Optimized PID Controller for FOPDT Processes with Constraints on Maximum Sensitivity and Measurement Noise Sensitivity

For first order plus dead time (FOPDT) models, the four parameter optimized PID controller is designed subjecting to constraints on maximum sensitivity M_s and sensitivity to measurement noise M_n. Typical value of M_s is in the range 1 to 2 is considered while selecting the constraint on maximum sensitivity. The design procedure leads to formulation of three nonlinear equations which can be solved iteratively using folve function available in MATLAB. The two FOPDT processes are analyzed and simulated for different performance criterion and robustness, considering different values of damping factor ζ. The optimal value of ζ normally ranges from 0.75 to 0.85.