Research On Chaos And Its Control Of Planar Closed Underactuated Mechanism

Chaos refers to a phenomenon which seems irregular and random in a deterministic system and is very sensitive to the initial conditions of the system. During the last ten years, chaotic science has been studied in various aspects of natural science and social science. At present the studies of chaos is being shifted from observation and study on some samples of chaos to investigation the mutual interaction and relationship among all kinds of chaos, and finding out the common rule and methods to deal with such complex problems. It is the great worthiness in science and applications in the future that make study of chaos and its control become a hot topic in the nonlinear science.Underactuated mechanism is a mechanism in which the number of independent driver is less than its number of degrees of freedom. In the past ten years, the analysis and control of underactuated system have attracted a large number of researchers. However, the closed underactuated mechanism, on which emphasis of this thesis is placed, has rarely been studied. To this end, the main work is the follo wings:1. Based on the theory of chaos, a new scheme to analyze chaotic system is proposed by employing MATLAB. Once the dynamic equations of the system are established, a model of Simulink can be also established only by manipulating computer mouse. Having set some necessary parameters, the simulation of the motion for the system can be carried out. The outputs of simulation can be directly utilized to plot the phase portraits, and further more produce the power spectra by using fast Fourier transformation. Whether or not the system exists chaotic motion will be determined by the phase portraits and power spectra. The scheme can be regarded as a simple but efficient method to analyze a chaotic system.2. A planar closed underactuated mechanism is focused on. The dynamic model of the system is established by employing Lagrange's formulation, and the simulation is carried out using MATLAB. The time domain waveform, power spectra, phase locus, Poincare maps and lyapunov exponent for the motion of the mechanism are obtained. The results show that there exists chaotic motion under some circumstances. The influence of the input speed of the independent driver on the motion of the mechanism is analyzed. The results show that the different input speeds will conduce to different dynamic responses of the mechanism, the bifurcation diagram with the input speed is plotted.3. An idea to unify the parameters for negative feedback control of a chaotic system is proposed. Linear negative feedback control is a simple and easy to be implemented method to control a multi-dimensional dynamic system. However, choosing the controlling parameters seems to be a hard task because there is no any efficient rule to deal with it at present. If taking all the controlling parameters at the same value, one can get the condition for the value that will lead the system to a regular motion by Routh-Hurwitz criterion. This idea is demonstrated by two examples, one is to control a chaotic circuit system toward a fixed point and another is to control the chaotic motion of the underactuated mechanism toward periodical motion.