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Simple analytic formulas for PID tuning

This paper proposes simple analytic formulas for proportional-integral-derivative (PID) controller tuning for typical process models. The formulas are obtained in a similar way to the simple internal model control (SIMC) tuning rules, while the leading analysis is more delicate. Compared to SIMC counterparts, the new tuning formulas lead to better load disturbance rejection while giving similar setpoint response and peak sensitivity.