Hello all,
Sorry for inconvenience done, there were some misprints on the thread posted before.
I need your kind help answering coursework questions(fig.1) with the following Z-transform open loop transfer function
Wo () = (0.04(z+ 0.675)/ (z− 1) (z− 0.584) (z − 0.563))
My attempt is as follows:
For desired poles: T = 0.1s, = wn=3rad/s, ζ=0.7, P1,2= e^(ζwnT)e^(±jwnT√(1−ζ^2))
P1,2 = 0.8105∠0.214= 0.792-+0.172j
Desired poles = 0.792+0.172j, Actual poles: 1, 0.584,0.563 Actual zeros: 0, -0.675
For angle theta, I plugged in 0.792+0.172j , Wo (z) = (0.04(z+ 0.675)/ (z− 1) (z− 0.584) (z − 0.563))
(12.5+6.687) -(140+39.58+36.9) =-197deg, 197-180= 17.56=theta degrees angle deficiency,
please refer root locus fig2
Digital compensator attempt answer is D(z)=K(z-0.7586)/(z-0.6983)
then I introduced compensator D(z) found before in the open loop TF to find gain K
plug in z=0.792+0.172j
Open loop (with compensator D(z)) Tf (z) = (K (0.04) (z-0.7586) (z + 0.675)/(z-0.6985) (z− 1) (z− 0.584) (z− 0.563)) =1
K=0.4458
And finally, I did Matlab simulation fig3 which is nearly to specs, but I am not totally sure
Kindly could you comment if my working(method) of the root locus(fig2) and Matlab simulation(fig3) if is it correct?
TY
Sorry for inconvenience done, there were some misprints on the thread posted before.
I need your kind help answering coursework questions(fig.1) with the following Z-transform open loop transfer function
Wo () = (0.04(z+ 0.675)/ (z− 1) (z− 0.584) (z − 0.563))
My attempt is as follows:
For desired poles: T = 0.1s, = wn=3rad/s, ζ=0.7, P1,2= e^(ζwnT)e^(±jwnT√(1−ζ^2))
P1,2 = 0.8105∠0.214= 0.792-+0.172j
Desired poles = 0.792+0.172j, Actual poles: 1, 0.584,0.563 Actual zeros: 0, -0.675
For angle theta, I plugged in 0.792+0.172j , Wo (z) = (0.04(z+ 0.675)/ (z− 1) (z− 0.584) (z − 0.563))
(12.5+6.687) -(140+39.58+36.9) =-197deg, 197-180= 17.56=theta degrees angle deficiency,
please refer root locus fig2
Digital compensator attempt answer is D(z)=K(z-0.7586)/(z-0.6983)
then I introduced compensator D(z) found before in the open loop TF to find gain K
plug in z=0.792+0.172j
Open loop (with compensator D(z)) Tf (z) = (K (0.04) (z-0.7586) (z + 0.675)/(z-0.6985) (z− 1) (z− 0.584) (z− 0.563)) =1
K=0.4458
And finally, I did Matlab simulation fig3 which is nearly to specs, but I am not totally sure
Kindly could you comment if my working(method) of the root locus(fig2) and Matlab simulation(fig3) if is it correct?
TY
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