Practice Problems

Practice Problems - Starting with the motor and flywheel at...

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Practice Problems No turn-in required 1. Problems from Franklin’s text: 4.7 part a Sketch required. 4.16 part a Ans. System type is 1. Ramp steady state error is r o /A 4.19 parts a,b,and c Ans. 2 and 0 c) 10 ) 10 20 ( 10 b) 10 ) 10 20 ( ) ( 10 a) 2 3 2 3 - + + + + + + + + + I p I I p I p I p K K K K s K s s s K s K s s K s K 2. A brushless dc motor has a rated speed of 6300 rpm and a rated torque of 15.16 N.m. Suppose we use this machine in a flywheel based uninterruptible power supply scheme where, upon loss of input power to the motor, we want to be able to deliver 10 kW for 15 sec with no more than a 5% drop in speed from the machine’s rated speed. a) Find the required combined motor and flywheel moment of inertia J eq . Ans. 7.069 kg-m 2 b) Suppose we design a control scheme to bring the motor and flywheel up to speed holding current at rated current (and thus torque at rated torque).

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Unformatted text preview: Starting with the motor and flywheel at 0 speed, how long will it take to bring the flywheel up to rated speed assuming negligible friction? Ans. 307.6 sec 3. A certain system has a controller: 8 1 ) ( + = s s D c a) Assume the sampling rate T is 10% of the controller time constant. Find approximate expressions for D c [z] for a digital realization of the controller using: Tustin’s method Ans. 152 168 1-+ z z Euler’s method Ans. 72 80 1-z b) Find a difference equation relating controller output to controller input for the D c [z] you found using Tustin’s method. Ans. ] 1 [ ] [ 168 1 ] 1 [ 168 152 ] [-+ +-= k e k e k u k u...
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Practice Problems - Starting with the motor and flywheel at...

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