Robust Limit Cycle Amplitude Suppression for a Class of Uncertain Nonlinear Control Systems

2006 ◽  
Author(s):  
Yuan-Jay Wang
Keyword(s):  
Nonlinear Control ◽  
Control Systems ◽  
Limit Cycle ◽  
Nonlinear Control Systems ◽  
Cycle Amplitude ◽  
Limit Cycle Amplitude

Reduction of Limit Cycle Amplitude in the Presence of Backlash

1999 ◽  
Vol 121 (2) ◽  
pp. 278-284 ◽  
Author(s):  
Ronen Boneh ◽  
Oded Yaniv
Keyword(s):  
Nonlinear Control ◽  
Limit Cycle ◽  
Closed Loop ◽  
Controller Design ◽  
Linear Time ◽  
Design Technique ◽  
Feedback Systems ◽  
Mass System ◽  
Cycle Amplitude ◽  
Limit Cycle Amplitude

The majority of feedback systems driven by an electric motor can be represented by a two-mass system connected via a flexible drive element. Owing to the presence of backlash, the closed-loop performance such as precision speed, position and force control that can be achieved using a linear time invariant controller is limited, and it is expected that a nonlinear control would be superior. In this paper a nonlinear control structure is proposed and a systematic design technique presented. The advantages of the proposed design technique are: (i) It is robust to plant and backlash uncertainty; (ii) it is quantitative to specifications on the maximum limit cycle amplitude; and (iii) the closed loop is superior to a linear controller design both in lower bandwidth and in lower limit cycle amplitude. A design example is included.

A New Algorithm for Limit Cycle Analysis of Nonlinear Control Systems

1988 ◽  
Vol 110 (3) ◽  
pp. 272-277 ◽  
Author(s):  
V. K. Pillai ◽  
H. D. Nelson
Keyword(s):  
Nonlinear Control ◽  
Control Systems ◽  
Limit Cycle ◽  
Error Function ◽  
Numerical Procedure ◽  
Nonlinear Control Systems ◽  
Critical System ◽  
Describing Functions ◽  
The Stability ◽  
Generalized Newton

A numerical method is presented for the limit cycle analysis of multiloop nonlinear control systems with multiple nonlinearities. Describing functions are used to model the first harmonic gains of the nonlinearities. Existence of a limit cycle is sought by driving the least damped eigenvalues to the imaginary axis. The evolution of the limit cycle is studied next as a function of a critical system-parameter. It is shown that by defining a suitable error function it is possible to use both eigenvalue as well as the eigenvector sensitivities to formulate a generalized Newton-Raphson method to solve simultaneously for the updates of state variable amplitudes in a minimum norm sense. Several case studies have been presented and the development of a numerical procedure to test the stability of the limit cycle has also been reported.

Sign in / Sign up

Export Citation Format

Share Document