SolSec 5.8

# SolSec 5.8 - 5 74 Problems and Solutions Section 5.8(5.81...

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5- 74 Problems and Solutions Section 5.8 (5.81 through 5.85) 5.81 Recall the definitions of settling time, time to peak, and overshoot given in Ex. 3.2.1 and illustrated in Fig. 3.5. Consider a single-degree-of-freedom system with mass m = 2 kg, damping coefficient c = 0.8 N s/m, and stiffness 8 N/m. Design a PD controller such that the settling time of the closed-loop system is less than 10 s. Solution: The settling time is ζω 3 = s t Since t s = 10 s, 3 . 0 = The equation of motion with a PD controller is mx c g x k g x ˙˙ ˙ ++ ()++ () = 21 0 So, ω ζ ωω = + = + = + = + kg m g cg m g 11 22 8 2 2 08 . Therefore, = + = =⋅ 4 03 04 2 2 . . . g g N s/m The gain g 1 can take on any value (including 0). 5.82 Redesign the control system given in Ex. 5.8.1 if the available internal damping is reduced to 50 N s/m. Solution: If the value of c is limited to 50 N s/m, then g 2 becomes gc 2 180 180 50 130 =− = N s/m

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5- 75 5.83 Consider the compressor rotor-shaft system discussed in Problem 5.74. Modern designers have considered using electromagnetic bearings in such rotor systems to improve their design.
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SolSec 5.8 - 5 74 Problems and Solutions Section 5.8(5.81...

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