# hw1 - 16.31 Prof J P How T.A TBD Handout#1 September 7 2007...

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16.31 Handout #1 Prof. J. P. How September 7, 2007 T.A. TBD Due: September 14, 2007 16.31 Homework Assignment #1 Goals: Refresh skills for Matlab and classical analysis. 1. (Root Locus Analysis) [FPE 3.32, page 159]. Suppose that you are to design a unity gain feedback controller for a ±rst order plant (see ±gure). A speci±c controller con±g- uration has been selected (it is PI). The objective is to pick the control gains so that the poles lie in the regions shown in the ±gure to the right. Figure 1: Problem # 1 (a) What values of ω n and ζ correspond to these shaded regions in the s ²plane Cal- culate these exactly (they will be nonlinear) and then approximate to something more useful for design? (b) Let K α = α = 2 . 5. Find the values of K and K I so that the poles of the closed² loop system lie in the shaded region. (c) Prove that, no matter what the values of K α and α , the controller provides suﬃ- cient ﬂexibility to place the poles anywhere in the s ²plane. 2.

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## This note was uploaded on 11/07/2011 for the course AERO 16.30 taught by Professor Ericferon during the Spring '04 term at MIT.

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hw1 - 16.31 Prof J P How T.A TBD Handout#1 September 7 2007...

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