This report presents a methodology to design simple and effective high-performance tracking controllers for small AC electrical machines. By taking advantages of the two-time-scale property of small electrical machines, a second-order nonlinear dynamical model is derived from a singular perturbation formulation of the full-order model of a small electrical machine. A globally stable, maximum-torque adaptive controller is developed based on this reduced-order model. Simulation results show that this controller is comparable to controllers based on the full model. In addition, this controller is computationally very simple and requires fewer sensory measurements for feedback purposes.<>
{"title":"Nonlinear tracking control of small electrical machines","authors":"K. Chin, S.-J. Huang, M. Ilic, A. Zobian","doi":"10.1109/CDC.1994.411019","DOIUrl":"https://doi.org/10.1109/CDC.1994.411019","url":null,"abstract":"This report presents a methodology to design simple and effective high-performance tracking controllers for small AC electrical machines. By taking advantages of the two-time-scale property of small electrical machines, a second-order nonlinear dynamical model is derived from a singular perturbation formulation of the full-order model of a small electrical machine. A globally stable, maximum-torque adaptive controller is developed based on this reduced-order model. Simulation results show that this controller is comparable to controllers based on the full model. In addition, this controller is computationally very simple and requires fewer sensory measurements for feedback purposes.<<ETX>>","PeriodicalId":355623,"journal":{"name":"Proceedings of 1994 33rd IEEE Conference on Decision and Control","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1994-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114703898","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We point out that the natural definitions of stability and causality in input-output control theory lead to certain inconsistencies when inputs and outputs are allowed to have support on the doubly-infinite time-axis. In particular, systems with right half plane poles cannot be considered to be both causal and stabilizable. In contrast, there is no such conflict when the semi-infinite time axis is used.<>
{"title":"Intrinsic difficulties in using the doubly-infinite time axis for input-output systems theory","authors":"T. Georgiou, M.C. Smith","doi":"10.1109/CDC.1994.411548","DOIUrl":"https://doi.org/10.1109/CDC.1994.411548","url":null,"abstract":"We point out that the natural definitions of stability and causality in input-output control theory lead to certain inconsistencies when inputs and outputs are allowed to have support on the doubly-infinite time-axis. In particular, systems with right half plane poles cannot be considered to be both causal and stabilizable. In contrast, there is no such conflict when the semi-infinite time axis is used.<<ETX>>","PeriodicalId":355623,"journal":{"name":"Proceedings of 1994 33rd IEEE Conference on Decision and Control","volume":"155 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1994-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114905467","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Despite the digital revolution, very little work has been reported on the qualitative response features of linear, discrete-time systems. This paper considers systems having a rational transfer function which is strictly proper, has real coefficients, and satisfies a basic and natural condition concerning the dominant response mode. For this class, a fundamental theorem on initial overshoot is established. The definition of initial undershoot is extended beyond that which is usually discussed in the literature, and is able to include responses which grow without bound and which decay geometrically to zero. With regard to unit step responses, new results are presented for final overshoot. Lower bounds are proved for undershooting characteristics, insofar as they relate to real zeros, and sufficient conditions are given for these bounds to be achieved.<>
{"title":"Qualitative features of discrete-time system responses","authors":"L. H. Mcwilliams, M. Sain","doi":"10.1109/CDC.1994.411053","DOIUrl":"https://doi.org/10.1109/CDC.1994.411053","url":null,"abstract":"Despite the digital revolution, very little work has been reported on the qualitative response features of linear, discrete-time systems. This paper considers systems having a rational transfer function which is strictly proper, has real coefficients, and satisfies a basic and natural condition concerning the dominant response mode. For this class, a fundamental theorem on initial overshoot is established. The definition of initial undershoot is extended beyond that which is usually discussed in the literature, and is able to include responses which grow without bound and which decay geometrically to zero. With regard to unit step responses, new results are presented for final overshoot. Lower bounds are proved for undershooting characteristics, insofar as they relate to real zeros, and sufficient conditions are given for these bounds to be achieved.<<ETX>>","PeriodicalId":355623,"journal":{"name":"Proceedings of 1994 33rd IEEE Conference on Decision and Control","volume":"70 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1994-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116935059","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Solves the exact output tracking problem for nonlinear time-varying systems. The technique is even applicable in the nonminimum phase case, and uses an inverse trajectory for feedforward. The feedforward is coupled with a more conventional feedback control law for stable trajectory tracking. The inversion technique is new, even in the linear time-varying case, and relies on partitioning the linearized system dynamics into time-varying stable and unstable manifolds. This so-called dichotomic split is used to build time-varying filters which, in turn, are the basis of a contraction used to find the inverse trajectory. The method is local to the time-varying trajectory, but represents a significant advance relative to available tracking controllers which are restricted to time-invariant nonlinear systems, are much more difficult to compute than the scheme presented here, and track only asymptotically.<>
