Dunstan Graham

Intended for the practicing engineer, this is a complete survey of mathernatical methods for predicting and regulating the behavior of nonlinear control systems. Despite the existe,nce of powerful theoretical tools for dealing with linear constant-parameter systerns, the dificulties arising from actual practice demanded a different approach, and this book, first published in 1961, was a pioneer in presenting nrodels which could be applied to nonlinear behavior, whether accidental or show more intentional.
Beginning with a description and classification of nonlinearities, the authors list general techniques for the solution of nonlinear control problerns; direct solutions, approximate solutions in terms of infinite series, step by step integration and piecewise linear solutions; with an evaluation of the strengths and particular uses of each. There follows a thorough treatment of the describing function technique, including the use of sinusoidal functions for isolated nonlinear elements, quasi-linear closed loop systems and random input describing functious; and of the phase plane method, including phase plane trajectories for linear systems, the method of isoclines, special constructions in the phase plane, constructions for time and the piecewise linear analysis of trajectories.
The emphasis throughout is on application, and the theoretical material is illustrated with a wide variety of physically meaningful, practical examples. In addition, there are a large number of figures and tables presenting design data for the solution of specific problems. The cornbination of solid theory with a thorough understanding of the exigencies of practice makes this book extremely useful to both the student and the engineer concerned with the stability, accuracy, and response of nonlinear systems. show less