Research On Adaptive PID Control Method Of Fractional-order System

With fractional calculus is widely applied in the field of engineering control, the control methods of fractional order system become an important direction of applied research of fractional order control. Good design of fractional order PIλDμ controller is very useful for fractional order system model. This thesis has done some researches for PID control method of fractional order systems, specific work is organized as follows.Firstly, the related theory of fractional calculus is introduced systematically, such as the common functions and relationship between various definitions. On the numerical simulation of fractional calculus operator, approximation of the operator is introduced in this thesis. Oustaloup method is introduced in detail, because its approximate result of bode diagram phase is bad around ωb and ωh, an improved Oustaloup method is researched. The simulation shows that the fractional order derivative curves are coincident through the calculation of original Oustaloup method, improved Oustaloup method and GL definition. Thus, improved Oustaloup method can get more accurate results of the fractional order differential.Secondly, the adaptive setting method of PID controller by Z-N method is researched. For integer order system model, setting effects between classic Z-N response curve method and Z-N critical gain method are compared. The simulation results show that Z-N critical gain method has better dynamic performance than classic Z-N response curve method. For the problem of long setting time when setting system model by Z- N critical gain method, this thesis studies an improved Z-N critical gain method which can achieve good control effect for integer order system. The classic Z-N critical gain method and improved Z-N critical gain method are all applied to fractional order system models, the simulation shows that the improved method can get better dynamic performance for fractional order system.Lastly, adaptive optimization algorithm in the application of fractional order PIλDμ controller parameters setting is introduced in this thesis. The fractional order PIλDμ controller parameters setting by basic genetic algorithm are studied, in order to get good dynamic characteristic, adaptive genetic operators is introduced which can improve the performance of system effectively. For the problem of large overshoot and long setting time in the process, an improved adaptive optimization algorithm is proposed in this thesis which can adjust crossover operator and mutation operator adaptively. For a practical temperature control system, the proposed method is applied on the system of fractional order model and integer order model simulation respectively, the feasibility of this algorithm in practical engineering is verified.