Nonlinear Dynamical Analysis,Control And Their Applications

As we all know, the world is nonlinear in essence. Actually, what we have got based on linear theory is approximate average value of the world. Therefore, it is very interesting to study chaos and bifurcation of nonlinear systems, for that we can understand the nature of the things more deeply. As for Hydropower system, it is a complex nonlinear system including hydro system, mechanical system and electrical system. In production practice, stability is a universal problem for hydropower system in all over the world. Also, it is hard to control. Correspondingly, the capacity of the hydropower is becoming larger and larger, and the requirement of the system is increasing higher and higher. Therefore, we study new physical system, physical phenomenon, new law and physical concepts by using nonlinear dynamics theory, and try to apply it to the stability analysis of the hydropower system.The contents and conclusions of this paper include:(1) A new three dimentional chaotic system was presented here. Then, we can get a new double-wing chaotic system by the absolute operation of a linear term. It shows that a slight change on the secondary part can change the mainly characters of the whole system, for that we all know that nonlinear is a requirement to the occurance of chaos, in other words, nonlinear term is the main part of the system. Finally, the circuit diagram was also derived. Its experimental results are agreement with the numerical simulation.(2) A new multi-scroll chaotic system was presented by using a new piecewise function. Moreover, the circuit diagram was also designed, the experimental results in which are agreement with numerical simulation. We can get conclusion that the phase trajectories, Poincare maps and bifurcation diagram are all uniform and can describe different aspects of the dynamical system.①the numbers of circles in fractal structure in Poincare maps is gradually increasing with the increase of the scroll number. Therefore, the phase trajectories and Poincare maps are agreement with each other. In other words, they are consistent in essence.②The number of dense points is consistent with the number of the scrolls. Obviously, the number of dense points region is increasing with the number of the scrolls. In other words, they are equal to each other. In the future, we can judge the number of the attractors by confirming the number of the dense points region in bifurcation diagram, while the attractors are more intuitive from the phase trajectories maps.At last, we cam get that the phase trajectories, Poincare maps and bifurcation diagram are all uniform and can describe different aspects of the dynamical system.(3) A new four-dimentional fractional-order chaotic system and a new double-wing fractional-order chaotic system were derived including circuit diagram.(4) As for chaos control, we first study the sliding mode control with bounded noise, and discuss the no-chattering sliding mode control by using saturation funciton. Furthermore, we also study the effection of different reaching rate. Second, we also study the control of a class of chaotic systems by using three typical examples. Finally, we implemented a class of four dimentional hyperchaotic systems with only one controller term.(5) As for chaos synchronization, I try to bridge the fractional order chaotic system and integer order chaotic system by reaching the synchronization of fractional-order chaotic system and integer order chaotic sytem based on LMI. We also point that synchronization and anti-synchronization are unified with each other. They could be realized by the same method. Furthermore, we get a conclusion that chaos control is a special case of chaos synchronization, and chaos synchronization is a generalized concept of chaos control. Finally, a class of n-dimentional chaotic systems was realized via fuzzy sliding mode control, which is also suitable for complex networks.(6) As for circuit design, a circuit diagram of chaos synchronization via mismatch synchronization. Also, a circuit diagram of fractional order chaotic synchronization via nonlinear feedback control. Finally, a unit circuit of response system was presented, which is suitable for any fractional-order or integer order chaotic system, which was proved by two typical examples. It is the first time to reach synchronization of fractional-order and integer order chaotic systems. After this work, the secure communication will meet new change based on chaotic circuit.(7) A new dynamical model for the hydro-turbine governing system with elastic water hammer-impact and the second order model of generator was established, which is based on the model of simple surge shaft. By virtue of bifurcation diagram, Poincare maps, the power spectrum diagram, the time domain diagram, the orbits diagram and the spectrum diagram, the nonlinear dynamical responses of generator’s relative deviation of rotational seed and the water pressure at the entrance of surge shaft were analyzed. Second, a new nonlinear mathematical model of a hydro-turbine governing system with a surge tank was presented. Finally, we introduce a new model of hydro-turbine system with the effect of surge tank based on state-space to study the dynamical behaviors of a hydro-turbine system.