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Unformatted text preview: 5- 86Problems and Solutions Section 5.8 (5.81 through 5.85) 5.81Recall the definitions of settling time, time to peak, and overshoot given in Example 3.2.1 and illustrated in Figure 3.6. 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 ts=3!"Since ts= 10 s, !"=0.3The equation of motion with a PD controller is m!!x+c+g2( )!x+k+g1( )x=So, !=k+g1m=8+g12"=c+g22m!=0.8+g22 2( )!Therefore, !"=0.8+g24"#$%&’("=0.3g2=0.4 N)s/mThe gain g1can take on any value (including 0). 5.82Redesign the control system given in Example 5.8.1 if the available internal damping is reduced to 50 N⋅s/m. Solution: If the value of cis limited to 50 N⋅s/m, then g2becomes g2=180!c=180!50=130 N"s/m5- 875.83Consider the compressor rotor-shaft system discussed in Problem 5.74. Modern designers have considered using electromagnetic bearings in such rotor systems to...
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- Fall '09