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Unformatted text preview: ME 475
Out: Feb. 11, 2011 Due: Feb. 17, 2011 PROBLEM 1: Given: HOMEWORK #5 Spring 2011 Reference temperature R(s) Heating system + D(s) + Normalized Temperature θ(s) Fig. 1(a): Open-loop temperature-control system. Reference temperature R(s) − Amplifier Heating system D(s) Normalized Temperature θ(s) + Temperature sensor Fig. 1(b): Closed-loop temperature-control system. Find: For each system: (a) (b) (c) (d) (e) θ(t) if r(t) is a unit step and the disturbance is zero; time constant τ steady-state error in temperature due to a unit step input percentage change in output temperature if there is a 5% change in K θ(t) if d(t) is a step input of size 0.1 advantage of the closed-loop system PROBLEM 2: GIVEN:
R + − K Y FIND: (a) Using Routh-Hurwitz, determine the range of proportional gain K for a stable closed-loop system. (Hint: generate the Routh array as function of K, then determine conditions on K that will guarantee that the 1st column of the array is strictly positive.) (b) Sketch the corresponding root locus as function of gain K, paying close attention to asymptotes, breakaway and/or break-in points, and imaginary axis crossings. (c) Use MATLAB to generate the root locus as K goes from 0 to infinity. Make sure you add arrowheads to your plot. On this plot, find the exact point(s) where the roots cross the imaginary axis and compare this gain with the range you provided in part (a). Also, determine locations for all 4 roots for this value of gain. PROBLEM 3: (repeat of problem 3 set 1…it has finally come due.) Compare the two structures shown in the figure below with respect to sensitivity to change in the overall gain owing to changes in the amplifier gain. Use the relation d ln F K dF S= = d ln K F dK as the measure. Select H1 and H2 so that the nominal system outputs satisfy F1 =F2, and assume KH1 > 0. ...
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This document was uploaded on 03/31/2011.
- Spring '09