Editing Proportional–integral–derivative controller (section)

==Cascade control==
One distinctive advantage of PID controllers is that two PID controllers can be used together to yield better dynamic performance. This is called cascaded PID control. Two controllers are in cascade when they are arranged so that one regulates the set point of the other. A PID controller acts as outer loop controller, which controls the primary physical parameter, such as fluid level or velocity. The other controller acts as inner loop controller, which reads the output of outer loop controller as setpoint, usually controlling a more rapid changing parameter, flowrate or acceleration. It can be mathematically proven{{Citation needed|date=January 2009}} that the working frequency of the controller is increased and the time constant of the object is reduced by using cascaded PID controllers.{{Vague|date=February 2009}}.

For example, a temperature-controlled circulating bath has two PID controllers in cascade, each with its own [[thermocouple]] temperature sensor. The outer controller controls the temperature of the water using a thermocouple located far from the heater, where it accurately reads the temperature of the bulk of the water. The error term of this PID controller is the difference between the desired bath temperature and measured temperature. Instead of controlling the heater directly, the outer PID controller sets a heater temperature goal for the inner PID controller. The inner PID controller controls the temperature of the heater using a thermocouple attached to the heater. The inner controller's error term is the difference between this heater temperature setpoint and the measured temperature of the heater. Its output controls the actual heater to stay near this setpoint.

The proportional, integral, and differential terms of the two controllers will be very different. The outer PID controller has a long time constant – all the water in the tank needs to heat up or cool down. The inner loop responds much more quickly. Each controller can be tuned to match the physics of the system ''it'' controls – heat transfer and thermal mass of the whole tank or of just the heater – giving better total response.<ref>[https://www.controleng.com/articles/fundamentals-of-cascade-control/] Fundamentals of cascade control | Sometimes two controllers can do a better job of keeping one process variable where you want it. | By Vance VanDoren, PHD, PE | AUGUST 17, 2014</ref><ref>[https://www.watlow.com/blog/posts/benefits-of-cascade-control] | The Benefits of Cascade Control | September 22, 2020 | Watlow</ref>