Question

SOLVE USING MATLAB

A servomechanism position control has the plant transfer function 10 s(s +1) (s 10) You are to design a series compensation transfer function D(s) in the unity feedback configuration to meet the following closed-loop specifications: . The response to a reference step input is to have no more than 16% overshoot. . The response to a reference step input is to have a rise time of no more than 0.4 sec. The steady-state error to a unit ramp at the reference input must be less than 0.02 (a) Design a lead compensation that will cause the system to meet the dynamic response specifications (b) If D(s) is proportional control, D(s) = kp, what is the velocity con- stant K,? (c) Design a lag compensation to be used in series with the lead you have designed to cause the system to meet the steady-state error specification (d) Give the MATLAB plot of the root locus of your final design. (e) Give the MATLAB response of your final design to a reference step

Answer 1

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d) matlab:

clc;

clear all;

close all;

s=tf('s');

g=10/(s*(s+1)*(s+10));

gclead=104*(s+1.721)/(s+21.2787);

gclag=(s+0.1)/(s+0.002);

rlocus(g*gclead*gclag)

File Edit View Insert Tools Desktop Window Help Root Locus 20 20 80 60 20 40 Real Axis (seconds )

e)

clc;

clear all;

close all;

s=tf('s');

g=10/(s*(s+1)*(s+10));

gclead=104*(s+1.721)/(s+21.2787);

gclag=(s+0.1)/(s+0.002);

step(feedback(g*gclead*gclag,1))

File Edit View Insert Tools Desktop Window Help Step Response Peak ampitude: 1.29 Overs oot (%): 28.9 At time (seconds): 0.627 12 System: untitied Hise time (sconds): 0244 04 0.5 1.5 25 3.5 Time (seconds)