Perturbation theory for nonlinear feedback control systems and spencer-goldschmidt integrability of linear partial differential equations

1990 ◽  
Vol 18 (1) ◽  
pp. 17-57 ◽  
Author(s):  
Robert Hermann
Keyword(s):  
Perturbation Theory ◽  
Partial Differential Equations ◽  
Feedback Control ◽  
Differential Equations ◽  
Control Systems ◽  
Nonlinear Feedback Control ◽  
Nonlinear Feedback ◽  
Partial Differential ◽  
Linear Partial Differential Equations ◽  
Feedback Control Systems

The Frequency Responses and Jump-Resonance Phenomena of Nonlinear Feedback Control Systems

1963 ◽  
Vol 85 (2) ◽  
pp. 236-242 ◽  
Author(s):  
H. Hatanaka
Keyword(s):  
Feedback Control ◽  
Control Systems ◽  
Amplitude Ratio ◽  
Nonlinear Feedback Control ◽  
Nonlinear Feedback ◽  
Frequency Responses ◽  
Input Amplitude ◽  
Resonance Phenomena ◽  
Feedback Control Systems ◽  
System Variables

A method is presented for analyzing the frequency responses and jump-resonance phenomena of nonlinear feedback control systems of any order. The nonlinearities treated in this paper are those whose outputs are single-valued odd functins of the inputs and are independent of frequencies of the inputs. The general conditions under which jump-resonance occurs are given and the system with saturation nonlinearity is analyzed fully as an example. The essential objective is to express the contours on the complex plane for the constant values of system variables, e.g., input amplitude, amplitude ratio, and phase shift.

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