20. Tuning Strategies 1

Up to now the focus has been on understanding the dominant effects of the proportional, integral, and derivative error terms. Now it is time to shift our attention to more systematic ways to choose PID gains. As you have seen from the examples, you can’t just set them all to 1000 and go home!

Over the years, there have been many different parameter tuning rules and guidelines proposed. Some of the oldest and still widely referenced, techniques are the two Ziegler-Nichols (ZN) methods.

Ziegler and Nichols published one of the most influential papers pertaining to PID control tuning, the paper was titled, “Optimum Settings for Automatic Controllers”. The opening paragraph reads,

*A purely mathematical approach to the study of automatic control is certainly the most desirable course from a standpoint of accuracy and brevity. Unfortunately, however, the mathematics of control involves such a bewildering assortment of exponential and trigonometric functions that the average engineer cannot afford the time necessary to plow through them to a solution of his current problem. *

To assist practicing controls engineers, Ziegler & Nichols published two empirically derived methods that can be used in the PID tuning process, at least as a starting point. The fact that the rules were simple to follow, involved a systematic process, and worked well enough for many systems, no doubt played a large part in the popularity of the methods.

Although the Z-N methods are no longer considered “industry standards”, it is worth having some familiarity with them because they are still frequently encountered, and many modern tuning guidelines are variants of the original. Some of the criticisms about the tuning methods are: (1) that the proposed gains are based on too little information from the system’s response to the test input, (2) tends to produce too much overshoot, and (3) has poor tracking performance.

ZN Method 1

Assumptions:

  1. The plant has an S-shaped response to a step input. (a.k.a., a first-order plus dead time model in control-speak),
  2. Is open loop stable.

The goal of method 1 is to achieve good disturbance rejection, which they defined as a system response with a “quarter decay ratio” (i.e., the amplitude of the second overshoot peak divided by the first overshoot peak = 1/4).

ZN Method 2

Assumption:

  1. The plant is a higher order system which can be excited to the point of steady oscillation using only proportional control in a closed loop system

The goal of the second method is to achieve a closed loop step response with 25% overshoot.

Both methods assume that the PID controller has the form,

where,

Notice that neither method is designed to give good reference tracking performance - something that is important for our application in this course.

For details on how to implement these methods, here are two excellent sources:

Simple Manual Tuning

In many cases, simple manual tuning can give reasonably good performance. As a first attempt, you can start by:

  1. Setting Kp to something small and Ki = Kd = 0,
  2. Slowly increasing Kp to decrease rise time,
  3. Slowly increase Kd to reduce overshoot and settling time.

By adjusting the gains “by hand”, you will quickly realize that the faster the system response is, the worse stability is. The converse is also true. The trick is to find a balance between the two. However, finding an approximate solution using the above stated method can often serve as a starting point for more systematic tuning methods, such as the gradient descent algorithm that we will discuss next!