Performance and gain and phase margins of well-known PID tuning formulas

The performance and robustness of well-known PID formulas for process with deadtime to time constant ratio between 0.1 and 1 are discussed in this paper. The Ziegler-Nichols, Cohen-Coon, and tuning formulas that optimize for load disturbance response (integral absolute error, integral squared error, and integral time-weighted absolute error) give gain margins of about 1.5. The phase margins increase from about 30 to 60/spl deg/ as the process deadtime to time constant ratio increases from 0.1 to 1. Tuning formulas that optimize setpoint response give gain margins of about two and phase margins of about 65/spl deg/. These formulas mostly make use of the proportional-integral derivative (PID) controller zeros to cancel the process poles. Approximate analytical formulas to compute gain and phase margins of PID control systems are also derived in this paper to facilitate online computation which would be particularly useful for implementing adaptive control.