A Graphical Turning Of Phase-Lead/Lag Compensators For Time-delay Systems

Lead/lag compensators are applied widely in the industrial field, which are only inferior to PID controller.The traditional design for the parameters of lead/lag compensator is based on the trial and error method. It needs to design and check repeatedly until all of the performance indicators reach requirements. So, this method leads to a lot of inconvenience and approximate designs, it is difficult to achieve the desired results. Then, a lot of researches have focused on the controller design based on analytical methods. But this method only gives a point of the controller parameters. In this thesis, we apply graphical stability criteria for the design of lead/lag compensator, and this method gives us a complete and stable regions.The controlled plants of this thesis are the industrial time-delay systems and uncertain time-delay systems. According to the characteristics of industrial time-delay systems, the thesis introduces the method based on the graphical stability criterion to design the integer-order lead/lag compensators. This design method is extended to the control of uncertain time-delay systems. On this basis, the application of fractional lead compensator is proposed. Main tasks are as follows:(1) Design the lead/lag compensators for the all-pole time-delay systems. We apply the graphical stability criteria to determine the complete parameters’ stable domain. The stability margin of system is determined in this domain, which get better dynamic performance. The design algorithm is concluded and a corresponding design example is used to show this algorithm.(2) Furthermore, the graphical stability criteria are applied to design the fractional-order lead compensators. The thesis introduces that how the changes of the order a to change the stable domain, and we summarize the relevant regularities. Fractional-order control system in the examples, compared with integer-order controllers, can achieve better control results by selecting the appropriate times, which make the stability region and the desire phase margin region enlarged.(3) Design the lead/lag compensators based on the graphic stability criteria for all-pole for a class of uncertain time-delay interval system. First order Pade was used to approximate time-delay factor and the generalized Kharitonov theorem can prove that graphical method can design a lead/lag compensator to make the uncertain interval approximation system stabilized. Simulated results show that the compensator can also stablize the original interval time-delay system, and maintain good system performance.The main contribution is that the graphical stability criteria is applied to all-pole time-delay system and a class of uncertain time-delay interval systems, and this method is extended to fractional-order control system design. The new method, compared with the previous design methods, can definite the complete parameters’ stability region, select flexibly parameters to facilitate practical application. Moreover, it is a practical application to the fractional order control system in the industrial field.