Discrete-time PIDA controller designed by Tustin's method with and without frequency pre-warping

Abstract

This paper proposes the formula used for finding the continuous-time PIDA (Proportional-Integral-Derivative-Acceleration) controller's parameters based on pole placement technique. Also, provide the formulas for designing the discrete-time PIDA controllers for both of Tustin's method with and without frequency pre-warping. The designers can use the frequency pre-warping to get the better specification as desired. Moreover, as both of these discrete-time PIDA controllers, theirs transfer functions are proper. Then, they are easy to implement in real-time by the Observable Canonical Form of the difference equations.