{"title":"Exact output tracking for nonlinear time-varying systems","authors":"Santosh Devasia, Brad Paden","doi":"10.1109/CDC.1994.411465","DOIUrl":"https://doi.org/10.1109/CDC.1994.411465","url":null,"abstract":"Solves the exact output tracking problem for nonlinear time-varying systems. The technique is even applicable in the nonminimum phase case, and uses an inverse trajectory for feedforward. The feedforward is coupled with a more conventional feedback control law for stable trajectory tracking. The inversion technique is new, even in the linear time-varying case, and relies on partitioning the linearized system dynamics into time-varying stable and unstable manifolds. This so-called dichotomic split is used to build time-varying filters which, in turn, are the basis of a contraction used to find the inverse trajectory. The method is local to the time-varying trajectory, but represents a significant advance relative to available tracking controllers which are restricted to time-invariant nonlinear systems, are much more difficult to compute than the scheme presented here, and track only asymptotically.<<ETX>>","PeriodicalId":355623,"journal":{"name":"Proceedings of 1994 33rd IEEE Conference on Decision and Control","volume":"461 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1994-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117015698","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper considers the problem of optimal guaranteed cost control of an uncertain system via output feedback. The uncertain system under consideration contains a single uncertainty block subject to an integral quadratic constraint. The cost function considered is a quadratic cost function defined over an infinite time interval. The main result of the paper gives a necessary and sufficient condition for the existence of a guaranteed cost controller guaranteeing a specified level of performance. This condition is given in terms of the existence of suitable solutions to an algebraic Riccati equation and a Riccati differential equation. The resulting guaranteed cost controller is in general time-varying.<>
{"title":"Output feedback guaranteed cost control of uncertain systems on an infinite time interval","authors":"A. Savkin, I. Petersen","doi":"10.1109/CDC.1994.411734","DOIUrl":"https://doi.org/10.1109/CDC.1994.411734","url":null,"abstract":"This paper considers the problem of optimal guaranteed cost control of an uncertain system via output feedback. The uncertain system under consideration contains a single uncertainty block subject to an integral quadratic constraint. The cost function considered is a quadratic cost function defined over an infinite time interval. The main result of the paper gives a necessary and sufficient condition for the existence of a guaranteed cost controller guaranteeing a specified level of performance. This condition is given in terms of the existence of suitable solutions to an algebraic Riccati equation and a Riccati differential equation. The resulting guaranteed cost controller is in general time-varying.<<ETX>>","PeriodicalId":355623,"journal":{"name":"Proceedings of 1994 33rd IEEE Conference on Decision and Control","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1994-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117074676","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
An overview of some of the existing important Krylov subspace methods that have been developed in the last few years for large-scale solutions of control problems, is given. These algorithms are suitable for large and sparse problems. Also included is a statement of a parallel-block algorithm for the Sylvester-observer matrix equation, suitable for high-performance computing. This is an emerging area of research. A need for an urgent and expanded research in the area of large-scale and parallel computations in control has been outlined in the NSF panel report (1988).<>
{"title":"Recent developments in large-scale and parallel matrix computations and their applications to linear control problems","authors":"B. Datta","doi":"10.1109/CDC.1994.410887","DOIUrl":"https://doi.org/10.1109/CDC.1994.410887","url":null,"abstract":"An overview of some of the existing important Krylov subspace methods that have been developed in the last few years for large-scale solutions of control problems, is given. These algorithms are suitable for large and sparse problems. Also included is a statement of a parallel-block algorithm for the Sylvester-observer matrix equation, suitable for high-performance computing. This is an emerging area of research. A need for an urgent and expanded research in the area of large-scale and parallel computations in control has been outlined in the NSF panel report (1988).<<ETX>>","PeriodicalId":355623,"journal":{"name":"Proceedings of 1994 33rd IEEE Conference on Decision and Control","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1994-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116292146","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper brings together results from a number of different areas in control theory to provide an algorithm for the synthesis of locally exponentially stabilizing control laws for a large class of driftless nonlinear control systems. The stability is defined with respect to a nonstandard dilation and is termed "/spl delta/-exponential" stability. The /spl delta/-exponential stabilization relies on the use of feedbacks which render the closed loop vector field homogeneous with respect to a dilation. These feedbacks are generated from a modification of Pomet's algorithm (1992) for smooth feedbacks. Converse Lyapunov theorems for time-periodic homogeneous vector fields guarantee that local exponential stability is maintained in the presence of higher order (with respect to the dilation) perturbing terms.<>
