# ETEC 415 – Control Systems – HW 5

ETEC 415 – Control Systems – HW 5

## Module 5 Homework Assignment

1. Use MATLAB to plot the root locus of
𝐺(𝑠)= (𝑠+3)/𝑠(𝑠+1)(𝑠+2);
𝐻(𝑠)= 1/(𝑠+4)
Provide the commands you used and a copy of root locus figure. Also calculate the asymptotes (real axis intercept and angles).
2. Use MATLAB to plot the root locus of
𝐺(𝑠)= (𝑠+3)/(𝑠2+4𝑠+13)(𝑠−1)
𝐻(𝑠)= 1
Provide the commands you used and a copy of root locus figure. Click on the root locus to determine at which K value the system will become stable.
3. Use MATLAB to plot the root locus of
𝐺(𝑠)= (𝑠+4)/ (𝑠2+6𝑠+13)
𝐻(𝑠)= 1
Provide the commands you used and a copy of root locus figure. Also calculate the angles that the root locus leaves the complex poles. Use sgrid to plot 𝜁 lines of 0.7, 0.8, 0.9, and 0.99 and 𝜔𝑛 circles of 2, 4, and 6. Provide command and plot of root locus with sgrid. Click on the root locus to determine the gain (K) where 𝜁=0.9 and 𝜁=0.99 intersect the root locus. Simulate the closed-loop system in Simulink with both gain values. Provide a screen shot of the Simulink model and the plot for both gain values. How did the system response change when the gain was changed?