# Pid Controller Tuning: a Short Tutorial

## Pid Controller Tuning: a Short Tutorial

PID Controller Tuning: A Short Tutorial
Jinghua Zhong
Mechanical Engineering, Purdue University

Spring, 2006

Outline
This tutorial is in PDF format with navigational control. You may press SPACE or →, or click the buttons in the lower right corner to move to the next slide. Clicking on the outlined items will take you directly to that section. Goals and Objectives What are we going to learn? Introduction What is a PID controller? Why do we want to learn the PID Controller? Tuning Rules How does the PID parameters aﬀect system dynamics? The Ziegler-Nichols tuning rule

What are we going to learn?

The goal of the tutorial is for you to learn about the PID controller and a few basic tuning rules of it. After taking this lesson, you will be able to 1. relate PID controller parameters to step response characteristics of the controlled system, and 2. apply the famous Ziegler-Nichols tuning method to come up with an initial set of working PID parameters for an unknown system.

What is a PID controller?
A PID controller is a simple three-term controller. The letters P, I and D stand for: P - Proportional I - Integral D - Derivative The transfer function of the most basic form of PID controller, as we use in ME475, is C (s) = KP + KI KD s 2 + KP s + KI + KD s = s s

where KP = Proportional gain, KI = Integral gain and KD = Derivative gain.

PID Controller structure

In this tutorial, we assume the controller is used in a closed-loop unity feedback system. The variable e denotes the tracking error, which is sent to the PID controller. The control signal u from the controller to the plant is equal to the proportional gain (KP ) times the magnitude of the error plus the integral gain (KI ) times the integral of the error plus the derivative gain (KD ) times the derivative of the error. u = KP e + KI edt + KD de dt

Why learn the PID controller?
Because PID Controllers are everywhere! Due to its simplicity and excellent if not optimal...