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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.
In particular, the integers are a PID, so one can always calculate the Smith normal form of an integer matrix. The Smith normal form is very useful for working with finitely generated modules over a PID, and in particular for deducing the structure of a quotient of a free module. It is named after the Irish mathematician Henry John Stephen Smith.
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]
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.
Example of a single industrial control loop; showing continuously modulated control of process flow. A closed-loop controller or feedback controller is a control loop which incorporates feedback, in contrast to an open-loop controller or non-feedback controller. A closed-loop controller uses feedback to control states or outputs of a dynamical ...
The following MATLAB code will plot the root locus of the closed-loop transfer function as varies using the described manual method as well as the rlocus built-in function: % Manual method K_array = ( 0 : 0.1 : 220 ). ' ; % .' is a transpose.