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gelb_ch9_ocr - 9 OSCILLATIONS IN NONLINEAR SAMPLED-DATA...

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9 OSCILLATIONS IN NONLINEAR SAMPLED-DATA SYSTEMS 9.0 INTRODUCTION All the material of the preceding chapters has been concerned with systems which process signals continuously around the loop. This chapter takes under consideration the describing function analysis of nonlinear systems which at some point process discrete samples of signals. It should not come as a surprise that the analysis of nonlinear sampled-data systems is more complicated, or at least more laborious, than the corresponding analysis of nonlinear continuous-data systems. The treatment in this chapter considers just bias and single-sinusoid signals present at the input to the nonlinear part of the system. Even in the simplest case of a single sinusoid, the presence of another periodic process in the system-the sampling operation-gives rise to complications of the same kind as are encountered in the study of continu- ous systems with two sinusoidal components at the nonlinearity input. These complications are significant when the frequencies of the two periodic processes are rationally related, and this is the case of first importance in the study of nonlinear sampled-data systems.
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462 OSCILLATIONS IN NONLINEAR SAMPLED-DATA SYSTEMS Sampled-data systems have come into practical importance for a variety of reasons. The earliest of these had primarily to do with economy in the design and use of equipment. Many problems in impedance matching or power-level matching can be avoided if critical components are isolated- disconnected-most of the time, and the connection made only briefly at periodic intervals to read out a sample of the signal. The possibility of time- sharing one component among several systems also gives rise to a sampled form of signal processing. A major increase in interest in sampled-data systems was caused by the development of radar systems during the 1940s. Most radars provide information only in the form of periodic samples either because of a periodic scanning process or because of pulsed transmission of the microwave energy. A more recent surge of interest has been due to the increasing utilization of digital computers as controllers in feedback systems. In some areas of application, especially aerospace guidance and control, the use of discrete-data processors is often a practical necessity. Thus many system engineers find themselves concerned almost exclusively with the design of sampled-data systems. And as with continuous systems, these systems may be designed with, or otherwise may suffer from, a number of important nonlinear effects. THE EFFECTS OF SAMPLING In this chapter, as in most of the preceding material, attention is centered on systems which can be reduced to single-loop configurations having a single nonlinear part separated from the linear part. The linear part in this case may include any number of continuous linear elements and discrete, or pulsed, linear elements.
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gelb_ch9_ocr - 9 OSCILLATIONS IN NONLINEAR SAMPLED-DATA...

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