit analytical representation is available. ..."
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This paper presents an approach for the global optimization of constrained nonlinear programming problems in which some of the constraints are nonanalytical (nonfactorable), defined by a computational model for which no explicit analytical representation is available.
1 Symmetrypreserving observers
, 2008
"... This paper presents three nonlinear observers for three examples of engineering interest: a nonholonomic car, a chemical reactor, and an inertial navigation system. For each example, the design is based on physical symmetries. This motivates the theoretical development of invariant observers, i.e, ..."
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This paper presents three nonlinear observers for three examples of engineering interest: a nonholonomic car, a chemical reactor, and an inertial navigation system. For each example, the design is based on physical symmetries. This motivates the theoretical development of invariant observers, i.e, symmetrypreserving observers. We consider an observer to consist of a copy of the system equation and a correction term, and we propose a constructive method (based on the Cartan movingframe method) to find all the symmetrypreserving correction terms. The construction relies on an invariant frame (a classical notion) and on an invariant outputerror, a less standard notion precisely defined here. For each example, the convergence analysis relies on the use of invariant stateerrors, a symmetrypreserving way to define the estimation error.
Printed in Great Britain ocm1098/97 $17.00 + 0.00 Global Stabilization of Exothermic Chemical Reactors under Input Constraints*
"... A generic class of exothermic chemical reactors can be globally stabilized by state feedback with input saturations at an equilibrium that is unstable in open loop conditions. The control is robust against modelling uncertainties in the dependence qf the kinetics with respect to temperature. Key Wor ..."
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A generic class of exothermic chemical reactors can be globally stabilized by state feedback with input saturations at an equilibrium that is unstable in open loop conditions. The control is robust against modelling uncertainties in the dependence qf the kinetics with respect to temperature. Key WordsExothermic chemical reactors; nonlinear temperature control; state feedback controllers; global stabilization; robustness to uncertainties; input constraints, adaptive control. Ah&actThis paper is devoted to the temperature control and the stabilization under input constraints of exothermic chemical reactors. We first consider a reactor in which a single and exothermic reaction takes place and design state feedback controllers to achieve the global and robust stabilization under input constraints of the reactor. Then, we extend these results to a general class of exothermic reactors in which multiple coupled chemical reactions can take place. 0 1997 Elsevier Science Ltd. 1.