International Journal of Information and Electronics Engineering, Vol. 2, No. 4, July 2012
Designing BELBIC to Stabilize Gyro Chaotic System
Alireza Khalilzadeh and Masoud Taleb Ziabari
has attributes of great utility to navigational, aeroneutical and Abstract—One of the most significantphenomenon in some space engineering, and has been widely studied. Generally, systems is chaos; so control chaotic system is troublesomeand gyros are understood to be devices which rely on inertial shows the abilities of control methods. Brain emotional learning measurement to determine changes in the orientation of an based intelligent controller (BELBIC) is an intelligent object. Gyros are recently finding application in automotive controller based on the model of emotional part of brain. In this article, BELBIC is applied to stabilize Gyro chaotic system. The systems for Smart Braking System, in which different brake contribution of BELBIC in improving the control system forces are applied to the rear tyres to correct for skids. performance is shown by in comparison with results obtained Recently, presented the dynamic behavior of a symmetric from backstepping controller. BELBIC stabilizes Gyro Chaos gyro with linear-plus-cubic damping, which is subjected to a with Shorter Setting Time and Lower Control Signal than harmonic excitation and the Lyapunov direct method was backstepping controller. used to obtain the sufficient conditions of the stability of the
Index Terms—Stability, belbic, arneodo Chaos, backstepping equilibrium points of the system. method The equation governing the motion of the gyro after necessary transformation is given by[8]:
I. INTRODUCTION (1)
Chaos, as an significant theme in nonlinear proficiency, 3 xbx= g(x )-ax−+β sin sin x x + has been examined and studied in arithmetical and physical 2122 12 communities in the recent years and the research attempts ftxusin sin sin sin ω 1 + have dedicated to chaos control and chaos synchronization problems in abundant dynamical systems. where and is control input. The In [1] suggested a more effective technique which uses a parameters of the system are chosen time-delayed feedback to certain dynamical variables of the 2 αβ======100, 1,ab 0.5, 0.05, ω 2, f 35.5 and the system. Control of spatiotemporal chaos in partial differential initial condition is , 1, 1 . The nonlinear gyro equations was also regarded [2], [3]. On the other side, given by equation.1 exhibits varieties of dynamic behavior sliding manner control, backstepping control, feedback including chaotic motion without control signal is displayed linearization and active control can be mentioned as some in "Fig.1" and "Fig.2". often used techniques of the second type [4]-[7]. In recent years, the uses of biologically inspired methods 4 3 such as the evolutionary algorithm have been increasingly 2 employed to solve and analyze complex computational 1 problems. The main contribution of this article is controlling 0 chaos in Arneodo system using Brain emotional learning X2 State -1 based intelligent controller (BELBIC). BELBIC is an -2 intelligent controller dependent upon the model of -3 -4 sentimental part of brain. -1.5 -1 -0.5 0 0.5 1 1.5 The paper is organized as follows. Section 2 describes X1 State Gyro chaotic system. Section 3 presents a brain emotional Fig. 1. Show the phase portrait of gyro system 4 based teach intelligent controller (BELBIC) and it is applied X1 X2 to stabilize Gyro chaotic system. In section 4 simulation 2 results of Gyro chaotic system is represented. In section 5 the overall discussion of the simulation results for different 0 systems presented. Section 6 provides conclusion of the State Trajectory study. -2
-4 0 5 10 15 20 25 II. GYRO CHAOTIC SYSTEM Time (sec) Fig. 2. Show the states trajectory variation for gyro system The model system which we study is the gyroscope which
Manuscript received April 17, 2012; revised May 30, 2012. III. BELBIC CONTROLLER The authors are with Faculty of Engineering, Computer Architect Group, Islamic Azad University Rudehen Branch, Iran (e-mail: BELBIC is the abbreviation for brain emotional learning [email protected]) based intelligent controller [9], [10]. Motivated by the
531 International Journal of Information and Electronics Engineering, Vol. 2, No. 4, July 2012