PID Parameter Tuning

Objective

Adjusting the Proportional (Kp), Integrator (Ki), & Derivative (Kd) parameters of the PID controller to reduce steady-state error.

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Approach

Aside from simple trial and error, the Ziegler-Nichols method seems to be suggested for narrowing down the parameter values that are suitable for our use case. The Ziegler-Nichols is the following:

• Begin with a Proportional Controller (KI & KD are disabled)
• Increase Kp until the vehicle begins oscillating
• Decrease Kp accordingly (perhaps by half)
• Add the integrator, repeating the previous two steps
• Keep adjusting accordingly

Most applications do not use the derivative (Kd) parameter, as it is sensitive to noise (the process variable must be clean, or the derivative-time must be small).

Sources

National Instruments: PID Theory Explained - for tuning based on the period of oscillations.

UM's Intro to PID Controller Design - demonstrates what each parameter is responsible for.

RealPars: How to Tune a PID Controller (Video) - illustrates the Ziegler-Nichols method.

MatLab: PID Tuning Guide (Video) - explains the various methods for narrowing down ideal parameters. Also gives insights on using a model to build a controller.