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Unformatted text preview: Lecture S11 Muddiest Points General Comments In this lecture, we looked at the definition of state , and applied state-space ideas to the derivation of the dynamics of a circuit. This approach leads to a set of first order, linear differential equations in a specific form. Hopefully, it will become a little more clear in the next lecture why this form is so nice. Responses to Muddiest-Part-of-the-Lecture Cards (36 cards) 1. What are state vectors used for? How does the equation x ˙ = Ax (15) predict the behavior of the circuit? (1 student) I don’t really understand the point behind state functions and how to derive them. (1) The state equation (in matrix / vector form) is a set of first order, coupled differential equations that describe the dynamics of the circuit, just as were the equations we found in previous lectures. The difference is that the state-space form is a special case, that expresses the dynamics in a very specific form that is easier to work with. It also has theoretical advantages that are diﬃcult to explain in only one or two lectures, but is truly the modern way to think about the dynamics of systems. For example, the state-space approach made possible advances in navigation technology that enabled travel to the moon. 2. In the example, why does e 1 = v 4 ? (1) The inductor L 4 is connected to the upper node with potential e 1 , and the ground node. The difference in potential across the inductor is then e 1 − 0 = e 1 . 3. Confused about the derivation of the state equations. (1) General confusion about the states of the circuit. Please re-read the notes, and see me at oﬃce hours Monday, or in recitation. 4. Your example was clear up to the application of KCL at v 1 . (2) After solving for all the unknown nodes, we solve for the current in the voltage sources (or capacitor in this case). The current out of the v 1 node is i 1 + G 2 v 1 + G 3 ( v 1...
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This note was uploaded on 01/28/2012 for the course AERO 16.01 taught by Professor Markdrela during the Fall '05 term at MIT.
- Fall '05