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Unformatted text preview: MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Aeronautics and Astronautics 16.060: Principles of Automatic Control Fall 2003 PROBLEM SET 3 Due: 9/25/2003 Problem 1: Review of Gain, Type Number, and Steady-State Errors R ( s )- C ( s ) G ( s )- Figure 1: Problem 1 In Figure 1, the transfer function between input and output is given by: 10( s + 2)(0 . 25 s + 1) G ( s ) = (0 . 1 s + 1)( s + 5) 1. Convert G ( s ) to root locus form and find the root locus gain. 2. Convert G ( s ) to standard form and find the gain, as defined in Van De Vegte, Equation (4.11). 3. What is the type number of the system? If you closed the loop around G(s) with unity feedback, and gave it a step input R , what would the steady-state error be? Problem 2: Graphical Determination of Residues For each of the following systems: • Write down C ( s ) = G ( s ) R ( s ). • Find the root locus gain of C ( s ). • Plot the poles and zeros of C ( s )....
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