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ME461_F11_Prelab8_11_06_11

# ME461_F11_Prelab8_11_06_11 - ME 461 Homework#8 Fall 2011...

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ME 461 1 Prelab #8 ME 461 Homework #8 Fall 2011 Due at the beginning of Lab #8 Suggested Reading: Study the Matlab help pages for the following functions: mldivide , sisotool , tf , zpk , pzplot and rltool . Lab 8 manual. 1. Write out the syntax for creating the following transfer functions in Matlab. Use 50ms sampling time. 2 3 2 2 4 ( ) 5 1 z z G z z z z + = + + ( ) ( )( ) 0.25 ( ) 5 0.5 0.7 z H z z z = + 2. Sketch the pole zero plots of the transfer functions in problem 1. Indicate whether each is stable and/or has minimum phase. You may use Matlab to check your answers. 3. Show that a first order plant ( ) τ = + 1 K G s s preceded by a zero order hold (ZOH) has a discrete transfer function given by ( ) ( ) τ τ = 1 T T K e V z U z z e . 4. Show that the transfer function derived in problem 3 results in a difference equation (which can be implemented in a microprocessor!) given by ( ) ( ) ( ) = + 1 2 1 1 v n c v n c u n , where c 1 and c 2 are constants. 5.
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