Control Theory prerequisites and learning

[tridianprime]

Hello, I have recently been doing a lot of research around designing quadcopters/hexcopters and so forth. I have come to the conclusion that it may be fun to learn bait of control theory on the side and it sounds useful for later on when I go to university. Do you know what the prerequisite are? I have heard that it is DE in mathematics(?) but what else? Also, what can you use to learn basic control theory?

Thanks, Sam.

 

[donpacino]

That depends on whether you want to look at things from a very high level, or you want to get down nitty gritty and do the math.

To do the math you at the very least need to have a very good understanding of algebra and Laplace transformations. A Laplace transformation converts an equation from the time domain to the frequency domain and vice versa. It allows you to solve extremely complex differential equations with algebra. You should also have a good understanding of basic calculus (I am assuming if you know Laplace you will know basic calc).

I would start out by studying topics in the following order

1. Block diagrams (dervive an equation from a block diagram and vice versa). This also includes
2. feedback theory
3. How the frequency domain relates to the time domain
4. Poles/Zeros (what they are, how they effect the system in both the time and frequency domain)
5. PID controllers

A good first project is controller the position or speed of a servo or motor. The cool thing about this is you can get very mathematical and design the system perfectly, or can just dive into tuning a PID controller. either method works.

Let me know if you have any questions

 

[tridianprime]

Okay, that looks great thanks. I have studied single variable calculus, first course in linear algebra, tiny bit of DE(no laplace), and multivariable calculus. Once I have refined these and done some more DE, what would you suggest next?

 

[tridianprime]

A good first project is controller the position or speed of a servo or motor. The cool thing about this is you can get very mathematical and design the system perfectly, or can just dive into tuning a PID controller. either method works.

I am working on a flight controller for a quad copter. Would this act as a good project if I did it in the right way(hence this thread)?

 

[donpacino]

I am working on a flight controller for a quad copter. Would this act as a good project if I did it in the right way(hence this thread)?

Yes it would act like a good project. However a quadcoptor can be a fairly complicated project due to the fact that it has multiple output (ie the speed of the four props).

At a very small and simple level, this is basically how a quadcoptor works. A gyroscope is used to measure the tilt of the quadcoptor. let's say the quadcoptor is tilted slightly to the right. The speed of the props on the left are increased until that tilt is normalized.

The control techniques are slightly different, but the concept is the same. At the end of the day, it may be easier for you to start with a simple one motor control system.

 

[donpacino]

Okay, that looks great thanks. I have studied single variable calculus, first course in linear algebra, tiny bit of DE(no Laplace), and multivariable calculus. Once I have refined these and done some more DE, what would you suggest next?

After that the only other mathematical prereq is linear algebra (primarily for state space representation). There is other math necessary for advanced work, but those are all grad school or higher level of detail.

The important thing to study after you get the math down is feedback theory, the effects of poles/zeros, and system dynamics

 

[tridianprime]

After that the only other mathematical prereq is linear algebra (primarily for state space representation). There is other math necessary for advanced work, but those are all grad school or higher level of detail.

The important thing to study after you get the math down is feedback theory, the effects of poles/zeros, and system dynamics

Brilliant, I will get started. You have been very helpful.

I will look into single motor projects as well, thanks.