This chapter discusses the fundamental notions on polynomial algebra and polynomial equations which are used in control theory. Specially mentioned are operations of conjugacy.
本章讨论了控制理论中使用的多项式代数和多项式方程的基本概念。特别提到的是共轭运算。
{"title":"Polynomial Equations, Conjugacy and Symmetry","authors":"J. Ježek","doi":"10.1049/PBCE049E_CH9","DOIUrl":"https://doi.org/10.1049/PBCE049E_CH9","url":null,"abstract":"This chapter discusses the fundamental notions on polynomial algebra and polynomial equations which are used in control theory. Specially mentioned are operations of conjugacy.","PeriodicalId":290911,"journal":{"name":"IEE control engineering series","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116138263","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 chapter discusses the theory and practice of discrete time control (i.e. the sort that is implementable in computers) to achieve closed-loop control of continuous time processes. Thus, we are concerned with the discrete time control of continuous time processes within a hybrid feedback loop. A natural initial question suggests itself: what are the advantages of discrete, as opposed to continuous, controllers? The answer is very disappointing. As far as control theory is concerned, there are no advantages (the proof of this is that every realisable discrete time signal is a continuous time signal, but the converse is false). The reason for studying discrete time control is essentially practical: to allow reliable miniature low-cost digital electronic devices to be used as controllers.
{"title":"Discrete controller design","authors":"J. Leigh","doi":"10.1049/PBCE041E_CH1","DOIUrl":"https://doi.org/10.1049/PBCE041E_CH1","url":null,"abstract":"This chapter discusses the theory and practice of discrete time control (i.e. the sort that is implementable in computers) to achieve closed-loop control of continuous time processes. Thus, we are concerned with the discrete time control of continuous time processes within a hybrid feedback loop. A natural initial question suggests itself: what are the advantages of discrete, as opposed to continuous, controllers? The answer is very disappointing. As far as control theory is concerned, there are no advantages (the proof of this is that every realisable discrete time signal is a continuous time signal, but the converse is false). The reason for studying discrete time control is essentially practical: to allow reliable miniature low-cost digital electronic devices to be used as controllers.","PeriodicalId":290911,"journal":{"name":"IEE control engineering series","volume":"77 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116313521","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}
The outline of the chapter is as follows. We begin with a brief resume of relevant concepts and results from the theory of differential inclusions. The class of uncertain systems to be considered in then made precise. We continue with a treatment of the variable structure systems concept of an invariant subspace ℒ (with prescribed dynamic behaviour therein) and construct a discontinuous feedback strategy which renders if globally finite-time attractive (thereby ensuring ultimate attainment of prescribed dynamic behaviour). The approach is essentially that of Ryan & Corless (1984) (with origins in Corless & Leitmann, 1981), subsequently recast in a differential inclusion setting by Goodall & Ryan (1986, 1988). Finally, our results are extended to problems of tracking and model following.
{"title":"Subspace attractivity and invariance: Ultimate attainment of prescribed dynamic behaviour","authors":"E. Ryan","doi":"10.1049/PBCE040E_CH4","DOIUrl":"https://doi.org/10.1049/PBCE040E_CH4","url":null,"abstract":"The outline of the chapter is as follows. We begin with a brief resume of relevant concepts and results from the theory of differential inclusions. The class of uncertain systems to be considered in then made precise. We continue with a treatment of the variable structure systems concept of an invariant subspace ℒ (with prescribed dynamic behaviour therein) and construct a discontinuous feedback strategy which renders if globally finite-time attractive (thereby ensuring ultimate attainment of prescribed dynamic behaviour). The approach is essentially that of Ryan & Corless (1984) (with origins in Corless & Leitmann, 1981), subsequently recast in a differential inclusion setting by Goodall & Ryan (1986, 1988). Finally, our results are extended to problems of tracking and model following.","PeriodicalId":290911,"journal":{"name":"IEE control engineering series","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129313101","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}
The most widely used type of digital signal processor is the stored program monolithic processor, used for general purpose signal processing and other applications requiring fast arithmetic. These three DSPs have some features in common, such as fast, synchronous serial ports, special addressing modes and on-chip memory.
