AME 437: Objectives for the Final Exam

To successfully complete the final exam in AME 437, you should be able to:
  1. List and explain the cause of the effects of varying the individual gains in a PID controller, on
    1. rise time;
    2. maximum overshoot;
    3. settling time; and,
    4. steady state tracking.
  2. Linearize a system of nonlinear differential equations about an equilibrium point.
  3. Solve a linear ordinary differential equation using Laplace transform technique, including, if necessary
    1. computing and/or using a table to determine the Laplace transform of a time function;
    2. applying the properties of Laplace transforms to convert a differential equation into an algebraic equation in the frequency domain;
    3. compute the partial fraction expansion of a function in the frequency domain; and,
    4. computing and/or using a table to determine the inverse Laplace transform of a frequency domain function.
  4. Identify transfer function, Y(s) to which the Final Value theorem can be used to compute y(t) as time becomes large.
  5. Apply the Final Value theorem to determine the steady state response of a transfer function, Y(s)/R(s) to different reference inputs, R(s) (steps, ramps, etc.).
  6. Represent the linear differential equation describing a mechanical, electrical, fluid or electromechanical system in block diagram form.
  7. Determine the algebraic form of transfer function(s) from a block diagram, including the transfer function from
    1. the input to the output;
    2. the disturbance to the output;
    3. the input to the error; and,
    4. the disturbance to the error.
  8. Determine the differential equation represented by a block diagram or transfer function.
  9. Determine the transient response characteristics (to a step input) of a transfer function based on a plot of the location of the transfer function's poles and zeros.
  10. Compute the percentage overshoot, peak time and settling time of a system from the location of the "dominant second order poles."
  11. Determine the stability of a system based upon the location of the system's poles and zeros.
  12. Specify the location in the s-plane of the poles and zeros of a system to meet overshoot, settling time and rise time specifications.
  13. Derive and explain the effect that an additional pole or zero, and the location of that pole or zero, has on the transient response of a second order system.
  14. Construct the Routh array to determine the stability of a transfer function.
  15. Construct the Routh array to determine the stability of a transfer function as a function of the value of certain parameters in the transfer function.
  16. Sketch the root locus of a (simple) transfer function K G(s) as K varies from zero to plus infinity, including
    1. computing asymptote angles;
    2. computing the intersection of the asymptote with the real axis;
    3. compute the departure angles of the locus from the poles of G(s);
    4. compute the arrive angles of the locus to the zeros of G(s);
    5. compute the break away point(s) from the real axis between two poles; and,
    6. compute the break in point(s) to the real axis between two zeros.
  17. Explain each of the rules or formulas for sketching root locus plots in terms of the phase of G(s).
  18. Explain the relationship between the phase of G(s) and the location of s relative to the poles and zeros of G(s).
  19. Explain the relationship between the magnitude of G(s) and the location of s relative to the poles and zeros of G(s).
  20. Determine the gain value, K corresponding to a particular point on a root locus plot.
  21. Identify if a lead compensator can be implemented to affect desired transient response characteristics.
  22. Design a lead compensator to achieve desired transient response characteristics based upon a root locus plot.
  23. Explain the effect that a lead compensator has on the root locus plot of a system, and the corresponding effect on the transient response of the system.
  24. Design a lag compensator to achieve a desired steady state error specification using the final value theorem.
  25. Explain the effect that a lag compensator has on the root locus plot of a system, and the corresponding effect on the transient response of the system.
  26. For a non-unity feedback system, compute the characteristic equation and manipulate it to be in a form so that the root locus can be plotted to determine transient response characteristics and stability of the sytsem.
  27. Explain why the phase of G(s) must always be -180o on the root locus plot of G(s).
  28. Explain in terms an Arts & Letters major can understand, what is represented on a Bode plot.
  29. Sketch the Bode plot for a (simple) transfer function G(s), including sketching the contribution to the Bode plot of each of the individual factos of G(s).
  30. Determine the stability of a system, if possible, from its Bode plot.
  31. Determine the gain and phase margin of a system from a Bode plot.
  32. Determine the steady state error of a unity feedback, closed loop system to different inputs (step, ramp, parabolic, etc.) from the Bode plot of the open loop transfer function.
  33. Design a lead compensator to achieve desired transient response characteristics based upon a Bode plot for the system.
  34. Explain the effect that a lead compensator has on the Bode plot of a system and the corresponding effect on the gain and phase margins.
  35. Design a lag compensator to achieve a desired steady state error specification based upon a Bode plot.
  36. Explain the effect that a lag compensator has on the Bode plot of a system, and the corresponding effect on the steady state error of the system.