Question

i am needing help with a b c o chris question thanks

1000 O(s) Gc(s) s(s2 110s 1250) Figure 2: Disc Drive System Block Diagram We will now try to design a compensator with the requirements that Overshoot 10% ii. Ts S 100ms II. eramp(oo) s 0.001 Do the following (you may use MATLAB at your leisure, but be sure to explain your logic for your design choices) a) Use MATLAB to draw the root locus when Gc K. Augment your root locus to include the boundaries of the region where the dominant closed-loop poles must be to satisfy the transient requirements. Comment on your ability to achieve these requirements with a gain-only controller. b) Design a PD controller for Gc to meet the transient requirements, i.e. i) and ii) above c) Compute the steady-state error to a ramp, eramp(o) Is it below your requirement in iii)? If not, design a Pl compensator to satisfy ii) above. d) Use MATLAB to compute the resulting closed-loop poles and discuss second order dominance e) Simulate the step and ramp response in MATLAB and verify that you have achieve the design objectives. If not, discuss you re-design strategy and re-design your PD and/or PI controller to achieve the objectives

Answer 1

Sel a) and 40, un 66, 6 วิ The loCatonoinarl- pole one S3.33 sus on at -106 , 8104 Чо 12.9

ne ZuOc oms 2S3 33 Tan (tos-1o nPD S (s+23.882 GuSxlooo 23.RPP ム ー S-う。

at 9 3441 St o010

matlab:

a) root locus:

clc;

clear all;

close all;

s=tf('s');

g=1000/(s*(s^2+110*s+1250));

rlocus(g)

File Edit View Insert Tools Desktop Window Help Root Locus 100 200 200 100 50 50 100 150 Real Axis (seconds )

d) closed loop response with PD and PID controller:

clc;

clear all;

close all;

s=tf('s');

g=1000/(s*(s^2+110*s+1250));

gpd=5.6*(s+23.8882);

gpi=(s+0.1)/(s+0.0107);

step(feedback(g*gpd,1),feedback(g*gpd*gpi,1));grid

legend('PD response','PID response')

File Edit View Insert Tools Desktop Window Help Step Response Sysem: PD respons0 Peak amplitude: 1.21 Overshoct (%): 20.9 At time (seconds) : 0。053 System: PD response Sutting time (seconds):0.0984 04 0.14 002 004 006 008 0.1 0,12 Time (seconds)
As the overshoot is more compared to the given specifications it indicates that the second oreder approximation is not exactly matching the specifications but can be tuned