Fractional-order Nonlinear System Control And Circuit Research

Since Mandelbort discovered the fractal phenomenon in the real system for the first time,more and more studies have pointed out that many systems in the real world have fractional properties.Compared with an integer-order system,using fractional calculus to establish a mathematical model and describing the characteristics of the system Accurate,more consistent with the nature and dynamic behavior of real engineering technology systems.On the other hand,the physical implementation of nonlinear systems provides the hardware basis for its engineering applications.Stability is one of the most basic and important performance requirements in system control.For the fractional-order nonlinear system control,the existing integerorder controllers are incapable of many times,and the fractional-order controllers can obtain better control effects and control precision that are more in line with the actual requirements of the engineering,but the parameters are followed by the parameters.It is still in the research stage and has not been widely used in the engineering and technology industry.Based on the fractional order control theory,this paper proposes a novel fractional order controller for fractional order system control and discusses the implementation of fractional order non-linear circuit control circuits.The main tasks are as follows:First,the development and new concepts of fractional order theory are introduced,including basic functions,definitions,and numerical calculation methods.Based on the stability theory of nonlinear systems,the sufficient conditions for the stability of fractional nonlinear systems are discussed.Then,the classical neuron model FitzHughNagumo system and Morris-Lecar system are extended to the fractional order system defined by Caputo function.The fractional order dynamic behaviors of the two new systems are analyzed,and the bifurcation characteristics are emphatically studied.Then,the traditional flushing filter design principle is introduced into the fractional order nonlinear system,and a novel fractional order filter feedback controller is proposed.In order to verify its validity and applicability,the FitzHugh-Nagumo fractional order system and the Morris-Lecar fraction are proposed.The controller is added to the order system and a sufficient condition for the stability of the fractional nonlinear system is used to study the stability control method.The simulation results show that both controlled systems can converge to the equilibrium point,and the effect is better than the integer-order flushing filter.Finally,based on Bode's frequency domain approximation and nonlinear system circuit design method,the circuit state feedback loop of fractional Lorenz system is designed.The simulation results show that the fractional Lorenz system can be stabilized at the equilibrium point after the circuit is controlled.