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Phase-plane analysis of automatic control systems with nonlinear gain elements

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1 Author(s)
E. Rudolf Kalman ; E. I. du Pont de Nemours & Company, Wilmington, Del.

This paper develops a unified method of transient analysis of second-order feedback control systems having nonlinear gain components and subjected to step or ramp inputs. Essentially, the technique is a decomposition of the phase plane into linear regions within which trajectories converge to corresponding critical points. Application of the method to several typical problems previously analyzed by other means shows that considerably more insight may be obtained.

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Transactions of the American Institute of Electrical Engineers, Part II: Applications and Industry  (Volume:73 ,  Issue: 6 )