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MULTIPLE-INPUT DESCRIBING FUNCTIONS AND NONLINEAR SYSTEM DESIGN Arthur Gelb, Sc.D. President and Technical Director The Analytic Sciences Corporation Reading, Massachusetts Wallace E. Vander Velde, Sc.D. Professor of Aeronautics and Astronautics Massachusetts Institute of Technology Cambridge, Massachusetts New York St. Louis Sun Francisco Toronto London Sydney MU L T I P L E - I N P U T D E S C R I B I N G F U N C T I O N S A N D N O N L I N E A R SYSTEM D E S I G N McGraw-Hill Electr
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  MULTIPLE-INPUT DESCRIBING FUNCTIONS AND NONLINEAR SYSTEM DESIGN Arthur Gelb Sc.D. President and Technical Director The Analytic Sciences Corporation Reading Massachusetts Wallace E Vander Velde Sc.D. Professor of Aeronautics and Astronautics Massachusetts Institute of Technology Cambridge Massachusetts ew York St Louis Sun Francisco Toronto London Sydney    ULTIPLE INPUT DESCRIBING FUNCTIONS AND NONLINEAR SYSTEM DESIGN  McGraw Hill Electronic Sciences Series Editorial Board Ronald Bracewell Colin Cherry Willis W Harman Edward W Herold John G Linvill Simon Ramo John G Truxal BR MSON Information theory and coding BATTIN Astronautical guidance BLACHMAN Noise and its effect on communication BREMER Superconductive devices BROXMEYER Inertial navigation systems GELB AND VANDER VELDE Multiple-input describing functions and nonlinear system design GILL Introduction to the theory of finite-state machines HANCOCK ND WINTZ Signal detection theory HUELSMAN Circuits, matrices, and linear vector spaces KELSO Radio ray propagation in the ionosphere MERRI M Optimization theory and the design of feedback control systems MUUM Biological control systems analysis NEWCOMB Linear multiport synthesis PAPOULIS The fourier integral and its applications R. N. BRACEWELL) TEINBERG AND LEQUEUX TRANSLATOR Radio astronomy WEEKS Antenna engineering  PREFACE The theory of automatic control has been advanced in important ways during recent years particularly with respect to stability and optimal control. These are significant contributions which appeal to many workers including the writers because they answer important questions and are both theoretically elegant and practically useful. These theories do not however lay to rest all questions of importance to the control engineer. The designer of the attitude control system for a space vehicle booster which for simplicity utilizes a rate-switched engine gimbal drive must know the characteristics of the limit cycle oscillation that the system will sustain and must have some idea of how the system will respond to attitude commands while continuing to limit-cycle. The designer of chemical process control system must be able to predict the transient oscillations the process may experience during start-up due to the limited magnitudes of important variables in the system. The designer of a radar antenna pointing system with limited torque capability must be able to predict the rms pointing error due to random wind disturbances on the antenna and must understand how these random disturbances will influence the behavior of the system in its response to command inputs. But more important than just being able to evaluate how a given system will behave in a postulated situation is the fact that these control engineers must esign their
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