tut5 - - 035188 Obj314 2011 - + 5+ 6 : . : : : - 035188...

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Unformatted text preview: - 035188 Obj314 2011 - + 5+ 6 : . : : : - 035188 Obj314 2011 - : , : , : . : , . - 035188 Obj314 2011 - , : . : : : - 035188 Obj314 2011 - , - . : . : - ,2 )). - 035188 Obj314 2011 - ' : - '-. - . 2 : : . .' . : - 035188 Obj314 2011 - 0- . , ' : ' . " ' . ' : : - 035188 Obj314 2011 - ' : . - ' : ' . . . . : - 035188 Obj314 2011 - - . : : . ) : : ( - 035188 Obj314 2011 - . : ) - ) ) - ): ) pzmap(sys) ): - 035188 Obj314 2011 - P ole-Zero M ap 1.5 1 0.5 Imaginary Axis 0 -0.5 -1 -1.5 -0.2 -0.15 -0.1 Real Axis -0.05 0 0.05 2- 2 ) 2 ( ) ) pole(sys)). c2d(sys,h) ( 2 . ) zero(sys)) 4 2 3 . , ) pzmap(sysd)): - 035188 Obj314 2011 - P ole-Zero M ap 1 0.8 0.6 0.4 Imaginary Axis 0.2 0 -0.2 -0.4 -0.6 -0.8 -1 -1 -0.8 -0.6 -0.4 -0.2 0 Real Axis 0.2 0.4 0.6 0.8 1 2 4 , 2- 2 . . : ctrb(sys); obsv(sys); % Calculate Mc % Calculate Mo : ," det(ctrb(sys)) . : det(obsv(sys)) - 035188 Obj314 2011 - , .( ) " . : , det(ctrb(sysd))=-0.0048 det(obsv(sysd))=-0.0885 (): P ole-Zero M ap 1.5 1 0.5 Imaginary Axis 0 -0.5 -1 -1.5 -0.2 -0.15 -0.1 R eal Axis -0.05 0 0.05 2 "" : . - 035188 Obj314 2011 - P ole-Zero M ap 1 0.8 0.6 0.4 Imaginary Axis 0.2 0 -0.2 -0.4 -0.6 -0.8 -1 -1 -0.8 -0.6 -0.4 -0.2 0 Real Axis 0.2 0.4 0.6 0.8 1 : : det(ctrb(sys))=0 det(obsv(sys))=-9 det(ctrb(sysd))=0 det(obsv(sysd))=-0.0885 . , . . : - 035188 Obj314 2011 - det(MC) vs k and 0 -10 det(M ) C -20 -30 -40 2 1 0 -1 0 -1 -2 -2 k 1 2 . - 035188 Obj314 2011 - det(M ) vs k and on a contour plot C 2 1.5 1 0.5 0 -0.5 -1 -1.5 -2 -2 -1.5 -1 -0.5 0 k 0.5 1 1.5 2 " " - . : - 035188 Obj314 2011 - Controllability limits 2 1.5 1 0.5 0 -0.5 -1 -1.5 -2 -2 -1.5 -1 -0.5 0 k 0.5 1 1.5 2 : : - 035188 Obj314 2011 - . : , : : . - 035188 Obj314 2011 - 2 , , :: . : . : : - 035188 Obj314 2011 - : : f(p1,p2) =p1(p2 - p2) 2 1 1 0.5 0 -0.5 -1 1 0.5 0 -0.5 p -1 2 1 0.5 0 -0.5 -1 p1 : - 035188 Obj314 2011 - stability limits 1 0.8 0.6 0.4 0.2 p2 0 -0.2 -0.4 -0.6 -0.8 -1 -1 -0.8 -0.6 -0.4 -0.2 0 p 0.2 0.4 0.6 0.8 1 1 6- : , . 2 - . - 2 - . - , ' . , . - 035188 Obj314 2011 - M M , . . : 2 : 1. ) ) 2. . - - : 035188 Obj314 2011 - M: - 035188 Obj314 2011 - " " . : . , : : Nyquist Diagram 25 20 15 10 Imaginary Axis 5 0 -5 -10 -15 -20 -25 -25 -20 -15 -10 -5 Real Axis 0 5 10 15 : - 035188 Obj314 2011 - Nyquist Diagram 1.5 1 Imaginary Axis 0.5 0 -0.5 -1 -2 -1.5 -1 -0.5 Real Axis 0 0.5 : . 0- . Nichols(P) : - 035188 Obj314 2011 - Nichols Chart 0.5 dB 20 1 dB -1 dB 10 Open-Loop Gain (dB) 3 dB 6 dB -3 dB 0 -6 dB -10 -20 -30 -720 -630 -540 -450 -360 -270 -180 -90 Open-Loop P hase (deg) . ' : , . , . . . - 035188 Obj314 2011 - "" , " " . 2- , "" "" . "" M : M ? - 035188 Obj314 2011 - M . - 035188 Obj314 2011 - : . : : - 035188 Obj314 2011 - Nichols Chart 0 dB 0.25 dB 0.5 dB 1 dB 3 dB 6 dB System P : P hase M argin (deg): 21.4 Delay M argin (sec): 0.547 At frequency (rad/sec): 0.682 Closed Loop Stable? Yes 20 Open-Loop Gain (dB) 0 System P : Gain M argin (dB): 6.02 At frequency (rad/sec): 1 Closed Loop Stable? Yes -20 -40 -60 -80 -315 -270 -225 -180 -135 -90 -45 Open-Loop P hase (deg) : . . , - . , . - 035188 Obj314 2011 - * -M grid on - 035188 Obj314 2011 - " : 1. 2. . . : - 035188 Obj314 2011 - " : , : . :: 1. " . 2. " :: - , :: 035188 Obj314 2011 - : " : ": 1. 2. : - 035188 Obj314 2011 - . , . : - 035188 Obj314 2011 - , : , " . - 035188 Obj314 2011 - - : 1. () 1 . : , . : - 035188 Obj314 2011 - - : : - 035188 Obj314 2011 - 0- . 2. . : . . , : : : : - 035188 Obj314 2011 - : . - 035188 Obj314 2011 - , ' , . 0- . , : - : 035188 Obj314 2011 - . ...
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This note was uploaded on 06/30/2011 for the course MECHANICAL 034406 taught by Professor Leonidmirkin during the Spring '10 term at Technion.

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