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MidTerm1_2009

MidTerm1_2009 - CHEE 455 Process Control Winter 2009...

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1 CHEE 455 – Process Control Mid-Term Exam #1 Winter 2009 15% of final grade Process Modelling and Dynamic Behaviour of Simple Processes Allowed: Pens, pencils, and calculators 3 pages of questions, with an appendix containing useful information 30 points total 1.) D ( s ), E ( s ), and F ( s ) below are all second-order transfer functions. One of them is underdamped, one is critically damped, and one is overdamped. 2 . 0 4 . 2 4 . 6 2 . 3 ) ( 2 + + = s s s D 2 2 1 2 2 2 5 ) ( + + + = s s s s E ) 1 3 ( ) 2 3 ( 3 2 ) ( + = s s s s F a.) [1 point] Write each of these transfer functions in the form 1 ) ( 2 + + = bs as K s G b.) [2 points] Identify which transfer function is underdamped, which is critically damped, and which is overdamped. c.) [1 point] For the overdamped transfer function, find the exponential time constants ( τ 1 and τ 2 ) which would appear in the time domain solution for the response to a step input. d.) [1 point] For the critically damped transfer function, find the exponential time constant ( τ ) which would appear in the time domain solution for the response to a step input. e.) [1 point] For the underdamped transfer function, identify the values of τ and ζ (the symbols used for writing second order transfer functions in standard form).

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MidTerm1_2009 - CHEE 455 Process Control Winter 2009...

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