Fractional-Order Process Control System Analysis And Design

Fractional calculus is the extension of traditional calculus theory.The combination of fractional calculus and control theory has provided new opportunities and challenges to the development of control field.The fractional calculus related control theory research has also attracted a lot of attention.However,the long term significance of research should focus on the application in industrial manufacturing process.Therefore,a systematic study of fractional-order process control strategies and controller design methods which combined fractional calculus and process control theories together is proposed in this dissertation.The existences of parameter uncertainties and unpredictable disturbance are always inevitable in control systems.The system robustness becomes one of the most important evaluation indicators while these kinds of problems appear in control systems.A thorough robustness analysis on a typical kind of fractional-order system has been made and the corresponding robust fractional-order PD/PID controllers are proposed in this dissertation.The tuning methods are demonstrated under different circumstances according to the system type and the number of tuning parameters.The frequency response,namely Bode phase plot of the controlled system will maintain a 'flat phase'characteristic at the system crossover frequency to improve the system robustness.The time delay problem of controlled system also brings troubles into the system analysis and controller design processes.Normally,PID control serves as the first choice when there is time delay in the system.Three kinds of fractional-order PID controllers,namely optimal fractional-order PI controller based on Ms Constraint,optimal fractional-order PID controller based on numerical Laplace transformation and fractional-order fuzzy PID controller,are presented in this dissertation.However,when it comes to systems with rather large time delay,the Smith Predictor is preferred rather than PID controller.One notable but not desirable feature of the Smith Predictor is that it retains the original system poles all the time,so it cannot be used for unstable systems.This issue limits its application to non-minimum phase system because it will result in unsatisfactory control performance.Therefore,an alternative time-delay compensation algorithm named Fractional-order Finite Spectrum Assignment(FFSA)which can be used on all kinds of plants including poorly damped ones and unstable ones is proposed in this dissertation.After the discussions of the regulation problems in fractional-order control systems,the trajectory tracking problem has also been taken into consideration in this dissertation.A continuous time fractional-order zero phase error tracking controller(FZPETC)is designed based on the zero-pole cancellation theory.In order to improve the tracking performance,the presented controller cancels the phase shift as well as the amplitude error caused by the controlled closed-loop fractional-order system zeros and poles.Moreover,a modified quasi-perfect tracking scheme is presented for those systems which may have problems in high frequency if the perfect tracking algorithm is applied.The multi-input-multi-output(MIMO)fractional-order system is also analyzed on top of the demonstration of the control strategies of the single-input-single-output(SISO)fractional-order system.Several decoupling methods are put forward together with their relative advantages aiming at the frequently appeared coupling problem in MIMO systems.More efforts should be put for further research.