PID Tuning Algorithm

Typical PID tuning objectives include:

Closed-loop stability — The closed-loop system

output remains bounded for bounded input.

Adequate performance — The closed-loop system

tracks reference changes and suppresses disturbances as rapidly as

possible. The larger the loop bandwidth (the frequency of unity open-loop

gain), the faster the controller responds to changes in the reference

or disturbances in the loop.

Adequate robustness — The loop design has enough

gain margin and phase margin to allow for modeling errors or variations

in system dynamics.

MathWorks® algorithm for tuning PID controllers

meets these objectives by tuning the PID gains to achieve a good balance

between performance and robustness. By default, the algorithm chooses

a crossover frequency (loop bandwidth) based on the plant dynamics,

and designs for a target phase margin of 60°. When you interactively

change the response time, bandwidth, transient response, or phase

margin using the PID Tuner interface, the algorithm computes

new PID gains.

For a given robustness (minimum phase margin), the tuning algorithm

chooses a controller design that balances the two measures of performance,

reference tracking and disturbance rejection. You can change the design

focus to favor one of these performance measures. To do so, use the DesignFocus option of pidtune at

the command line or the Options dialog

box in PID Tuner.

When you change the design focus, the algorithm attempts to

adjust the gains to favor either reference tracking or disturbance

rejection, while achieving the same minimum phase margin. The more

tunable parameters there are in the system, the more likely it is

that the PID algorithm can achieve the desired design focus without

sacrificing robustness. For example, setting the design focus is more

likely to be effective for PID controllers than for P or PI controllers.

In all cases, fine-tuning the performance of the system depends strongly

on the properties of your plant. For some plants, changing the design

focus has little or no effect.