StudAy On Fractional Order Pl~λD~μ Controller Parameter Tuning Methods And Design

Since the begging of the21st century, the fractional order calculus theory hasachieved lots of breakthough. The fractional order calculus control theory has becomda new hotspot in control field. It is found that the physical meaning of the practicalsystem or nonlinear system described by the fractional order calculus equation isclearer and the physical characteristics of those systems are more precise. Besides,due to the two additional tuning parameters of the fractional orderPl~λD~μcontrollerparameter tuning method, namely the integral order λ and the differential μ, thesystem control is more flexible and the control effect is better. However, since thefractional order control theory is still in the theoretical study stage, the fractionalorderPl~λD~μcontroller parameter tuning method mainly exploits the integer orderPID controller parameter tuning method. The design and the implementation of thefractional order controller is complex and high computing capabilities are required.Therefore, the theory and the application of the fractional orderPl~λD~μcontrollerneed to be further improved. This dissertation studied the fractional orderPI λ Dμcontroller parameter tuning method, the discretization method of the fractional ordercalculus operators (s±α), the design and the implementation of the fractional orderPl~λD~μcontroller and the dynamic response charactieristics simulation experimentsof the fractional order control system in details, the main research work andachievements are as follows:1. For the stable minimum phase controlled plant of the known plant model, onthe basis of the traditional integral order PID controller parameter tuning method suchas the phase margin and the gain margin, we propose the fractional orderPI λ Dμcontroller parameter tuning method of which the control system open-loop transferfunction phase Bode diagram has flat-phase near the cutoff frequencyω cand isrobust to the gain variation. But for the stable minimum phase controlled plant of the unknown plant model, by using a relay feedback test experimental method, wepropose the autotuing fractional orderPl~λD~μcontroller parameter tuning methodwhich has the iso-damping characteristics. The simulation results indicate that theproposed method not only improve the dynamic response characteristics of thecontrolled system, but also obtain stronger robustness compared to the integer orderPID controller parameter tuning method.2. By employing the proposed fractional orderPl~λD~μcontroller parametertuning method, we achieved the fractional orderPl~λD~μcontroller design orientedfor different plants.(1) We propose and design the IOPID, FOPI, FO[PI], FOPD,FO[PD] and FOPID controller for the first order, the second order and the third orderplants respectively.(2) We propose and design the IOPID, FOPI, FO [PI], FOPD,FO[PD] and FOPID controller for the time-delay plants.(3)We propose and designthe IOPID, FOPI, FO [PI], FOPD, FO[PD] and FOPID controller for the fractionalorder plants.(4) We propose and design the autotuning FOPI and FO[PI] controllerfor the stable and minimum-phase plants for which the model is unknown and thesystem has the iso-damping characteristics.3. We systematically study the analytical numerical approximation method, thedirect and indirect discrete approximation method for the fractional order calculusoperator s±α(α∈R). Furthermore, we study the Al-Alaoui+CFE direct discretediscretization method and the Oustaloup and the modified Oustloup indirectdiscretization method all of which have good approximation effect and accomplishthe numerical discretization for the fractional orderPl~λD~μcontroller by employingthese methods.4. On the basis of the numerical discretization for the fractional orderPI λ Dμcontroller, we design the simulation systematic diagram for different fractional orderPl~λD~μcontroller by exploiting Matlab/Simulink toolbox and obtain the unit stepresponse characteristics of the different control system. We compare and analyze thedynamic response characteristics for different systems.5. We achieve the experimental study for the parameter tuning method of thefractional orderPl~λD~μcontroller based on the LabVIEW platform for the first time.We establish the experimental simulation platform through the rational configuration of the data acquisition board, control software, peripheral interface, amplifier andphysical device and do the system simulation and experiments based on IOPID,FOPD, FO[PD] controllers on this platform. We further verify that by employing theparameter tuning method of the fractional orderPl~λD~μcontroller, we not onlyimprove the system dynamic response characteristics but also obtain better systemrobustness and interference immunity than traditional PID controller parameter tuningmethod, which promote the application of the fractional orderPl~λD~μcontroller inthe real-time control system.Finally, we summarize the done work and look forward to the future researchwork.