Fractional Order PID Controller Synthesis, Auto-tuning And Experiment Studies For Robust Motion Control Systems

With the progress of fractional calculus, its application research has attracted more and more attention. Now, fractional order calculus is being employed in many literatures to more precisely model many real world systems. It is natural to explore the potentials of fractional order systems and control theory in engineering developments. In fact, fractional order models used to characterize the systems in real world can more concisely and precisely reflect the nature or essence of the systems. Fractional calculus is emerging as one of the best useful mathematic instruments in engineering application, hence the applications of fractional calculus has been explored in many subject areas, and one of the fruitful areas is in control engineering. Literatures have offered several valuable models and structures of fractional order controllers, however, compared with the integer order controllers, a lot of investigations yet need to be done. FOPID (Fractional Order Proportion Integration Differentiation) controller is a new area of research in fractional order calculus’ applications. Advantages of the fractional order PID controller include its structural simplicity and its direct generalization of tranditional PID controller, most-widely usedin industry. Tuning rules development for the fractional order PID parametersetting have been an important research topic with many unsolved issues depending on prior information assumed about the plant to be controlled. These issues include, for example, the lack of systematic tuning method; high complexity in parameter calculation in tuning the controllers and the lack of fair comparison with the integer order controllers. Therefore, it is of practical importance to develop FOPID tuning methods and explore its potential applications in engineering.Robustness of a control system is a very important topic in control theory, which should be considered during the controller design. In real world control system, variations in system’s properties and physical parameters are unavoidable due to many factors, such as environment changes. To avoid the performance change due to parameter variations, the robustness of the controller is the central topic on which this dissertation focuses. FOPID focused in this dissertation is more flexible in achieving robust performance. The controlled systemunder FOPID controller not only can meet the stability requirement, but also meet the robust requirement with respect to uncertainties in system model such as gain to time constant variations. This dissertation focuses on developing a systematic fractional order PID controller tuning rule to achieve system performance robustness against variations in system gain and time constant DC motor experiment is used to validate the developed tuning methods.The main contribution of this thesis is on the development of FOPID robust tuning rule based on different controlled systems Meanwhile, for practical use in industry, an auto-tuning design method has been developed. Both simulation and experimental results are included to illustrate the developed FOPID tuning methods.Specifically, the research results in this dissertation include:(1)FOPID tuning rules based on the system robustness requirement against system gain variations is developed. Systematic tuning rules about FOPD, FO[PD], FOPI,FO[PI] are derived. Simulation results are presented to verify that the performance of the designed fractional order controller is better than the integer order PID controller.(2)A FO[PD] tuning rule based on systemrobustness requirement with respect to time constant uncertainty is developed for the first time. Detailed mathematic derivations are presented and the requirements on the existence of solution in the tuning equations are studied, too. To simplify the computational method for online implement, an online computational method is developed. Results of both simulation and experiments are included to show the correctness and effectiveness of this new tuning rule.(3)For unknown, stable, minimum phase systems, a set of auto-tuning rules for four types of FOPID controllers:FOPI, FO[PI], FOPD, FO[PD] having the desirable iso-damping property are derived. A relay feedback experiment method is introduced for easy implemention of the fractional order PID controller in real world control systems.(4)We extend the fractional order controller application areas to synchronized tracking control systems. We study how fractional order controller can better synchronize the multiple motion control systems. Simulation results are presented to verify that this fractional order control method can improve muti-system synchronization.(5)For the first time the FOPID controller has been implemented on the LabVIEW experiment platform. The experiment results have verified that the FOPID can offer outstanding performance.