CONTROL ENGINEERING EXAM Name: ______

EE III./Fall

January 25, 2000. Code: ______

Test
Problem #1
Problem #2
Problem #3
Problem #4
Total
Final mark
  1. Show the block diagram of a sampled-data control system!
Sketch the nature of the signals existing in the control loop! / 2 pt.

2. Formulate the Shannon sampling theorem. / 2 pt.

3. The transfer function of a continuous system is
.
Give the absolute value of the frequency function at . / 2 pt.

4. Poles of a second order system are:
p1=-3+j4 és p2=-3-j4.
Find the time period of the sinusoidal component in the step response and the damping factor of the system! / 3 pt.

5. The transfer function of a continuous system is:.
Its input signal is: ,
its output in steady state is: .
Find the values of and A! / 3 pt.

6. In a closed-loop control system the open-loop transfer function is:
.
Determine the value of K to ensure the available maximum phase margin! / 3 pt.

7. In a state-space realization we have
.
Assuming u(t)0 and find x(t)
at t=4 sec! / 3 pt.

8. Find the size (dimension) of matrices A,B,C and D in a multivariable state-space realization assuming that we have 7 states,
2 inputs and 3 outputs! / 2 pt.

  1. State matrices of a system are:

Is the system fully state controllable?
Is it output controllable?
Is it observable? Explain your answers! / 2 pt.

10. Find y(t) in analytical form if
/ 3 pt.

11. Formulate the general Nyquist stability criterion ! / 2 pt.

12. We build a feedback with unity gain around a linear system given by the transfer function . Is there any K>0 value stabilizing the closed-loop system? Explain your answer! / 2 pt.

13. The transfer function of a system is:
.
Its input signal is .
Give the analytical expression of the transient and quasistationary components of its output signal y!.
(Help: determine the two components of the Laplace transform of the output signal.) / 3 pt.

14. A continuous system given by transfer function
is sampled with sampling time T=0.2. Zero order hold is applied. Give the pulse transfer function and the difference equation of the system! / 3 pt.

  1. Sketch the Bode diagram of a continuous system given by transfer function
and the Bode diagram of the sampled system with sampling time T=0.2 assuming zero order hold (absolute values and phase angles) in frequency domain . (Give the continuous and discrete functions in the same diagram).
Characterize the difference between the continuous and the discrete functions! / 3 pt.

16. Give the pulse transfer function of a discrete PI controller! / 2 pt.

17. In a sampled control system the pulse transfer function of the open-loop is:
. Unity feedback is applied. Determine the critical value of K, where the system is on the boundary of stability and unstability. / 2 pt.

  1. The transfer function of a continuous controller is: .
What kind of compensation is realized by it?
Give the shape of its unit step response!
Determine its initial and final values. / 3 pt.

19. What is meant by the type number of a control system? / 2 pt.

20.In a closed-loop control system the open-loop transfer function is:
. Give the steady state error for unit step, ramp and quadratic reference input signal! / 3 pt.

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