- Email: [email protected]
071 Robust sliding mode control for servo systems
392
069 Reduction of Input Chattering of a Robust Controller for Uncertain Linear Systems - A Proposal for a FictitiousSet Point N. Sakamoto, M. Masubuchi, pp 296-299 The deterministic controller of Leilmann and/or variablestructure controllers have been used as the robust control strategy which assures stability for linear systems having uncertainties caused by parameter variations and disturbances. For both control strategies, however, chattering may be generated at the manipulating variable, due to the input delay when implemented by digital computers. This paper proposes a revised form of the authors' new Fictitious Set Point (FSP) control algorithm for reducing this chattering. It is shown by computer simulation that the manipulated variable is reduced, and that the chattering can be reduced remarkably.
Abstracts and observability, realization, input-output inversion, and model-matching.
074 Impulsive-Smooth Behaviors A.H.W. Gcerts, J.M. Schumncher, pp 320-323
070 Robust Stabilization Problem for a System with Delays in Control A. KoJima, S. lshlJima, pp 304-307
Using the vocabulary of J.C. Wiliems, the term "impulsive-smooth behavior" may be used for any subset of the space of vector-valued impulsive-smooth disturbances introduced by M.L.J. Hautus. This paper is particularly concerned with those behaviors that can be represented by sets of linear differential and algebraic equations. Both polynomial representations without auxiliary variables, and fast-order representations with auxiliary variables are considered. It is shown how these representations may be transformed into one another. For both types of representations, necessary and sufficient conditions for minimality are described, and the extent to which minimal representations are unique. In the present context, "controllability at infinity" is not necessary for minimality.
A robust stabilization problem is discussed for a system with delays in control. A robust stabilizing law against the uncertainties such as addidve/multiplicative perturbations is derived. Motivated by the feature of predictive controllers, the authors also provide some interpretations of the structure of the required control law.
075 Remarks on Input-Acceptance, OutputUniqueness for Implicit Linear Systems and Their Interpretation for the yon Neumann Model of an Economy M. Koclecki, A. Banaszuk, F.L Lewis, pp 324-327
071 Robust Sliding Mode Control for Servo Systems M.M.F. Sakr, pp 308-311 Variable structure controllers (VSS) with sliding mode have proved to exhibit satisfactory performance for servo systems concerning disturbance rejection and time response. In the presence of disturbances, teachability of the system cannot be guaranteed and the sliding curve may not be reached. In this paper a new method is proposed, based on maintaining the sliding mode all over the trajectory. New sliding lines are proposed to ensure robustness over the whole trajectory. Straightforward equations for the gain variations are derived.
072 External Reachabllity for Implicit Descriptions M.E. Bonilla, M. Malabre, pp 312-315 Even for fiat implicit linear systems (i.e.. having more state components that state equations), reachability is a well-defined concept in terms of the set of state trajectories: it characterizes the property that from any initial state a smooth state trajectory can start, which reaches any final state. What can happen, however, is that a system with no control input can be completely reachable. The notion of "external teachability" is introduced here, where trajectories can actually be controlled through the input (by proportional and derivative state feedback). Geometric necessary and sufficient conditions are given for external teachability. A new design method is proposed.
073 An Algebraic Definition of Time-Varying Transfer Matrices M. FHess, pp 316-318 Tensoring the module of a linear system with the quotient field of the ring of linear differential operators yields an algebraic framework where transfer matrices most naturally appear and which easily applies to the time-varying case. Several basic structural properties are examined: transfer algebra, matrix fraction decomposition and their connections with controllability
In the paper the problem of input-acceptance (i.e., the question of the extatence of a trajectory corresponding to a given input sequence) and output-uniqueness properties for a linear (respectively controlled and observed) implicit discrete-time system are introduced and saldied. Geometric and algebraic conditions for all considered properties are provided. It is shown that the input and output notions are dual counterparts. A natural interpretation of all the notions in terms of a linear von Neumann model of an economy is presented.
076 Remarks on Implicit Linear Continuous-Time Systems K.M. Przyluski, A. Sosnowskl, pp 328-331 Given a (not necessarily reqular or square) linear implicit system Ex (t)=Fx(t)+Gu(t), the space of admissible initial conditions and the controllable space of the system are studied. Distributional trajectories are considered.
077 Structural Properties of Singular Systems Part 2: Observability and Duality K. Oz~aldiran, pp 332-334 This paper investigates the structural properties of the (rectangular) singular system Ex'=Ax; y=Cx. It is shown that the very basic notion of observing an initial condition results in a number of different definitions of observability, depending on the way the output data is given. These different definitions are discussed and characterized geome¢ically.
