In this chapter we concentrate our attention on the problem of state observation of nonlinear dynamical systems whose nonlinearities/uncertainties are bounded. The main tool used in the design of observers for such systems is the Lyapunov method.
{"title":"State observation of nonlinear control systems via the method of Lyapunov","authors":"S. Żak, B. Walcott","doi":"10.1049/PBCE040E_CH16","DOIUrl":"https://doi.org/10.1049/PBCE040E_CH16","url":null,"abstract":"In this chapter we concentrate our attention on the problem of state observation of nonlinear dynamical systems whose nonlinearities/uncertainties are bounded. The main tool used in the design of observers for such systems is the Lyapunov method.","PeriodicalId":290911,"journal":{"name":"IEE control engineering series","volume":"249 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":"116524359","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 main goal of this chapter is to describe new tools in the analysis of discontinuous control systems and to show, with some significant control problems, how the VSC approach yields efficient and robust control, compared with other techniques used to deal with the same problems.
{"title":"Some extensions of variable structure control theory for the control of nonlinear systems","authors":"G. Bartolini, T. Zolezzi","doi":"10.1049/PBCE040E_CH14","DOIUrl":"https://doi.org/10.1049/PBCE040E_CH14","url":null,"abstract":"The main goal of this chapter is to describe new tools in the analysis of discontinuous control systems and to show, with some significant control problems, how the VSC approach yields efficient and robust control, compared with other techniques used to deal with the same problems.","PeriodicalId":290911,"journal":{"name":"IEE control engineering series","volume":"41 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":"128540566","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 has essentially two goals: first it introduces a new variable structure controller using a canonical system representation, orthogonal sliding hyperplanes, and a straightforward synthesis and analysis procedure. The second goal is more didactically oriented. Some basic facts of VSC will become evident from the special formulation. In first section it has been shown that the canonical formulation and the rank conditions are equivalent. In second section the new controller is presented which consists of two distinct terms. The first is linear state feedback which produces a pole-zero cancellation leaving only integrators in the transfer matrix of the known part of the system. The second term, a relay type controller, forces the initially nonzero outputs to zero and stabilises the pole-zero cancellation in the presence of parameter disturbances. In third section some interesting remarks on the nature of sliding variable structure systems are listed. Fourth section shows that the presented regulator can be modified in a straightforward way in order to accomplish the requirements of model-following VSC . The numerical example demonstrates the synthesis and analysis procedure.
{"title":"Canonical formulation and general principles of variable structure controllers","authors":"L. Guzzella, H. Geering","doi":"10.1049/PBCE040E_CH6","DOIUrl":"https://doi.org/10.1049/PBCE040E_CH6","url":null,"abstract":"This chapter has essentially two goals: first it introduces a new variable structure controller using a canonical system representation, orthogonal sliding hyperplanes, and a straightforward synthesis and analysis procedure. The second goal is more didactically oriented. Some basic facts of VSC will become evident from the special formulation. In first section it has been shown that the canonical formulation and the rank conditions are equivalent. In second section the new controller is presented which consists of two distinct terms. The first is linear state feedback which produces a pole-zero cancellation leaving only integrators in the transfer matrix of the known part of the system. The second term, a relay type controller, forces the initially nonzero outputs to zero and stabilises the pole-zero cancellation in the presence of parameter disturbances. In third section some interesting remarks on the nature of sliding variable structure systems are listed. Fourth section shows that the presented regulator can be modified in a straightforward way in order to accomplish the requirements of model-following VSC . The numerical example demonstrates the synthesis and analysis procedure.","PeriodicalId":290911,"journal":{"name":"IEE control engineering series","volume":"46 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":"120966922","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 considers the problem of obtaining memoryless stabilising feedback controllers for uncertain dynamical systems described by ordinary differential equations. Various classes of controllers are presented. The design of all these controllers is based on Lyapunov theory. The results to obtain tracking controllers for a general class of uncertain mechanical systems was utilised. These controllers are illustrated by application to a model of the Manutec r 3 robot which has an uncertain payload. Before proceeding with the problem, some basic notions and results for ordinary differential equations is introduced.
