The following paper derives IMC-based PID controllers for “real PID” control: Chien, I.-L., and P. S. Fruehauf , “Consider IMC Tuning to Improve Controller Performance,” Chem. Eng. Prog., 86(10), 33–41 (1990).
The IMC procedure is fully developed in the following monograph: Morari, M., and E. Zafiriou , Robust Process Control, Prentice-Hall, Englewood Cliffs, NJ (1989).
Initial IMC-based tuning parameters were presented in the following paper: Rivera, D. E., M. Morari, and S. Skogestad , “Internal Model Control. 4. PID Controller Design,” Ind. Eng. Chem. Proc. Des. Dev., 25, 252–265 (1986).
The following paper discusses the IMC-based tuning rules for open-loop unstable systems: Rotstein, G. E., and D. R. Lewin , “Simple PI and PID ...