Design And Implementation Of The Controller Based On The Fractional-Order Internal Delay Model

Fractional calculus is an old and young field in the field of mathematics.In the more than 200 years since the concept of fractional calculus was proposed,researchers focused mainly on the mathematics study.With the development of computer technology,many problems that can't be solved before have been solved now,and objectively the development of computer technology created the conditions for factional calculus's application practice.Fractional calculus provides richer information and more flexibility than integer calculus.The fractional-order control system adds order parameters to the original integer order control system.Better results can be expected whether it is used to model the system model or to design the controller for the system.On the basis of the predecessors,from the perspective of practical engineering application,this dissertation improves on the imperfection in fractional-order control theory.It has studied the fractional-order model existing internal delay,and designed the fractional-order PID controller and fractional-order Fuzzy PID controller,the specific work is as follows:(1)The concept of integer-order model with internal delay is extended to fractional-order model,Author has solved the mathematical description of fractional-order model with internal delay and has solved the interconnection problems between these models such as series connection,parallel connection,Feedback connection,The author has solved the problem of time-domain response and frequency-domain response of such models,and verifies the correctness of the results through experiments.(2)Two methods for designing fractional PID controller based on time-domain response and frequency-domain response has been expounded,and the characteristics of these two methods has been analyzed.The time-domain method builds the objective function through the ITAE criterion to optimize the values of parameters in the controller.The frequency-domain method constructs the objective function and constraint function to optimize controller according to the system crossover frequency and phase margin.The advantages and disadvantages of the two controllers has been analyzed:The time-based controller can get a better dynamic response and the frequency-based controller makes the system more robust.(3)Design fractional fuzzy PID controller through matlab software.By analyzing the influence of various parameters in the fractional PID controller changes on the dynamic response of the system a reasonable fuzzy control rule table of 2 inputs and 5 outputs has been designed.The 2 inputs refer to the error e and the derivatives of error ec,and the 5 outputs refer to incremental proportional value of the parameter in the fractional controller.According to the fuzzy rule table,the five parameters of fractional PID controller can be dynamically adjusted according to the error signal in the response process.Finally,the experiment proved the effectiveness of the controller.