{"title":"DSP chips - a comparison","authors":"R. Chance","doi":"10.1049/PBCE042E_CH18","DOIUrl":"https://doi.org/10.1049/PBCE042E_CH18","url":null,"abstract":"The most widely used type of digital signal processor is the stored program monolithic processor, used for general purpose signal processing and other applications requiring fast arithmetic. These three DSPs have some features in common, such as fast, synchronous serial ports, special addressing modes and on-chip memory.","PeriodicalId":290911,"journal":{"name":"IEE control engineering series","volume":"128 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115550447","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 chapter discusses the control of uncertain system with negative dynamics. The prototype for the class of systems considered in this chapter consists of a dynamical process controlled by a feedback law acting on state data generated by sensor and implemented via actuator.
{"title":"Control of uncertain systems with neglected dynamics","authors":"M. Corless, G. Leitmann, E. Ryan","doi":"10.1049/PBCE040E_CH12","DOIUrl":"https://doi.org/10.1049/PBCE040E_CH12","url":null,"abstract":"This chapter discusses the control of uncertain system with negative dynamics. The prototype for the class of systems considered in this chapter consists of a dynamical process controlled by a feedback law acting on state data generated by sensor and implemented via actuator.","PeriodicalId":290911,"journal":{"name":"IEE control engineering series","volume":"3 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120816910","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}
The application of conventional 8 and 16 bit microcomputers to control systems is now well established. Such processors have general purpose (usually Von Neumann) architectures which make them applicable to a wide range of tasks, though not remarkably efficient in any. In control applications such devices may pose problems such as inadequate speed, difficulties with numerical manipulation and relatively high cost for the completed system. This latter being due to both the programming effort and the cost of the peripheral hardware. These problems may be overcome by the design of specially tailored architectures, provided that there is a sufficient volume of production to carry the overheads inherent in this approach. Special purpose I/O processors and signal processors are examples of applications where dedicated design has been successfully applied.
{"title":"Implementation of digital control algorithms","authors":"P. Witting","doi":"10.1049/PBCE042E_ch13","DOIUrl":"https://doi.org/10.1049/PBCE042E_ch13","url":null,"abstract":"The application of conventional 8 and 16 bit microcomputers to control systems is now well established. Such processors have general purpose (usually Von Neumann) architectures which make them applicable to a wide range of tasks, though not remarkably efficient in any. In control applications such devices may pose problems such as inadequate speed, difficulties with numerical manipulation and relatively high cost for the completed system. This latter being due to both the programming effort and the cost of the peripheral hardware. These problems may be overcome by the design of specially tailored architectures, provided that there is a sufficient volume of production to carry the overheads inherent in this approach. Special purpose I/O processors and signal processors are examples of applications where dedicated design has been successfully applied.","PeriodicalId":290911,"journal":{"name":"IEE control engineering series","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126725275","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}
In this chapter this second type of variable structure control system is described, beginning with scalar control systems. The basic structure, the sliding conditions and the state equations in the sliding mode will be considered. The pole assignment method will be used to design the switching strategy. Afterwards the sliding mode domain and the switching frequency will be studied. These theoretical considerations will be illustrated with a practical example, the position control of a DC drive. Next, for multivariable systems, the sliding mode conditions, the design of the multivariable switching strategy with a pole assignment method and robustness, i.e. invariance properties with regard to parameter variations, will be described.
