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state_space_problem

# state_space_problem - 3 Using your state-space model...

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� � Practice State-Space Problem for Quiz 1 16.060: Principles of Automatic Control October 8, 2003 For the following differential equation: ¨ w + 6 w = ¨ w + 5 ˙ r + ˙ r + 2 r 1. Derive a state-space model in the form: u x ˙ = Ax + B y x + D = C u Take r to be the input and w to be the output. 2. Draw a block diagram for the system, and clearly label the input, the state variables, and the output. (Hint: look at the diagram on page 4 of the Lecture 13 notes.)
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Unformatted text preview: 3. Using your state-space model, determine the transfer function G ( s ) from the input to the output. 4. Calculate the state-transition matrix Φ( t ). 1 x (0) = , and there are no inputs, what is the state vector ± 5. If the initial state is ± x ( t ) at time t > 0? 1 1...
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