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115 Controlling chaos and targeting in a thermal convection loop
396
Abstracts
109 DecoupHng by State Feedback in Singular Systems L. G6ren, M. Gfizelkaya, pp 464.467
In this paper, a row-by-row decoupling problem of singular square systems is studied by static state feedback. The problem is handled in a polynomial matrix equation setting and a related theorem is introduced. The theorem is based on a new necessary and sufficient condition for the constant solution of a matrix polynomial equation.
110 Transfer Function of Linear Discrete TimeVarying Systems via Non-Commutatlve Algebra M.Gngllelmi, pp 468-471
113 Commutation of Polynomial Coefficient on a Finite Time Horizon I. Nagy, J. Je~h.k, pp 480-483 Commutation of time-varying coefficients and operators of a single polynomial operating on a finitetime horizon is studied. Two types of operators, namely the shift operator (4) and the dfffegertce operator (V) are considered. The task is a special case of polynomial commutation equations which have to be solved for the synthesis of control law minimizing a quadratic loss function.
114 Interpretations of the Gap Topology: A Survey J. de Does, J.M. Schumacher, pp 488-492
This paper considers linear systems (Z) described by difference equations with non-constant coefficients. Here, it is shown that it is also possible to define, as in the continuous case, an isomorphism between the difference equation of (5"_) and the non-commutative polynomials of V, where V is the difference operator. In this case, the operator ~ (delay) acts on the time-varying coefficients. The association rules for serial systems are defined from the computation rules over rational "skew" fractions.
This paper gives a survey of several descriptions of the graph topology, summarizing a tendency towards moregeneral mathematical concelxs that do not depend for their definition on a specific representation of a system. Simple proofs are given of the equivalence of a number of different ways of introducing the gap topology for linear input-output systems.
111 The Linear Constrained Regulation Problem for Some Linear Continuoos-Time Singular systems S. Tarbourlech, E.B. Castelan, pp 472-475
115 Controlling Chaos and Targeting in a Thermal Convection Loop Hua Wang, E.H. Abed, pp 494-497
A major issue in control system design is the direct integration of technological and security constraints in the control law. This can generally be obtained by constructing a stabilizing controller which makes positively invariam a domain included in the set def'med by the constraints. In most practical control problems, state and/or input constraints generate convex polyhedra in the state space. This paper shows that for a controllable singular system with a sufficient number of stable f'mite poles, it is always possible to construct a stabilizing state feedback control, a(t) = Faft), guaranteeing the closed-loop positive invariance of the polyhedron determined by the feedback matrix F. A numerical example is given.
The stabilizing control of a deterministic chaotic system is investigated. The thermal convection loop under study exhibits bifurcations, transient chaos, and fully developed chaos. The paper shows how the control of primary bifurcations in the model can result in the taming of chaos. A linear-plus-nonlinear controller, which delays and stabilizes the primary (Hop0 bifurcations, effectively suppresses both chaos and transient chaos for any parameter range. The design of "targeting" controllers which result in the system preferring one equilibrium to another is given. These controllers all employ washout filters, resulting in robusmcss with respect to model uncertainties,especially with respect to the system equilibrium points.
112 A Deadbeat Controller for Time Varying Plants Following the Reference Model Output Y. Yamane, P.N. Nikiforuk, pp 476-479 A design method for controllers based on modelmatching techniques is a useful simple approach to design a linear time invariant plant control system so that the transfer function of the resulting control system coincides with that of the reference model. This paper is concerned with an extension of a previous generalized mode!-ma.tching controller design approach for a class of ume mvmant plants to use for a class of time varying plants. It is illustrated that a deadbeat tracking of the state norm between the plant and the reference model is observed in controllable companion forms, as is shown in the case of time invariant plants.
116 A Special Analog Computer for Direct State Space Formulation (A,B,C,D) V.R. Sitar, A.N. Ponce, pp 498-500 For teaching control techniques, it is necessary to understand the relationship between real systems and their models. For this reason, a special modern analog computer was designed to formulate direct state variable formulation (A.B.C.D matrices) for education and demonstration purposes. The main advantage is that the computer permits the formulation of models for time invariant linear systems with state space representation (including all canonical forms).
