Chaotic study and chaos control in a half-vehicle model with semi-active suspension using discrete optimal Ott–Grebogi–Yorke method

Abstract

The chaotic dynamics along with the control of chaos in a half-car model with semi-active suspension system is considered in this paper. The time series responses, phase space trajectories, Poincaré sections, and Lyapunov exponent methods are used to analyze the chaotic behavior in the open-loop system. In order to suppress the chaotic responses in the system, a chaos controller is applied based on the development of Ott-Grebogi-Yorke algorithm. In this new control strategy, the Poincaré map of the system is estimated using the support vector machine innovatively. After linearization of the Poincaré map, the optimal discrete-time linear quadratic regulator is designed for the linear map as a main contribution. The discrete optimal Ott-Grebogi-Yorke controller improves the performance of the system along with the rejection of chaos in the responses. This improvement involves the reduction in settling time, control effort, and energy consumption in the suspension system.

Suppression of chaotic vibrations in suspension system of vehicle dynamics using chattering-free optimal sliding mode control

“…Also, behavior of the tires deflection can be Table 2 The values of the parameters of the system acceptable against the motion of tires on the sinusoidal profile road. Also, the results of feedback system under the optimal sliding mode control in this work are compared with the results of paper [2] especially, because the chaotic model of vehicle along with the parameters values in this work and paper [2] is totally similar. Also, chaos control algorithm in paper [2] is on the basis of the optimal OGY method.…”

“…In the semi-active suspension, the dynamical model of MR fluid damper with adjustable viscosity is derived on the basis of the modified Bouc-Wen model. The vertical displacement of the system is described using the second Newton's law, and the angular dynamics of the chassis is stated via the Euler equation as follows [1][2][3].…”

“…where and "n (1,2) " represents the nonlinearity order of the springs, and " ̇y (1,2) " is the internal velocity in the MR fluid damper computing as:…”

“…In the above optimal problem, the constraint is described as differential equations based on the dynamical model of the suspension system according to Eqs. (1)(2)(3)(4)(5)(6)(7)(8). In order to solve the optimal control, firstly, V(x) is selected as a candidate Lyapunov function.…”

“…In addition to the passengers comfort subject in the vehicles, the chaotic vibrations can be caused the fatigue failure in the components of chassis and suspension system. Consequently, the researchers are motivated recently to analyze and control the vertical oscillations based on chaos [1][2][3][4][5]. In the vibrational analysis of bounce motion, first problem is the distinction of chaotic vibrations from the stochastic oscillations.…”