Feedback Control Systems
You set your car to cruise control. How does it keep its speed constant? Simple right? Just set a constant rotational speed for the driving wheels. What if you’re on a hilly road? How do you tell the engine to throttle more when you’re heading uphill and less when downhill? The engine MUST be in some sort of feedback loop. A sensor must be able to tell when the car is going uphill or downhill via some minute dip or rise in wheel rotational speed given constant engine output. If the speed begins dipping because you start heading uphill, by how much should you tell the engine to work harder? Do you want it to be a sudden, drastic change that overshoots past the set cruise speed and eventually oscillates back to the set speed? Do you want it to be a slow, gradual change that works its way back up to the set cruise speed? Ideally, you want it to respond instantaneously and never waver from that set cruise speed. How do you accomplish that (or at least get as close to that outcome as possible)? That’s feedback control. The things that keeps cars at set speeds, your computer at the right temperature, and satellites on the right orbit.
I loved this class. This class had everything I could ask for in an engineering class: fascinating (yet not unreasonably difficult) curriculum, multidisciplinary topics, and hands-on experience. Drawing equally from the archives of my mechanical and electrical engineering knowledge, this course ignited an interest in dynamics and controls within me. Countless times throughout my undergraduate career, I wondered whether I would have been a better EE than ME. After all, my GPA in my EECS minor was better than my ME GPA. I also found my EE classes consistently more interesting than my ME classes. Yet, I could never bring myself to only learn about currents and voltages without learning about stresses and strains. Controls uses both! You CANNOT design controller hardware without knowledge of your mechanical system. You CANNOT build the electronics needed for cruise control without knowing the physics of your engine. Needless to say, I will be seriously looking to start a career in controls engineering.
As an added plus, it’s always great when your work yields such pretty diagrams and graphs :). Could do without some of the matrix algebra though :/.
Food for Thought
The Laplace Transform is the king of control theory. It transforms a signal from the time domain f(t) to the ‘s’ domain F(s). This ‘s’ is a complex number that consists of a real and imaginary component. This transform is given in the equation below.
Convince yourself that the Laplace Transform is a convolution across the original signal f(t). What dominant features in the original signal does the transform identify? Hint: one starts with ‘f’ and the other starts with ‘e’.
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