The feedback control-system design methods presented in previous chapters were restricted to linear constant systems, that is, systems that can be represented by linear differential equations with constant coefficients. In practice, linear systems possess the property of linearity only over a certain range of operation; all physical systems are nonlinear to some degree. Therefore it is important that one acquire a facility for analyzing control systems with varying degrees of nonlinearity.

Any attempt to restrict attention strictly to linear systems can only result in severe complications in system design. To operate linearly over a wide range of variation of signal amplitude and frequency would require components of an extremely high quality; such a system would probably be impractical from the viewpoints of cost, space, and weight. In addition, the restriction of linearity severely limits the system characteristics that can be realized.

In practice, linear operation is required only for small deviations about a quiescent operating point. The saturation of amplifying devices having large deviations about the quiescent operating point is usually acceptable. The presence of nonlinearities in the form of dead zones for small deviations about the quiescent operating point is also usually acceptable. In both cases one attempts to limit the effects of nonlinearities to acceptable tolerances, as it is impractical to eliminate the problem ...

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