Control systems are all around us, and understanding them is going to make you much better at hardware design. In the last article — Beyond Control: The Basics of Control Systems — we looked at an overview of what a control systems are in general with the example: “everything in between water and time is a control system”. We also observed control systems in nature, where I described my keen ability to fill a glass of water without catastrophic results. That discussion involved the basic concept of a block diagram (without maths) and we expanded that a bit to see what our satellite dish example would look like (still without maths).
I promised some big ugly maths in this article, and we’ll get to that in a bit, never you fear. First let’s have a look at how some basic elements: resistors, inductors, and capacitors are defined in the time domain. Don’t let these first few definitions turn you off. No matter how you feel about calculus, you don’t necessarily need to fully understand each equation. What’s more important is how the equations themselves combine to solve the circuit. Also important is that I will do everything possible to get out of doing difficult math. So stick with me through the article and you’ll learn that agony-saving trick for yourself!
A quick recap on transfer functions before we get going might be beneficial. A control system is used to define electromechanical behavior. For example: our satellite dish (from the previous article) at some point will need to be moved from one position to another position and as control engineers it is our job to determine just how this action will take place. I’m not talking about setting the mood for the big emotional robotic rotation, more like: not damaging the equipment or any people that might be nearby when moving the dish. For many reasons the dish would need to be moved with extreme care and in a very precise manner. The control system is the mathematical definition of that movement. Often the maths of the definition are nasty differential equations, (remember I’m avoiding any math that can be avoided, right?) so, instead of using differential equations to define the system, the transfer function will define the system with algebra, relating the output of the system to the input.
Continue reading “Beyond Control: Maths Of A Control System”