{"title":"Exponential stabilization of driftless nonlinear control systems via time-varying, homogeneous feedback","authors":"R. M’Closkey, R. Murray","doi":"10.1109/CDC.1994.411139","DOIUrl":"https://doi.org/10.1109/CDC.1994.411139","url":null,"abstract":"This paper brings together results from a number of different areas in control theory to provide an algorithm for the synthesis of locally exponentially stabilizing control laws for a large class of driftless nonlinear control systems. The stability is defined with respect to a nonstandard dilation and is termed \"/spl delta/-exponential\" stability. The /spl delta/-exponential stabilization relies on the use of feedbacks which render the closed loop vector field homogeneous with respect to a dilation. These feedbacks are generated from a modification of Pomet's algorithm (1992) for smooth feedbacks. Converse Lyapunov theorems for time-periodic homogeneous vector fields guarantee that local exponential stability is maintained in the presence of higher order (with respect to the dilation) perturbing terms.<<ETX>>","PeriodicalId":355623,"journal":{"name":"Proceedings of 1994 33rd IEEE Conference on Decision and Control","volume":"299302 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1994-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123450944","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
V. Andriano (Systems & Control Letters, vol. 20, p. 361-4, 1993) proved a result on global stabilizability of the angular velocity equations of a symmetric rigid body. The aim of this paper is to show that a simpler proof can be given for a general version of the result.<>
V. Andriano (Systems & Control Letters, vol. 20, p. 361-4, 1993)证明了对称刚体角速度方程全局稳定性的一个结果。本文的目的是证明一个更简单的证明可以给出一般版本的结果
{"title":"On global feedback stabilization of the angular velocity of a rigid body","authors":"R. Outbib","doi":"10.1109/CDC.1994.410944","DOIUrl":"https://doi.org/10.1109/CDC.1994.410944","url":null,"abstract":"V. Andriano (Systems & Control Letters, vol. 20, p. 361-4, 1993) proved a result on global stabilizability of the angular velocity equations of a symmetric rigid body. The aim of this paper is to show that a simpler proof can be given for a general version of the result.<<ETX>>","PeriodicalId":355623,"journal":{"name":"Proceedings of 1994 33rd IEEE Conference on Decision and Control","volume":"9 1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1994-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123651526","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study the existence and computation of extremal solutions of a system of inequations defined over lattices. Using the Knaster-Tarski fixed point theorem, we obtain sufficient conditions for the existence of supremal as well as infimal solution of a given system of inequations. Iterative techniques are presented for the computation of the extremal solutions whenever they exist, and conditions under which the termination occurs in a single iteration are provided. These results are then applied for obtaining extremal solutions of various inequations that arise in computation of maximally permissive supervisors in control of logical discrete event systems (DESs). Thus our work presents a unifying approach for computation of supervisors in a variety of situations.<>
{"title":"Extremal solutions of inequations over lattices with applications to supervisory control","authors":"Ratnesh Kumar, V. Garg","doi":"10.1109/CDC.1994.411720","DOIUrl":"https://doi.org/10.1109/CDC.1994.411720","url":null,"abstract":"We study the existence and computation of extremal solutions of a system of inequations defined over lattices. Using the Knaster-Tarski fixed point theorem, we obtain sufficient conditions for the existence of supremal as well as infimal solution of a given system of inequations. Iterative techniques are presented for the computation of the extremal solutions whenever they exist, and conditions under which the termination occurs in a single iteration are provided. These results are then applied for obtaining extremal solutions of various inequations that arise in computation of maximally permissive supervisors in control of logical discrete event systems (DESs). Thus our work presents a unifying approach for computation of supervisors in a variety of situations.<<ETX>>","PeriodicalId":355623,"journal":{"name":"Proceedings of 1994 33rd IEEE Conference on Decision and Control","volume":"141 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1994-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121964955","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
For a given implicit linear system, necessary and sufficient conditions for the existence of a feedback gain such that all finite eigenvalues of the resulting closed-loop system lie in a fixed subset of C are presented. The existence of a feedback gain satisfying some additional requirements is also considered.<>
{"title":"Remarks on feedback stabilization of implicit linear systems","authors":"K. Przyluski, A. Banaszuk","doi":"10.1109/CDC.1994.411271","DOIUrl":"https://doi.org/10.1109/CDC.1994.411271","url":null,"abstract":"For a given implicit linear system, necessary and sufficient conditions for the existence of a feedback gain such that all finite eigenvalues of the resulting closed-loop system lie in a fixed subset of C are presented. The existence of a feedback gain satisfying some additional requirements is also considered.<<ETX>>","PeriodicalId":355623,"journal":{"name":"Proceedings of 1994 33rd IEEE Conference on Decision and Control","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1994-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117164608","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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