Sharif Digital Repository

This paper presents a method to determine the denominator and numerator polynomials of a closed-loop transfer function in order to obtain desired transient and steady-state responses in terms of the overshoot, speed (time needed for the relative error to become less than a specific amount) and the steady-state error when the desired output is a ramp signal. Meanwhile, a controller is designed with the same characteristic equation for the closed-loop system to eliminate step and ramp disturbances  

Five different approaches are presented to assign characteristic ratios for commensurate fractional order systems having order in (0,0.5]. Through the indirect methods, a closed-loop or plant transfer function is converted to a commensurate order one with an order greater than 0.5 so that the previously designed CRA method by the authors is applicable. The first method among the proposed direct ones is based on increasing the order of the desired closed-loop transfer function that allows the employment of positive characteristic ratios. In the second method the closed-loop response is sped up by augmenting an appropriate zero. The final method uses negative characteristic ratios to reach the... 

This paper presents a new analytical method to design fractional-order proportional- integral-derivative (PID) controllers. The control parameters are calculated so that the closedloop system approximates a desired transfer function with transient response requirements. This function is determined based on the characteristic ratio assignment method. The control parameters are calculated by matching the first three moments of the closed-loop transfer function with the corresponding values of the desired system. Furthermore, to ensure closed-loop stability the proposed method is improved by using the shifted moments around the crossover frequency. Illustrative examples are given to show the...