{"title":"Deterministic control of uncertain systems : a Lyapunov theory approach","authors":"M. Corless, G. Leitmann","doi":"10.1049/PBCE040E_CH11","DOIUrl":"https://doi.org/10.1049/PBCE040E_CH11","url":null,"abstract":"This chapter considers the problem of obtaining memoryless stabilising feedback controllers for uncertain dynamical systems described by ordinary differential equations. Various classes of controllers are presented. The design of all these controllers is based on Lyapunov theory. The results to obtain tracking controllers for a general class of uncertain mechanical systems was utilised. These controllers are illustrated by application to a model of the Manutec r\u00003 robot which has an uncertain payload. Before proceeding with the problem, some basic notions and results for ordinary differential equations is introduced.","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":"132166700","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 describes the role of symbolic computation in several phases of the control system design cycle, namely modelling, analysis and synthesis. It provides some mathematical background of nonlinear system theory and presents a guided tour through those phases using typical examples, both contrived and real life. To name them, the symbolic computation of (i) the zero dynamics, used for different purposes, (ii) the input-output exact linearising state feedback, and (iii) the state-space exact linearising state feedback, all for nonlinear dynamic systems, are discussed. The examples come from a diverse range of applications and provide a picturesque landscape of this area of research. The possibilities and limitations of the so-called NON^CON package, based on the symbolic computation program Maple, are outlined with these examples. This package was developed to aid with analytical computations in the area of nonlinear control systems.
{"title":"Symbolic aids for modelling, analysis, and synthesis of nonlinear control systems","authors":"De Jager","doi":"10.1049/PBCE056E_CH12","DOIUrl":"https://doi.org/10.1049/PBCE056E_CH12","url":null,"abstract":"This chapter describes the role of symbolic computation in several phases of the control system design cycle, namely modelling, analysis and synthesis. It provides some mathematical background of nonlinear system theory and presents a guided tour through those phases using typical examples, both contrived and real life. To name them, the symbolic computation of (i) the zero dynamics, used for different purposes, (ii) the input-output exact linearising state feedback, and (iii) the state-space exact linearising state feedback, all for nonlinear dynamic systems, are discussed. The examples come from a diverse range of applications and provide a picturesque landscape of this area of research. The possibilities and limitations of the so-called NON^CON package, based on the symbolic computation program Maple, are outlined with these examples. This package was developed to aid with analytical computations in the area of nonlinear control systems.","PeriodicalId":290911,"journal":{"name":"IEE control engineering series","volume":"15 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":"133861756","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 review a brief summary is given of the current trends and new directions in the development of algorithms, architectures and devices for signal processing. This, of necessity, is a personal view point, nevertheless, with significant new developments over the horizon, the subject area of signal processing is set to grow and grow. As a final statement, the integration of fast algorithms, parallel architectures, and high performance multiprocessors, the field of parallel signal processing and its applications is one which will lead to rich rewards.
{"title":"Review and outlook for the future","authors":"T. Durrani","doi":"10.1049/PBCE042E_CH28","DOIUrl":"https://doi.org/10.1049/PBCE042E_CH28","url":null,"abstract":"In this review a brief summary is given of the current trends and new directions in the development of algorithms, architectures and devices for signal processing. This, of necessity, is a personal view point, nevertheless, with significant new developments over the horizon, the subject area of signal processing is set to grow and grow. As a final statement, the integration of fast algorithms, parallel architectures, and high performance multiprocessors, the field of parallel signal processing and its applications is one which will lead to rich rewards.","PeriodicalId":290911,"journal":{"name":"IEE control engineering series","volume":"136 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":"123257220","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 self-tuning control can in certain process control problems lead to improvements in economic, safety and control performance. However, the components of a self-tuning controller are more complex than conventional loop controllers and require considerable knowledge of a variety of advanced algorithmic techniques. In addition, as much detailed process specific knowledge as possible must be built into the self-tuner in order to select good design parameters for a given application. We identify a two-way knowledge threshold which must be crossed before self tuning control can be used and fully exploited on industrial processes. This chapter examines the components of the knowledge threshold present for self tuning controllers and considers some possible solutions. The use of expert systems to lower the knowledge threshold is discussed with reference to a prototype system.
