Analytical Solution of Optimal Filter Design for Internal Model Control for First and Second Order Dead-Time Processes

This work presents a systematic path towards the analytical design of the optimal parameters of a two parameter second order Internal Model Control (IMC) filter for the first-order plus dead- time and the second-order plus dead-time processes. The IMC parameters are designed to minimize the control objective function comprising of weighted sum of (1) error between the process variable and set point, and (2) rate of change of the manipulated variable. The proposed IMC controller design yields the analytical expression of best/optimal value of the IMC controller parameters in terms of process parameters without any trial and error.