Intelligent Parameter Identification And Control Of Fractional Order System

As a new mathematical tool,fractional calculus with arbitrary fraction order of differential and integral is a generalization of the regular calculus.The number of applications of fractional calculus rapidly grows such as biomedical engineering,mechanics of materials,financial theory,control science and engineering in addition to theoretical research in the field of mathematics,in which is primarily to model an actual system and design a fractional order controller.Due to some instability,uncertainty and unknown factors of the internal operation and the reaction mechanism of some arbitrary complex system,the accurate description of the dynamic characteristics of some actual system is difficult.Fractional calculus has a good performance because the development of system function subjects to its own history information.These mathematical characteristic allow us to describe some actual system more accurately than the classical integer methods.It overcomes the shortcoming which would be assuming some ideal operation conditions and ignoring some system dynamic behavior and introducing some empirical parameters described by the classical integer methods.If the system description is not accurate,even using an intelligent technology to design the system controller,the performance is not good enough.Therefore,the research of fractional calculus has an important theoretical and practical significance.Firstly,the paper introduces the research background and the purpose of the fractional calculus topic,summarizes the current research of fractional calculus in control field,numerical solving of fractional differential equation,parameters identification and fractional order controller design.In order to improve the identification accuracy,speed up the convergence rate of system parameters identification problem and optimize controller adjustable parameters,the particle swarm optimization algorithm and its improved algorithm are studied.The main contributions in this thesis are as follows:For a class of fractional order chaotic systems with time-delay,the system parameters identification problem is studied.The identification parameters mainly include system structure parameters,system orders and also time-delay parameter.A linear interpolation numerical solution of fractional order differential equation with time-delay based on predictor-corrector method is proposed.In order to solve the identification issue problem effectively,an improved particle swarm optimization algorithm with increasing inertia weight is proposed.The Mackey-Glass chaotic system with time-delay is studied to identity system parameters,the fractional differentiation orders and time-delay adopting the improved particle swarm optimization algorithm with increasing inertia weight algorithm,particle swarm optimization algorithm and differential evolution algorithm,respectively,which illustrate the effectiveness of the proposed method.For the fractional order systems,a novel method based on Legendre wavelet operational matrix is proposed to identify the system parameters and the system orders at the same time even if the system differential orders are unknown or incommensurate.This method converts the fractional differential equation to an algebraic one through an operational matrix via Legendre wavelet.It avoids the drawbacks of the current identification methods and reduces the computational complexity during the identification process.Illustrative examples are included to demonstrate the validity showing that the identification accuracy also meets the requirements.For the automatic voltage regulation system,a fractional order PI~?D~?controller based on an improved particle swarm optimization is designed to maintain the output voltage at some expect value.In order to tune the fractional order PI~?D~?controller adjustable parameters effectively,an adaptive particle swarm optimization algorithm is used to minimize the integral absolute error between the actual system output and the reference model output.Simulation results show that the designed fractional order controller has a better performance and the adaptive particle swarm optimization algorithm is effective for tuning the fractional order controller adjustable parameters.