Based Pi-Controller Tuning

The order of the process model determines the order of the controller, and therefore has an impact on the achievable performance of the control system. Thus, a PID controller, which is of second order, is generated on the basis of a model, p s, of the same order. To design c(s) as a PI controller, the process model is limited to a first-order transfer function p s = 

For processes exhibiting time delay, for example, p s = Kp (tj + 1) , Rivera et al. (1986) recommend the IMC tuning rules  

EXAMPLE 21.9 Tuning PI Control Loops for a Binary Distillation Column (Example 21.8 Revisited) 

the dimensionless process gain is Kp = —0.7/10 = —0.07, with direct action control needed due to the negative process gain. Furthermore, the open-loop process time constant is approximately 10 min (assuming the settling time is on the order of five time constants). Thus, the IMC-based PI tuning parameters for this loop, computed using Eq. (21.67), are 

The value of X is tunable, allowing the designer to trade-off between robustness and performance. With X = 5 min, Kc = 29. A similar approach for the bottom loop leads to the PI tuning Kc = 6, t, = 10 min.  

---

Using model-based tuning methods, as discussed in the section on Model-Based PI Controller Tuning, higher-order models are needed to tune a PID controller. In many cases, the additional engineering effort is not justified. 

---