{"title":"Sliding mode control with switching command devices","authors":"H. Buhler","doi":"10.1049/PBCE040E_CH2","DOIUrl":"https://doi.org/10.1049/PBCE040E_CH2","url":null,"abstract":"In this chapter this second type of variable structure control system is described, beginning with scalar control systems. The basic structure, the sliding conditions and the state equations in the sliding mode will be considered. The pole assignment method will be used to design the switching strategy. Afterwards the sliding mode domain and the switching frequency will be studied. These theoretical considerations will be illustrated with a practical example, the position control of a DC drive. Next, for multivariable systems, the sliding mode conditions, the design of the multivariable switching strategy with a pole assignment method and robustness, i.e. invariance properties with regard to parameter variations, will be described.","PeriodicalId":290911,"journal":{"name":"IEE control engineering series","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129013545","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}
In this chapter some of the issues related to the off-line design of single-input single-output (SISO) and multiple-input multiple-output (MIMO) control systems are discussed. Particular emphasis has been placed on the issues concerning the transfer of the expertise implicit in control theoretical knowledge into the design environment for general use by industrial design engineers. It is noted that considerable insight is obtained by the analysis of the procedures (both implicit and explicit) of classical SISO design.
{"title":"Expert system issues for multivariable control","authors":"D. Owens, F. Ahmed","doi":"10.1049/PBCE044E_CH17","DOIUrl":"https://doi.org/10.1049/PBCE044E_CH17","url":null,"abstract":"In this chapter some of the issues related to the off-line design of single-input single-output (SISO) and multiple-input multiple-output (MIMO) control systems are discussed. Particular emphasis has been placed on the issues concerning the transfer of the expertise implicit in control theoretical knowledge into the design environment for general use by industrial design engineers. It is noted that considerable insight is obtained by the analysis of the procedures (both implicit and explicit) of classical SISO design.","PeriodicalId":290911,"journal":{"name":"IEE control engineering series","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130215759","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}
The lack of well-tried and reliable knowledge engineering techniques has been a limiting factor in the development of expert systems. The initial successes of early systems resulted in too much emphasis being placed upon the bottom-up strategy for knowledge acquisition. At the present time the technology used for implementing knowledge based systems tends to exert too great an influence on the acquisition process itself. There is an urgent need for better tools to aid the knowledge acquisition process. In the process control area we need better tools for creating models of the process and relating these to operator actions and cognitive processes. There is also a need for tools to assist in validating expert systems since progress will almost certainly be limited by safety considerations.
{"title":"Knowledge engineering and process control","authors":"J. Alty","doi":"10.1049/PBCE044E_CH4","DOIUrl":"https://doi.org/10.1049/PBCE044E_CH4","url":null,"abstract":"The lack of well-tried and reliable knowledge engineering techniques has been a limiting factor in the development of expert systems. The initial successes of early systems resulted in too much emphasis being placed upon the bottom-up strategy for knowledge acquisition. At the present time the technology used for implementing knowledge based systems tends to exert too great an influence on the acquisition process itself. There is an urgent need for better tools to aid the knowledge acquisition process. In the process control area we need better tools for creating models of the process and relating these to operator actions and cognitive processes. There is also a need for tools to assist in validating expert systems since progress will almost certainly be limited by safety considerations.","PeriodicalId":290911,"journal":{"name":"IEE control engineering series","volume":"47 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131658293","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}
In this chapter two special problems of mixed H2/H∞ control have been presented. The corresponding two-degrees-of-freedom controller is made up by a feedforward part solving the underlying H∞ mixed sensitivity problem and by a feedforward part that can be carried out independently by solving an H2-norm optimization problem.
{"title":"Mixed H2/H∞ Stochastic Tracking and Servo Problems","authors":"A. Casavola, E. Mosca","doi":"10.1049/PBCE049E_CH4","DOIUrl":"https://doi.org/10.1049/PBCE049E_CH4","url":null,"abstract":"In this chapter two special problems of mixed H2/H∞ control have been presented. The corresponding two-degrees-of-freedom controller is made up by a feedforward part solving the underlying H∞ mixed sensitivity problem and by a feedforward part that can be carried out independently by solving an H2-norm optimization problem.","PeriodicalId":290911,"journal":{"name":"IEE control engineering series","volume":"191 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123086997","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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