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ps5 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of...

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- �� �� �� MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Aeronautics and Astronautics 16.060: Principles of Automatic Control Fall 2003 PROBLEM SET 5 Due: 10/23/2003 Problem 1: State Space Models for MIMO Systems State-space models are extremely useful for studying systems with more than one input and/or more than one output. Problem 11.9 in Van de Vegte gives two block diagrams. The first is for a system with two inputs and one output, and the second is for a system with two inputs and two outputs. For each system, determine a state-space model. Show your choice of state variables on the original block diagram. Hint 1: Look at Example 11.3.4. Hint 2: Deal with blocks that contain 2nd-order transfer functions (e.g. in 11.9b) by breaking them up into two 1st-order transfer functions. Hint 3: When deriving the state equations, use the fact that the following block diagrams are equiv- alent (you should prove to yourself that they are): U X u �� + x ˙ ± x ± k ± ± k ± ± ± dt s + a ��
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