Question

For the unity feedback system in the below figure, 1. EGO) R(s)) C(s) G(s)K (s 1) (s + 4) a) Sketch the bode plot with Matlab command bode0 b) Plot the nyquist diagram using Matlab command nyquist(0, find the system stability c) Find phase margin, gain margin, and crossover frequencies using Matlab command margin(0 and find the system stability

Answer 1

matlab code for a) b) c)

clc;

clear all;

s=tf('s');

g=1/((s+1)*(s+4)); % plant transfer function

bode(g);grid % bode plot

figure

nyquist(g);% nyquist plot

figure

margin(g);grid % bode plot with margins

Figures - Figure File Edit View Insert Tools Debug Desktop Window Help | Figure 1 × Bode Diagram 30 40 T0 90 -180 102 10 101 10 Frequency (rads) Property Editor-Waveform Display Name: g Click and drag to move Property Editor

File Edit View Insert Tools Desktop Window Help Nyquist Diagram dS 10 dB dB 0.05 0.05 0.1 0.8 0.2 0.6 02 04 0.4 Real Axs

Figures - Figure 3 File Edit View Insert Tools Debug Desktop Window Help Figure 3x Bode Diagram Gm= Inf dB {at Inf rad/s), Pm= Inf 50 103 102 10 Frequency (rads) Property Editor-Waveform Display Name: g
the ststem is asymptotically stable ...ie stable for all values of positive gain