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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 Ziegler–Nichols tuning (represented by the 'Classic PID' equations in the table above) creates a "quarter wave decay". This is an acceptable result for some purposes, but not optimal for all applications. This tuning rule is meant to give PID loops best disturbance rejection. [2]
The Smith predictor (invented by O. J. M. Smith in 1957) is a type of predictive controller designed to control systems with a significant feedback time delay. The idea can be illustrated as follows.
For example, the position of a valve cannot be any more open than fully open and also cannot be closed any more than fully closed. In this case, anti-windup can actually involve the integrator being turned off for periods of time until the response falls back into an acceptable range.
Provides a set of commands for controller design such as PID working with plant models designed by MapleSim. These commands are used in Maple. MapleSim Explorer. Viewer version of MapleSim that can run simulation of MapleSim models. MapleSim Server. Web deployment option that can serve MapleSim models on web browser or tablets.
PID controllers do not have this predictive ability. MPC is nearly universally implemented as a digital control, although there is research into achieving faster response times with specially designed analog circuitry. [3] Generalized predictive control (GPC) and dynamic matrix control (DMC) are classical examples of MPC. [4]
With the present example, if you turn off the hot then (apart from the water actually in flight) the temperature cannot continue to rise, and so PID control is unnecessary. Previously, when talking about the water as it came out of the tap, the example described a 1st order system with a built-in pure time delay.
A water heater that maintains desired temperature by turning the applied power on and off (as opposed to continuously varying electrical voltage or current) based on temperature feedback is an example application of bang–bang control. Although the applied power switches from one discrete state to another, the water temperature will remain ...