Data Structure for the Transporter Controller File (TCF)



CONTROL ENGINEERING EXAM Name: ______________________

EE III./Fall

January 25, 2000. Code: ______________________

| |Test | |

| |Problem #1 | |

| |Problem #2 | |

| |Problem #3 | |

| |Problem #4 | |

| |Total | |

| |Final mark | |

|Show the block diagram of a sampled-data control system! | |2 pt. |

|Sketch the nature of the signals existing in the control | |( |

|loop! | | |

| | | |

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

| | |( |

| | | |

| | | |

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|3. The transfer function of a continuous system is | |2 pt. |

|[pic]. | |( |

|Give the absolute value of the frequency function at | | |

|[pic]. | | |

|4. Poles of a second order system are: | |3 pt. |

|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! | | |

|5. The transfer function of a continuous system | |3 pt. |

|is:[pic].[pic] | |( |

|Its input signal is: [pic], | | |

|its output in steady state is: [pic]. | | |

|Find the values of [pic] and A! | | |

|6. In a closed-loop control system the open-loop transfer| |3 pt. |

|function is: | |( |

| | | |

|[pic]. | | |

|Determine the value of K to ensure the available | | |

|maximum phase margin! | | |

|7. In a state-space realization we have | |3 pt. |

|[pic]. | |( |

|Assuming u(t)(0 and [pic] find x(t) | | |

|at t=4 sec! | | |

|8. Find the size (dimension) of matrices A,B,C and D in a| |2 pt. |

|multivariable state-space realization assuming that we | |( |

|have 7 states, | | |

|2 inputs and 3 outputs! | | |

|State matrices of a system are: | |2 pt. |

|[pic] | |( |

|Is the system fully state controllable? | | |

|Is it output controllable? | | |

|Is it observable? Explain your answers! | | |

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

|[pic] | |( |

| | | |

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

| | |( |

|12. We build a feedback with unity gain around a linear | |2 pt. |

|system given by the transfer function [pic] . Is there | |( |

|any K>0 value stabilizing the closed-loop system? | | |

|Explain your answer! | | |

|13. The transfer function of a system is: | |3 pt. |

|[pic]. | |( |

|Its input signal is [pic]. | | |

|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.) | | |

|14. A continuous system given by transfer function [pic]| |3 pt. |

|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! | | |

|Sketch the Bode diagram of a continuous system given by | |3 pt. |

|transfer function [pic] | |( |

|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 [pic]. (Give the | | |

|continuous and discrete functions in the same diagram). | | |

|Characterize the difference between the continuous and | | |

|the discrete functions! | | |

|16. Give the pulse transfer function of a discrete PI | |2 pt. |

|controller! | |(( |

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|17. In a sampled control system the pulse transfer | |2 pt. |

|function of the open-loop is: | |(( |

|[pic]. Unity feedback is applied. Determine the critical| | |

|value of K, where the system is on the boundary of | | |

|stability and unstability. | | |

|The transfer function of a continuous controller is: | |3 pt. |

|[pic]. | |( |

|What kind of compensation is realized by it? | | |

|Give the shape of its unit step response! | | |

|Determine its initial and final values. | | |

|19. What is meant by the type number of a control | |2 pt. |

|system? | |(( |

|20. In a closed-loop control system the open-loop | |3 pt. |

|transfer function is: | |(( |

|[pic]. Give the steady state error for unit step, ramp | | |

|and quadratic reference input signal! | | |

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