TUT_wk10 - Compute the unit-step response y kT for k = 0 to...

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Tutorial questions for week 10 Part A: 1. Apply the w -transform to the following characteristic equations of discrete-data control systems, and determine the conditions of stability (stable, marginally stable, or unstable) using the Routh-Hurwitz criterion. Answer: (b) two roots outside of the unit circle. 2. The characteristic equation of a linear digital control system is Determine the values of K for the system to be asymptotically stable. Answer: -0.2<k<0.07
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Part B: 1. The block diagram of a sampled-data control system is shown below. (a) Derive the forward-path and the closed-loop transfer functions of the system in z -transforms. The sampling period is 0.1 second.
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Unformatted text preview: Compute the unit-step response y ( kT ) for k = 0 to 100. (c) Repeat parts (a) and (b) for T= 0.05 second. Answer: (a) When T=0.1s, 8187 . 8187 . 1 021904 . 02341 . ) ( ) ( 2 +-+ = z z z z E z Y 8406 . 7953 . 1 021904 . 02341 . ) ( ) ( 2 +-+ = z z z z R z Y (b) (c) When T=0.05s, 9048 . 9048 . 1 0058484 . 0060468 . ) ( ) ( 2 +-+ = z z z z E z Y 91069 . 8988 . 1 0058484 . 006046 . ) ( ) ( 2 +-+ = z z z z R z Y 2. The block diagram of a sampled-data control system is shown below. (a) Derive the transfer functions Y ( z )/ E ( z ) and Y ( z )/ R ( z ). (b) Find the error constants * p K , * v K and * a K . Answer: (a) (b)...
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