Study On Design And Application Of Fractional Order PI~?D~? Controller

The theory of fractional order calculus is the theory of arbitrary order integral and differential. With the continuous development of the fractional order calculus theory study, the application of fractional order calculus theory in the field of control has become research hotspots gradually. Among them, the proposing of fractional order PI?D? controller is a milestone of the fractional order calculus theory applying in the field of control. Control parameters ? and ? are added to fractional order PI?D? controllers on the base of integer order PID controller, which makes the design of controller more flexible and has better control performances, however, fractional order calculus is introduced into the fractional order PI?D? controller which makes implement fractional order PI?D? controller digitally more difficult, the increase of control parameters also makes the controller parameters tuning becomes more complex, at the same time, the performance of fractional order PI?D? controller in practical application also needs to be further verified. Based on the above problems, the following research work were mainly done in this thesis.Firstly, the basic concepts of the fractional order calculus and the form of fractional order PI?D? controller were introduced, the approximation methods and the digital implementation methods were studied, including the time domain and Z domain approximation methods; then, the methods for design of the parameters of fractional order PI?D? controller were studied, including the roots and orders searching method, the gain and phase margin method and optimization method, and the genetic algorithm, particle swarm algorithm and quantum particle swarm algorithm were researched and compared in the thesis, quantum particle swarm algorithm was used in fractional order PI?D? controller parameters tuning for the first time in the thesis. Comparing the effects of the traditional methods and these optimization algorithms in fractional order PI?D? controller parameters tuning, the result shows that the quantum particle swarm algorithm performs better than other methods in fractional order PI?D? controller parameters tuning. At the same time, the integer order PID controller and the fractional PI?D? controller were designed for different types of controlled systems in the thesis, the control performance of two controllers were compared, the results showed that the fractional order PI?D? controller has better control performance than integer order PID controller for different types of controlled system, changing the parameters of controller and controlled system in a small range respectively and comparing the curves of step response, which verify the fractional order PI?D? controller has strong robustness, at the same time, changed five parameters of fractional order PI?D? controller and studied the influence on the controller performances while the parameters varying; Finally, on the basis of theoretical research, the high-low temperature test box was selected as the controlled object, and experimental platform was built to conduct the experimental study, the time domain approximation method was used on the digital implementation of fractional order PM)*1 controller, achieved the integer order PID controller and fractional order PM)*1 controller controlled the high-low temperature test box under the same temperature settings and experimental conditions, comparing the control effects of integer order PID controller and fractional order PM)*1 controller in the practical application, which verified the availability and superiority of the fractional orderPM)*1 controller, the fractional order PM)*1 controller applied to the temperature control process has good practical significance.