{"title":"Expert systems for self-tuning control","authors":"K. Hunt, G. Worship","doi":"10.1049/PBCE044E_CH13","DOIUrl":"https://doi.org/10.1049/PBCE044E_CH13","url":null,"abstract":"The application of self-tuning control can in certain process control problems lead to improvements in economic, safety and control performance. However, the components of a self-tuning controller are more complex than conventional loop controllers and require considerable knowledge of a variety of advanced algorithmic techniques. In addition, as much detailed process specific knowledge as possible must be built into the self-tuner in order to select good design parameters for a given application. We identify a two-way knowledge threshold which must be crossed before self tuning control can be used and fully exploited on industrial processes. This chapter examines the components of the knowledge threshold present for self tuning controllers and considers some possible solutions. The use of expert systems to lower the knowledge threshold is discussed with reference to a prototype system.","PeriodicalId":290911,"journal":{"name":"IEE control engineering series","volume":"31 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":"125406252","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 case study illustrates the now classical Linear Predictive Coding (LPC) method of speech compression used to reduce the bit rate in digital speech transmission systems. The chapter begins with a non-rigerous introduction to the theory of linear predictive coding. This is followed by an explanation of the real-time algorithms used to calculate the parameters required to synthesise individual pitches of voiced speech. The study ends with a description of how these algorithms are implemented on the TMS32010, the problems incurred and results obtained.
{"title":"Speech processing using the TS32010 - a case study","authors":"R. E. Stone","doi":"10.1049/PBCE042E_CH25","DOIUrl":"https://doi.org/10.1049/PBCE042E_CH25","url":null,"abstract":"This case study illustrates the now classical Linear Predictive Coding (LPC) method of speech compression used to reduce the bit rate in digital speech transmission systems. The chapter begins with a non-rigerous introduction to the theory of linear predictive coding. This is followed by an explanation of the real-time algorithms used to calculate the parameters required to synthesise individual pitches of voiced speech. The study ends with a description of how these algorithms are implemented on the TMS32010, the problems incurred and results obtained.","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":"127492971","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}
Much work has been done in developing basic representational paradigms for the qualitative representation of complex systems. This work, however, is just the beginning. Much more needs to be done in determining the relationship between the various approaches so that the systems modeller can select the most appropriate method for the particular problem under study. Also, further work on developing other quantity spaces that reduce the qualitative ambiguity and hence result in less spurious behaviors needs to be done. Finally, realistic applications need to be tack led to determined whether these techniques will 'scale-up' to real size practical applications.
{"title":"A review of the approaches to the qualitative modelling of complex systems","authors":"R. Leitch","doi":"10.1049/PBCE044E_CH6","DOIUrl":"https://doi.org/10.1049/PBCE044E_CH6","url":null,"abstract":"Much work has been done in developing basic representational paradigms for the qualitative representation of complex systems. This work, however, is just the beginning. Much more needs to be done in determining the relationship between the various approaches so that the systems modeller can select the most appropriate method for the particular problem under study. Also, further work on developing other quantity spaces that reduce the qualitative ambiguity and hence result in less spurious behaviors needs to be done. Finally, realistic applications need to be tack led to determined whether these techniques will 'scale-up' to real size practical applications.","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":"115161349","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}
Control engineers have not been slow in making use of recent developments in artificial neural networks: a pioneering paper was written by Narendra and Partnasarathy and more recent developments are surveyed in this book. Neural networks allow many of the ideas of system identification and adaptive control originally applied to linear (or linearised) systems to be generalised, so as to cope with more severe nonlinearities. Such strong nonlinearities occur in a number of applications e.g. in robotics or process control. Two possible schemes for 'direct' adaptive and 'indirect' adaptive control are shown and other schemes will be found elsewhere in this book, but in this chapter we shall concentrate on the modelling to be carried out by the artificial neural networks.
{"title":"Selection of neural network structures : some approximation theory guidelines","authors":"J. Mason, P. Parks","doi":"10.1049/PBCE053E_CH4","DOIUrl":"https://doi.org/10.1049/PBCE053E_CH4","url":null,"abstract":"Control engineers have not been slow in making use of recent developments in artificial neural networks: a pioneering paper was written by Narendra and Partnasarathy and more recent developments are surveyed in this book. Neural networks allow many of the ideas of system identification and adaptive control originally applied to linear (or linearised) systems to be generalised, so as to cope with more severe nonlinearities. Such strong nonlinearities occur in a number of applications e.g. in robotics or process control. Two possible schemes for 'direct' adaptive and 'indirect' adaptive control are shown and other schemes will be found elsewhere in this book, but in this chapter we shall concentrate on the modelling to be carried out by the artificial neural networks.","PeriodicalId":290911,"journal":{"name":"IEE control engineering series","volume":"34 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":"114134106","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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