Stability Criteria Analysis And Application For A Class Of Fractional Order Delayed Systems

The world never ceases its steps to progress. The existed high technology has become more and more mature, but the requirement of high accuracy and good performance also become stronger and stronger. The mathematical system model is demanded to be more accurate to reflect realistic system dynamic, and the controller is demanded to be more robust and efficient. Fortunately, fractional order concepts appeared as a interesting area in controlling community to help achieve the goal, which perform a unique advantage in system modeling and an unique effect in system controlling. Because fractional order concept is the extension of integral order, it extends wider room when describing system dynamics. In addition, PID controller, because of its simple structure and tuning convenience, is the most practical controller. Compared to traditional PID controllers, fractional order PID controllers have two more degrees of freedom. Thus the controlling effects of fractional order PID controllers extend to a broader space. They can break up the limits resulted by traditional controllers inherently, and achieve unexpected results.Additionally, time delay is very common in manufacture controlling and message transmitting. In reality, the collection and using of information must need time to transmit and process, which means absolute synchronism of information can not be achieved. Unfortunately, time delay is vital to the stability of controlled system. However, stability is the most important and basic target in controllers’ designing. According to these points, time delay is an essential item to be considered, as we do in this paper.This paper aims at resolving delay intervals which guarantee the linear fractional-order delayed system to be stable and getting restrictions between controller parameters and delay. The restrictions are displayed by graphs in parameter-delay plane, and simulations are made to verify the validity. Resulted stability regions of parameters help to observe the system properties clearly and to tune controllers or even the delay part to realize the design goal. The existing of resulted regions and graphs make great favor for designers to choose proper controller. Additionally, the proposed method can also guarantee robust stability of controlled system, such as phase margin, amplitude margin, H-inf specification and so on.