Limit-cycle prediction of a fuzzy control system based on describing function method

2000 ◽  
Vol 8 (1) ◽  
pp. 11-22 ◽  
Author(s):  
Euntai Kim ◽  
Heejin Lee ◽  
Mignon Park
Keyword(s):  
Control System ◽  
Fuzzy Control ◽  
Limit Cycle ◽  
Function Method ◽  
Describing Function ◽  
Fuzzy Control System ◽  
Describing Function Method

Stability Analysis of Nonlinear Dynamic Systems by Nonlinear Takagi–Sugeno–Kang Fuzzy Systems

2013 ◽  
Vol 136 (2) ◽  
Author(s):  
Zahra Namadchian ◽  
Assef Zare ◽  
Ali Namadchian
Keyword(s):  
Control System ◽  
Stability Analysis ◽  
Fuzzy Control ◽  
Limit Cycle ◽  
Phase Margin ◽  
Fuzzy Control System ◽  
Gain Margin ◽  
The Stability ◽  
Takagi Sugeno ◽  
System 1

This paper proposes a systematic procedure to address the limit cycle prediction of a Nonlinear Takagi–Sugeno–Kang (NTSK) fuzzy control system with adjustable parameters. NTSK fuzzy can be linearized by describing function method. The stability of the equivalent linearized system is then analyzed using the stability equations and the parameter plane method. After that the gain–phase margin (PM) tester has been added, then gain margin (GM) and phase margin for limit cycle are analyzed. Using NTSK fuzzy control system can help to have fewer rules. In order to analyze the stability with the same technique of stability analysis, the results of NTSK fuzzy control system will be compared with Dynamic fuzzy control system [1]. Computer simulations show differences between both systems.

Predicting the Autonomous Behaviour of Simple Nonlinear Feedback Systems

1990 ◽  
Vol 43 (10) ◽  
pp. 251-260
Author(s):  
D. P. Atherton
Keyword(s):  
Limit Cycle ◽  
Chaotic Motion ◽  
Function Method ◽  
Nonlinear Feedback ◽  
Feedback Systems ◽  
Describing Function ◽  
Relay Systems ◽  
Software Implementations ◽  
Describing Function Method ◽  
Nonlinear Feedback Systems

The paper examines in depth two approaches, namely the describing function and Tsypkin methods, for predicting the autonomous behaviour of simple nonlinear feedback systems. Both procedures are supported by software which, in the case of the describing function method, allows iteration to the exact limit cycle solution and, for both methods, enables display of resulting limit cycle waveforms. One advantage of the Tsypkin method, which is applicable primarily to relay systems, is that the exact stability of the limit cycle solution can be found. It is shown how this may be helpful in indicating the possibility of chaotic motion. Several examples are given to show the advantages and limitations of the software implementations of the methods.

Anti-Windup Control of Second-Order Plants With Saturation Nonlinearity

1993 ◽  
Vol 115 (4) ◽  
pp. 715-720 ◽  
Author(s):  
Ming C. Leu ◽  
Sangsik Yang ◽  
Andrew U. Meyer
Keyword(s):  
Control System ◽  
Control Systems ◽  
Real World ◽  
System Performance ◽  
Function Method ◽  
Second Order ◽  
Describing Function ◽  
Saturation Nonlinearity ◽  
Integral Action ◽  
Describing Function Method

All real-world control systems have saturation nonlinearity in final control elements (including actuators). When controllers involve integral action, reset windup can cause instability as well as make system performance unsatisfactory. Based on the describing function method and the generalized Popov criterion, this paper presents analysis of the global stability of a control system having a saturating second-order plant, both with and without using a deadbeat limiting scheme to constrain its controller output. The improvement of system performance by incorporating the anti-windup feature in the controller is illustrated by computer simulations.

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