Controls/Spring 2026/Test 3

• Closed-book (in-class) part
  • Given a system, be able to determine the system type, appropriate static error constants, and steady state errors for step, ramp, and parabolic inputs. Know how to adjust when these are not unit step, ramp, or parabolic inputs.
  • Given a system with gain control, be able to determine the minimum possible error by using a Routh Array to determine the range of stability and the static error constants and steady state errors calculated as functions of gain.
  • Given a system with gain control, be able to accurately sketch the root locus, including the real axis portions, calculations of the asymptotes center and directions, \(j\omega\) axis crossings and K values for them (also meaning when the system is marginally stable and the frequency of oscillation), and break points. For the latter, you will be given solutions to \(dK/d\sigma=0\) but will need to know what those solutions mean and how to get the \(K\) value for them. You will not need to calculate or apply angles of departure or arrival.
    • Be able to determine the gain ranges where the dominant pole / poles of the system is / are underdamped, critically damped, and overdamped.
    • Be able to determine the fastest approximate settling time for a system, the gain at which it occurs, and the likelihood that the approximation is accurate

• Open-book (out-of-class) part
  • Given a specific set of transient design criteria that pinpoint a desired set of system poles, be able to locate those poles. For example, if you are given a system and a particular OS% and Ts.
    • Be able to determine the system pole values for those points.
    • Be able to determine the location of a PD controller zero to make this happen and the gain for the compensator in that case.
    • Be able to discuss when you may want to use a Lead controller and place the zero somewhere other than the PD location; also be able to determine the location of the lead pole and the compensator gain in cases where you are told where to put the compensator zero.
  • Given a specific desired type, static error constant, or steady-state error for a system, be able to design a PI or Lag controller to make that happen. Also be able to discuss the main considerations for where to place the poles and zeros for these kinds of compensators.
  • Be able to "put it all together" to design a compensator that can both adjust the short-term transient as well as the steady-state error.
  • For a system with a forward transfer function G and a feedback transfer function H, be able to determine where the overall system zeros are.
  • The circuits for compensation will not be on the test.

• Good older problems to look at:
  • 2015 Fall Test 3 - whole thing
  • 2012 Spring Test 2 - whole thing
  • 2010 Spring Test 3 Closed Book - whole thing; note this mainly goes through Ch. 8
  • 2009 Spring Test 3 Closed Book - whole thing; note this mainly goes through Ch. 8

• Not on the test:
  • State Space
  • Bode or Nyquist Plots