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QUESTION

# Assignment

Assignmentt 3

The Stability of Linear Feedback Systems

1. Watch video “EE495 – Week 3 – Lecture”
2. Read Chapter 6 in the text Modern Control Systems, 12th Edition.
3. Work the following problems:
1. A system has a characteristic equation: q(s) = s3 + 20s2+ 5s + 100 = 0
• Determine whether the system is stable using the Routh-Hurwitz criterion.
• Determine the roots of the characteristic equation.
2. A system has the characteristic equation: q(s) = s3 + 10s2+ 29s + K = 0
• Shift the vertical axis to the right by 2 by using s = sn – 2, and determine the value of gain K so that the complex roots are s = -2 ± j.
4. Save work in a file with the title: “HW3_StudentID”, with your student id substituted in the file name.  Show all work for full credit.

Lab 3

The Stability of Linear Feedback Systems

1. A unity negative feedback system with Gc(s)G(s) = K(s + 2) / (s(1 + τs)(1 +2s)) has two parameters to be selected.
1. Determine and plot the regions of stability for this system.
2. Select τ and K so that the steady-state error to a ramp input is less than or equal to 25% of the input magnitude.
3. Determine the percent overshoot for a step input for the design selected in part (b).Use MATLAB to plot y(t) for a step input R(s).
2. Include all MATLAB code, calculations and screenshots in a Word entitled “Lab3_StudentID”.