Controls has become one of the biggest (and most important) areas in electrical engineering. However, many times when implementing a controls solution, we need to work with linear systems. The majority of real life systems are not linear! So how do we fix this? With linearization. In this article I’ll walk you through an example of how to linearize a system around a certain state vector and control input!
Example control system
So time for some application of mechanics. In this problem, we’ll explore the applications of Newton’s second law of motion, for the static case. This means nothing is moving, acceleration is zero — therefore the sum of forces always equals zero. Take a look at this truss:
If you look at this beast, you’ll notice two 100 newton forces at certain joints. The left end is anchored at a pin joint, and the right has rollers under it. In practice, you usually want to account for expansion and contraction of beams and supports; rollers let one end move back and forth slightly in the corresponding direction (in this case, the x-direction), solving this dilemma.
As structural engineers, we want to find the forces (compression or tension) in members HC, AH, and AB. This is quite simple, and can be solved with the “method of joints” or “method of sections.” This article shows how to find the forces using the method of joints. Continue reading »