A simple method of tuning PI controllers for unstable systems with a zero

A simple method is proposed to design PI controllers for unstable first order plus time delay systems with a zero. The method is based on (i) matching the coefficient of corresponding first power of s in the numerator and that in the denominator of the closed loop transfer function for a servo problem and (ii) by specifying the initial (inverse) jump. This method gives simple equations for controller settings in terms of model parameters. Simulation results are given for robust performance of the controller for uncertainty in the value of the unstable pole and zero. The performance of the controller is evaluated by simulation on a CSTR with non-ideal mixing carrying out an enzymatic reaction.