Question

PROBLEM 1 A plane system is depicted in Figure 1, Here, τ denotes the delay of the pilot. A sluggish pilot is denoted by t 0.6 and a rapid pilot is denoted by t-0.1. Other parameters of the system are given by K- 1, T 2,and t 0.5. Write a piece of MATLAB code to calculate the closed-loop poles for rapid and sluggish pilots. Make remarks based on the outcomes of your experiments. Find the maximum pilot delay that can be tolerated for stability. (Ts )Ts +2) s(s2 3s 6) Figure 1: A pilot model, elevator servo, and a plane model respectively.

Answer 1

matlab code:

clc;

clear all;

close all;

s=tf('s');

g1=-(2*s+1)*(0.6*s-2)/((0.5*s+1)*(0.6*s+2));

g2=-(2*s+1)*(0.1*s-2)/((0.5*s+1)*(0.1*s+2));

g3=-10/(s+10);

g4=-(s+6)/(s*(s^2+3*s+6));

gs=g1*g3*g4;% sluggish system open loop TF

gr=g2*g3*g4;% rapid system open loop TF

sys1=feedback(gs,1);% close loop TF for sluggish system

sys2=feedback(gr,1);% close loop Tf for rapid system

pole(sys1)% closed loop poles of sluggish system

pole(sys2)% closed loop poles of rapid system

rlocus(gs);

figure

rlocus(gr)

ans =

-9.4526 + 0.0000i
-4.5228 + 2.2595i
-4.5228 - 2.2595i
0.2793 + 2.0314i
0.2793 - 2.0314i
-0.3937 + 0.0000i

ans =

-19.6267 + 0.0000i
-10.7712 + 0.0000i
-3.8885 + 0.0000i
-0.1697 + 2.7880i
-0.1697 - 2.7880i
-0.3742 + 0.0000i

File Edit View Insert Tools Desktop Window Help Root Locus 20 10 20 20 15 10 10 15 20 Real Axis (seconds )

File Edit View Insert Tools Desktop Window Help Root Locus 100 50 100 80 20 40 60 80 100 Real Axis (seconds )

sluggish pilot:

The gain should be less than 0.65

rapid pilot:

The gain should be less than 1.2