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Chapter 22, Problem 3DP
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The role of materials engineering in “green design”.

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Consider the following static route choice problem where 110 vehicles travel from point A to point B. The corresponding travel time (in minutes) of each link is as follows: t₁ = x1 ; t₂ = = x2 + 20; t3 = x3 + 10; t₁ = 3x4 where Xi denotes the number of vehicles that choose link i. Find the number of vehicles that travel on each link when a. The user equilibrium condition (UE) is satisfied, where vehicles select the route with the minimum travel time; and b. The system optimum condition (SO) is satisfied, where the total travel time is minimised. C. Report the total delay savings when satisfying SO instead of UE. 2 A B 3 4
2. Using Routh Hurwitz criterion, determine the stability of a system whose transfer function is given by the following. 10 H(s) = s5+2s4+3s3+6s²+5s+3
4. Consider a unity (negative) feedback control system whose open-loop transfer function is given by the following. 1 G(s): s³ (s + 2) What is the steady state error of the system for input u(t) = t³ 1(t)? Recall from the class lecture that steady-state error is given by the following formula. S ess = lim S-01 + G(s) U(s)

Chapter 22 Solutions

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