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Control Theory

Control Theory

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Control Theory

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  1. ControlTheory Session 5 – Transfer Functions

  2. Transfer function of • A • B • C • None of the above A B [Default] [MC Any] [MC All] C

  3. Step response of z(t) A t B Definition of step response: Δz(t) ifΔu(t) is a step of size 1

  4. A, B on previous graph? • A=2, B=3 • A=2, B=6 • A=4, B=6 • None of the above [Default] [MC Any] [MC All]

  5. Standard form of first order TF Step response:

  6. Second order processes Typicalexample: mass-spring-damper z(t) u(t) (set-up in a horizontal plane, spring in rest positionwhen x=0)

  7. The step response of the m-c-k • Will oscillate • Will not oscillate • Might oscillate, depending on the values of m,cand k [Default] [MC Any] [MC All]

  8. The step response will oscillate if • Thatdoesn’tdependon [Default] [MC Any] [MC All]

  9. Standard form of second order TF

  10. Step respones of 2nd order processes >1: Overdamped =1: Critically damped = fastest without oscillations <1: Underdamped: Oscillations! +

  11. The step response of anunderdamped 2nd order system • Shows no overshoot • Shows overshoot of which the sizedependsonnbutnoton • Shows overshoot of which the sizedependson butnoton n • Shows overshoot of which the sizedependson and n [Default] [MC Any] [MC All]

  12. Overshoot in 2nd order systems

  13. Overshoot in 2nd order systems

  14. Group Task m=1 [kg] k=1 [N/m] Find the TF and plot the step response for c= 4 [Ns/m] c=2 [Ns/m] c=1 [Ns/m]

  15. Group Task 2 m=1 [kg] k=1 [N/m] Can we nowadd a P controller and calculate the Transfer function of the closed loop? (by the way, what’s the transfer function of a P controller?)