Closed-form formulas for continuous/discrete-time PID controllers´ parameters

This paper proposes the formulas for finding the Proportional gain, Integral gain and Derivative gain simultaneously of the PID controllers in both continuous-time and discrete-time systems. Once, the satisfied PID controller in continuous-time system is obtained. Then, just discretises it by using trapezoidal approximation or bilinear transformation, the discrete-time PID controller is easily achieved as well. The results from simulations revealed that this discrete-time controller provides a faster response than the continuous-time case.