PrePrelab - State Space

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This pre-prelab is intended to help you get started learning about state space while you wrap up the continuous-time copter and maglev lab. And we think that a good way to start is to connect transfer functions and state-space descriptions, and to show you that poles are related to matrix eigenvalues. We will start with a 2x2 pendulum example to introduce state-space. Then we will look at a more realistic model of an operational amplifier, starting with its transfer function representation and deriving a state-space model. Then we will reverse the process, and start with a motor state-space model, and derive its transfer function. In each case, we will show the direct connection between poles and eigenvalues.

In addition to the lecture scribbles and video, chapters 6 and 7 from the on-line (and free) textbook Feedback Systems: An Introduction for Scientists and Engineers by Karl J. Åström and Richard M. Murray are particularly good matches to the the material over the next few weeks. Those interested in standing robots will be particularly interested in Example 7.2.

Links to Åström and Murray Chapter 6 , Chapter 7