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Describing function analysis of uncertain fuzzy vehicle control systems

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Abstract

In this paper, some useful frequency domain methods including describing function, parameter space, and Kharitonov approach are applied to analyze the stability of an uncertain fuzzy vehicle control system for limit cycle prediction. A systematic procedure is proposed to solve this problem. The fuzzy controller can be linearized by the use of classical describing function firstly. By doing so, it is feasible to treat the stability problem of a fuzzy control system as linear one. In order to consider the robustness of a fuzzy vehicle control system, parameter space method and Kharitonov approach are then employed for plotting the stability boundaries. Furthermore, the effect of transport delay is also addressed. More information of limit cycles can be obtained by this approach. This work shows that the limit cycles caused by a static fuzzy controller can be easily suppressed if the system parameters are chosen carefully.

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Abbreviations

V i :

Voltage applied to the throttle valve

V :

Forward velocity of the vehicle

p 1(V), p 2(V), p 3(V):

Nonlinear velocity–dependent functions

T p (V):

Function with the propulsion system and the roadway interface

ψ(V):

Function with the tire–roadway interface

k p , k d , k u :

Scaling factors of fuzzy control system

a, b, c :

Perturbation parameters

M i :

Fuzzy variables

Ω i (x):

Fuzzy basis function

Φ i :

Fuzzy membership functions

e(t):

Error signal

x(t):

Reference input signal

K 1(s), K 2(s), K 3(s), K 4(s):

Kharitonov polynomials

q i :

Uncertainty

u(x):

Static fuzzy control

N 1 :

Describing function

A :

Amplitude of limit cycle

δ i :

Angles

α, β:

Adjustable parameters

ω:

Frequency

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Authors and Affiliations

  1. Department of Mechanical and Electro-Mechanical Engineering, National Sun Yat-sen University, 70, Lienhai Road, Kaohsiung, 80424, Taiwan, ROC

    Jau-Woei Perng

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  1. Jau-Woei Perng
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Correspondence to Jau-Woei Perng.

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Perng, JW. Describing function analysis of uncertain fuzzy vehicle control systems. Neural Comput & Applic 21, 555–563 (2012). https://doi.org/10.1007/s00521-011-0532-7

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  • DOI: https://doi.org/10.1007/s00521-011-0532-7

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