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Assignment 7

The Design of Feedback Control Systems

1. Watch video “EE495 – Week 7 – Lecture”
2. Read Chapter 10 in the text Modern Control Systems, 12th Edition.
3. Work the following problems:
   1. 1. A unity feedback control systems for a robot submarine has a plant with a third-order transfer function

    G(s) = K / (s(s + 10)(s +50))

   We want the overshoot to be approximately 7.5% for a step input and the settling time (with a 2% criterion) of the system be 400ms.  Find a suitable phase-lead compensator by using root locus methods.  Let the zero of the compensator be located at s = -15, and determine the compensator pole.  Determine resulting Kv.

   1. 1. A system of the form below with unity feedback has G(s) = K / (s + 5)2

   We desire the steady-state error to a step input to be approximately 5% and the phase margin of the system to     be approximately 45 degrees.  Design a lag network to meet these specifications. 

4. Save work in a file with the title: “HW7_StudentID”, with your student id substituted in the file name.  Show all work for full credit.
5. Upload file “HW7_StudentID”

Lab 7

The Design of Feedback Control Systems

1. For the HW problem problems use MATLAB to plot the Root Locus for problem (i) and the compensated Bode plot for problem (ii)
2. Include all MATLAB code, calculations and screenshots in a Word entitled “Lab7_StudentID”.
3. Upload file “Lab7_StudentID”

Assignment 8

Digital Control Systems

1. Watch video “EE495 – Week 8 – Lecture”
2. Read Chapter 13 in the text Modern Control Systems, 12th Edition.
3. Work the following problems:
   1. 1. A closed-loop system has a hold circuit and process as shown below.  Determine G(z) when T = 1 and

    Gp(s) = 2 / (s + 2)

   1. 1. A sampled-data system such as that presented in problem (i) has a sampling period T = 0.05s and has

   G(z) = K (z3 + 10.3614z2 + 9.758z + 0.8353) / (z4 – 3.7123z3 + 5.1644z2 – 3.195z + 0.7408)

   • Determine K when the two real poles break away from the real axis.
   • Calculate the maximum K for stability.

Lab 8

Digital Control Systems

1. For the HW8 problems use MATLAB to plot the Root Locus for problem (ii).
2. Include all MATLAB code, calculations and screenshots in a Word entitled “Lab8_StudentID”.
3. Upload file “Lab8_StudentID”