PID Control using MATLAB

Part1: What is PID Control?

Explore the fundamentals behind PID control. Chances are you’ve interacted with something that uses a form of this control law, even if you weren’t aware of it. That’s why it is worth learning a bit more about what this control law is, and how it helps.

PID is just one form of feedback controller. It is the simplest type of controller that still uses the past, present, and future error, and it’s these primary features that you need to satisfy most control problems. That is why PID is the most prevalent form of feedback control across a wide range of physical applications.

However, often when learning something new in control theory, it’s easy to get bogged down in the detailed mathematics of the problem. So, this video skips most of the math and instead focuses on building a solid foundation.

Part 2: Expanding Beyond a Simple Integral

The first video in this series described a PID controller, and it showed how each of the three branches help control your system. That seemed simple enough and appeared to work. However, in practice, an ideal PID controller introduces several problems that you need to protect against when dealing with imperfect systems. This includes saturation, which is a common nonlinear problem found in real-life situations.

This video expands beyond a simple integral and outlines several changes that protect your system against integral wind-up. Integral wind-up occurs when the summation within the integral increases beyond the saturation limit of the actuators it’s controlling, causing reduced performance.

Part 3: Expanding Beyond a Simple Derivative

This video describes how to make an ideal PID controller more robust when controlling real systems that don’t behave like ideal linear models. Noise is generated by sensors and is present in every system. The derivative in an ideal PID controller amplifies high frequency noise. Even if that noise is relatively low amplitude, the derivative will sense it and possibly amplify it enough to impact the controller. To protect against high frequency noise impacting the system, you can modify the derivative path with a low pass filter to reduce the noise before it causes any problems.

Part 4: A PID Tuning Guide

It can be difficult to navigate the all the resources that promise to explain the secrets of PID tuning. Some proclaim that PID tuning is an art that requires finesse and experience, while others are adamant that tuning requires a few rigid rules. Why is there such a vast difference? It is because PID tuning depends on the characteristics of the system. For that reason , a one-size-fits all tuning method doesn’t exist.

Therefore, rather than just show a single method, this video presents a tuning guide that helps you understand the overall picture. Understanding how to approach PID tuning based on the situation provides better context around each of the different tuning methods.

Part 5: Three Ways to Build a Model

Tuning a PID controller requires that you have a representation of the system you’re trying to control. This could be the physical hardware or a mathematical representation of that hardware.

If you have physical hardware, you could guess at some PID gains, run a test to see how it performs, and then tweak the gains as necessary. This guess-and-check brute force tuning method might work, but you have other, more precise, options available if you have a mathematical model of the system. Therefore, this video presents three different ways to model your system so that you can take advantage of each of these methods when tuning your controller.

The first method uses a detailed understanding of the system to develop the model with first principles. The second method uses system identification, the known input, and resulting output signal to fit the data to the model structure of your choice. The third method creates a model by linearizing an existing nonlinear model around a given operating point.

With any of these models, you can start the process of developing and tuning a PID controller.

Part 6: Manual and Automatic Tuning Methods

The previous video showed three different approaches to developing a mathematical model of your physical system. Now that we have this model, we can use it to tune a PID controller that will work to control the physical system.

PID tuning can be thought of in two ways: Adjusting the three path gains (Kp, Ki, and Kd), or placing two moveable zeros and adjusting the loop gain to get the desired response. This video shows how thinking of PID tuning using moveable zeros allows you to approach the problem with loop shaping and pole placement methods. These methods provide a more systematic approach over the brute force method of guessing gain values and checking the response.

In addition to manually tuning a controller, this video introduces how automatic tuning can be a way to quickly get a controller design to meet the system requirements.

Part 7: Important PID Concepts

Now that you ’ve gotten an overview of PID tuning techniques, this video moves on to discussing two important concepts in PID control: cascaded loops and discrete systems. Both concepts are fundamental to most practical control systems, and they each change the way you approach and think about your problem.

Cascaded loops occur when there are two feedback loops in your system - one nested inside the other. Cascaded loops occur in a lot of typical practical control designs. This video explains what cascaded loops are, why implementing them is beneficial, and how to tune them.

Control systems that run on digital computers are necessarily discrete systems. The second part of this video describes the differences between continuous and discrete PID controllers, how stretching the sample time of a discrete system can cause problems, and why we tend to design PID controllers in the continuous domain even when they will operate on a digital computer.