Stability comparison of different controllers for hydraulic turbine fractional order interval parameter time-delay system

This paper studies the stability comparison of four controllers for a hydraulic turbine fractional order interval parameter time-delay system. Considering the terms of parameter uncertainty and time-lag, the hydraulic turbine fractional order interval parameter time-delay system is established by using fractional calculus and identification technology. Through the edge theorem and D-decomposition method, the calculation process of controller parameter stability region is derived in every detail. Subsequently, the four different controllers including the PID, PID plus second order derivative (PID2D), fractional order PID (FOPID) and fractional order PID plus second order derivative (FOPID2D) controllers, are applied in the hydraulic turbine fractional order interval parameter time-delay system. According to the experimental results, the effect of the controller parameters k(d) , k(d) (2), alpha and lambda on the stability region of the parameters k(p) and k(i) is analysed and the variable law of stability regions of the hydraulic turbine governing system is presented. Finally, the stability region of these four controllers is compared and the results validate the superiority of the FOPID2D controller over the other controllers.