078 An Exterior Algebra Based Characterization of the Fundamental Subspnces of Singular Systems U. Baser, N. Kareanins, pp 336-339 In this study, s¢ict equivalence invariants of a matrix pencil sF-G and the basic families of the subspaces corresponding to these invariants are charactea'i~.ed by means of Exterior Algebra. These results ~e used to characterlse some properties of the suprernal (A,E,B) invariant subspace (/s), supremal almost (E,A,B) is,
069 Reduction of Input Chattering of a Robust Controller for Uncertain Linear Systems - A Proposal for a FictitiousSet Point N. Sakamoto, M. Masubuchi, pp 296-299 The deterministic controller of Leilmann and/or variablestructure controllers have been used as the robust control strategy which assures stability for linear systems having uncertainties caused by parameter variations and disturbances. For both control strategies, however, chattering may be generated at the manipulating variable, due to the input delay when implemented by digital computers. This paper proposes a revised form of the authors' new Fictitious Set Point (FSP) control algorithm for reducing this chattering. It is shown by computer simulation that the manipulated variable is reduced, and that the chattering can be reduced remarkably.
Abstracts and observability, realization, input-output inversion, and model-matching.
074 Impulsive-Smooth Behaviors A.H.W. Gcerts, J.M. Schumncher, pp 320-323
070 Robust Stabilization Problem for a System with Delays in Control A. KoJima, S. lshlJima, pp 304-307
Using the vocabulary of J.C. Wiliems, the term "impulsive-smooth behavior" may be used for any subset of the space of vector-valued impulsive-smooth disturbances introduced by M.L.J. Hautus. This paper is particularly concerned with those behaviors that can be represented by sets of linear differential and algebraic equations. Both polynomial representations without auxiliary variables, and fast-order representations with auxiliary variables are considered. It is shown how these representations may be transformed into one another. For both types of representations, necessary and sufficient conditions for minimality are described, and the extent to which minimal representations are unique. In the present context, "controllability at infinity" is not necessary for minimality.
A robust stabilization problem is discussed for a system with delays in control. A robust stabilizing law against the uncertainties such as addidve/multiplicative perturbations is derived. Motivated by the feature of predictive controllers, the authors also provide some interpretations of the structure of the required control law.
075 Remarks on Input-Acceptance, OutputUniqueness for Implicit Linear Systems and Their Interpretation for the yon Neumann Model of an Economy M. Koclecki, A. Banaszuk, F.L Lewis, pp 324-327
071 Robust Sliding Mode Control for Servo Systems M.M.F. Sakr, pp 308-311 Variable structure controllers (VSS) with sliding mode have proved to exhibit satisfactory performance for servo systems concerning disturbance rejection and time response. In the presence of disturbances, teachability of the system cannot be guaranteed and the sliding curve may not be reached. In this paper a new method is proposed, based on maintaining the sliding mode all over the trajectory. New sliding lines are proposed to ensure robustness over the whole trajectory. Straightforward equations for the gain variations are derived.
072 External Reachabllity for Implicit Descriptions M.E. Bonilla, M. Malabre, pp 312-315 Even for fiat implicit linear systems (i.e.. having more state components that state equations), reachability is a well-defined concept in terms of the set of state trajectories: it characterizes the property that from any initial state a smooth state trajectory can start, which reaches any final state. What can happen, however, is that a system with no control input can be completely reachable. The notion of "external teachability" is introduced here, where trajectories can actually be controlled through the input (by proportional and derivative state feedback). Geometric necessary and sufficient conditions are given for external teachability. A new design method is proposed.
073 An Algebraic Definition of Time-Varying Transfer Matrices M. FHess, pp 316-318 Tensoring the module of a linear system with the quotient field of the ring of linear differential operators yields an algebraic framework where transfer matrices most naturally appear and which easily applies to the time-varying case. Several basic structural properties are examined: transfer algebra, matrix fraction decomposition and their connections with controllability
In the paper the problem of input-acceptance (i.e., the question of the extatence of a trajectory corresponding to a given input sequence) and output-uniqueness properties for a linear (respectively controlled and observed) implicit discrete-time system are introduced and saldied. Geometric and algebraic conditions for all considered properties are provided. It is shown that the input and output notions are dual counterparts. A natural interpretation of all the notions in terms of a linear von Neumann model of an economy is presented.
076 Remarks on Implicit Linear Continuous-Time Systems K.M. Przyluski, A. Sosnowskl, pp 328-331 Given a (not necessarily reqular or square) linear implicit system Ex (t)=Fx(t)+Gu(t), the space of admissible initial conditions and the controllable space of the system are studied. Distributional trajectories are considered.
077 Structural Properties of Singular Systems Part 2: Observability and Duality K. Oz~aldiran, pp 332-334 This paper investigates the structural properties of the (rectangular) singular system Ex'=Ax; y=Cx. It is shown that the very basic notion of observing an initial condition results in a number of different definitions of observability, depending on the way the output data is given. These different definitions are discussed and characterized geome¢ically.
078 An Exterior Algebra Based Characterization of the Fundamental Subspnces of Singular Systems U. Baser, N. Kareanins, pp 336-339 In this study, s¢ict equivalence invariants of a matrix pencil sF-G and the basic families of the subspaces corresponding to these invariants are charactea'i~.ed by means of Exterior Algebra. These results ~e used to characterlse some properties of the suprernal (A,E,B) invariant subspace (/s), supremal almost (E,A,B) is,