Abstracts
109 DecoupHng by State Feedback in Singular Systems L. G6ren, M. Gfizelkaya, pp 464.467
In this paper, a row-by-row decoupling problem of singular square systems is studied by static state feedback. The problem is handled in a polynomial matrix equation setting and a related theorem is introduced. The theorem is based on a new necessary and sufficient condition for the constant solution of a matrix polynomial equation.
110 Transfer Function of Linear Discrete TimeVarying Systems via Non-Commutatlve Algebra M.Gngllelmi, pp 468-471
113 Commutation of Polynomial Coefficient on a Finite Time Horizon I. Nagy, J. Je~h.k, pp 480-483 Commutation of time-varying coefficients and operators of a single polynomial operating on a finitetime horizon is studied. Two types of operators, namely the shift operator (4) and the dfffegertce operator (V) are considered. The task is a special case of polynomial commutation equations which have to be solved for the synthesis of control law minimizing a quadratic loss function.
114 Interpretations of the Gap Topology: A Survey J. de Does, J.M. Schumacher, pp 488-492
This paper considers linear systems (Z) described by difference equations with non-constant coefficients. Here, it is shown that it is also possible to define, as in the continuous case, an isomorphism between the difference equation of (5"_) and the non-commutative polynomials of V, where V is the difference operator. In this case, the operator ~ (delay) acts on the time-varying coefficients. The association rules for serial systems are defined from the computation rules over rational "skew" fractions.
This paper gives a survey of several descriptions of the graph topology, summarizing a tendency towards moregeneral mathematical concelxs that do not depend for their definition on a specific representation of a system. Simple proofs are given of the equivalence of a number of different ways of introducing the gap topology for linear input-output systems.
111 The Linear Constrained Regulation Problem for Some Linear Continuoos-Time Singular systems S. Tarbourlech, E.B. Castelan, pp 472-475
115 Controlling Chaos and Targeting in a Thermal Convection Loop Hua Wang, E.H. Abed, pp 494-497
A major issue in control system design is the direct integration of technological and security constraints in the control law. This can generally be obtained by constructing a stabilizing controller which makes positively invariam a domain included in the set def'med by the constraints. In most practical control problems, state and/or input constraints generate convex polyhedra in the state space. This paper shows that for a controllable singular system with a sufficient number of stable f'mite poles, it is always possible to construct a stabilizing state feedback control, a(t) = Faft), guaranteeing the closed-loop positive invariance of the polyhedron determined by the feedback matrix F. A numerical example is given.
The stabilizing control of a deterministic chaotic system is investigated. The thermal convection loop under study exhibits bifurcations, transient chaos, and fully developed chaos. The paper shows how the control of primary bifurcations in the model can result in the taming of chaos. A linear-plus-nonlinear controller, which delays and stabilizes the primary (Hop0 bifurcations, effectively suppresses both chaos and transient chaos for any parameter range. The design of "targeting" controllers which result in the system preferring one equilibrium to another is given. These controllers all employ washout filters, resulting in robusmcss with respect to model uncertainties,especially with respect to the system equilibrium points.
112 A Deadbeat Controller for Time Varying Plants Following the Reference Model Output Y. Yamane, P.N. Nikiforuk, pp 476-479 A design method for controllers based on modelmatching techniques is a useful simple approach to design a linear time invariant plant control system so that the transfer function of the resulting control system coincides with that of the reference model. This paper is concerned with an extension of a previous generalized mode!-ma.tching controller design approach for a class of ume mvmant plants to use for a class of time varying plants. It is illustrated that a deadbeat tracking of the state norm between the plant and the reference model is observed in controllable companion forms, as is shown in the case of time invariant plants.
116 A Special Analog Computer for Direct State Space Formulation (A,B,C,D) V.R. Sitar, A.N. Ponce, pp 498-500 For teaching control techniques, it is necessary to understand the relationship between real systems and their models. For this reason, a special modern analog computer was designed to formulate direct state variable formulation (A.B.C.D matrices) for education and demonstration purposes. The main advantage is that the computer permits the formulation of models for time invariant linear systems with state space representation (including all canonical forms).