Distillation Column Example
Temperature control of a distillation column is an important industrial application of process control. It is important to have tight temperature control of a column in order to optimize separation, avoid flooding, minimize steam costs, and maximize profit.
The temperature control of the distillation column involves taking a temperature measurement and sending it to a distributed control system (DCS). The DCS contains software which manipulates a control valve that regulates steam flow to the reboiler. The block diagram is below:
For this example, we'll assume that the process is second-order with the following transfer function:
Gp = 1/(s2 + 10s + 20)
For simplicity's sake we are assuming no gains in the instrumentation. The goal for this example is to control the distillation column temperature to 100 °F, minimize response time, and minimize overshoot.
Open Loop Response
The open loop response tells us what we need to work on with our controller. As most steam control valves fail to a closed position, without any control, the temperature will only rise 5 °F.
Proportional control is used to improve the rise time. It does bring the temperature close to the setpoint, but there is still a steady-state error. The following graph has a proportional gain, Kc = 300.
The proportional-integral control response shows the steady-state error is eliminated. However, the settling time is still very large. We reduce the proportional gain to 30 because integral control accomplishes the same functon (reduces rise time and increases overshoot). The following graph displays the response of Kc = 30 and tI = 0.429.
Proportional-derivative control improves the overshoot, but fails to improve the steady-state error. The following graph displays the response of PD control with Kc = 300 and tD = 0.033.
Tuning proves the best response with Kc = 350 and tI = 1.17 and tD = 0.143. As shown below, the closed loop response for the combined proportional-integral-derivative control gives the quickest response with no overshoot and converges to the desired 100 °F.
Thus, we can see that PID control is the optimal technique for temperature control of a distillation column.