1 / 18

Control Theory

Control Theory. Bode Stability Criterion. Other view on stability of CL. Where the PHASE of the open loop TF equals -180°(+/-n.360°), we have positive feedback. If the AMPLITUDE RATIO at these frequencies > 0db: unstable closed loop. Two important measures. GAIN MARGIN

zada
Télécharger la présentation

Control Theory

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. ControlTheory Bode StabilityCriterion

  2. Other view onstability of CL Where the PHASE of the open loop TF equals -180°(+/-n.360°), we have positive feedback. If the AMPLITUDE RATIO at these frequencies > 0db: unstableclosed loop.

  3. Two important measures GAIN MARGIN = Howmuch dB of amplitude ratio we canstilladd in the open loop before the amplitude ratio goesabove 0dB at a frequencywhere the phase crosses -180° 2. PHASE MARGIN = ?

  4. Phase Margin = • How much the phase can still be increased before it reaches 0° at a frequency where the amplitude ratio is 0dB. • Howmuch the phasecanstillbedecreasedbeforeitreaches -180° at a frequencywhere the amplitude ratio is 0dB. • None of the above makes sense. [Default] [MC Any] [MC All]

  5. Example 1 rad/s

  6. Given the previous Bode plot of the OPEN LOOP, • GM = 50 dB, PM = 40° • GM = 50 dB, PM = 90° • GM = 30 dB, PM = 40° • GM = 30 dB, PM = 90° • None of the above [Default] [MC Any] [MC All]

  7. On the phase margin The bigger the phase margin, the lessovershoot in the closed loop. First approximation: the “damping ratio” of the closed loop = PM/100 Example: How big do youthink the overshootwillbeif the open loop TF is

  8. The estimated overshoot is • ca. 15% • ca. 30% • ca. 45% • ca. 60% [Default] [MC Any] [MC All]

  9. We can now state that the “disadvantage” of the I action is • thatitincreases the OL gain at low frequencies • thatitincreases the OL gain at high frequencies • that it decreases the OL phase at low frequencies • that it both decreases the OL phase and increases the OL gain at low frequencies [Default] [MC Any] [MC All]

  10. We canuse the stabilitycriterion to design controllers as well • GROUP TASK 1: • A second order processwithgain 2, damping ratio 0.5 and naturaleigenfrequency 20 rad/s is controlledwith a P controller. The time delay in the loop is 0.01s. • What is the maximallyallowedcontrolgain • in order for the CL to bestable • in order for the overshoot to be smaller than 50%?

  11. Group Task II Drug-inducedanasthesia Reaction of the patient’s arterial blood pressure to a drug may vary. Therefore a closed loop system is used. However: Amount of drug supplied to the patient Desired pressure Blood pressure 2e-sT/s 2(s+5) Controller Body 2/(s+2) Sensor • Remark: What kind of control? Why? • Whatis the maximum time delay of the body’s response before the system willbecomeunstable? • Determine the PM and the GM when T=0.05s? When T=0.1s? • What is the influence of T on the step response?

  12. Open loop Bode plot

  13. Use of the Bode plot in control Exercise: Drug-induced anasthesia a) Maximum T? Zonder de dode tijd! ωPM= 8.94 rad/s: PM = 73.4° Tmax = 0.1433s

  14. Use of the Bode plot in control Exercise: Drug-induced anasthesia: b) PM and GM when T=0.05s? When T=0.1s? Zonder de dode tijd! A- Without time delay: PM = 73.4° ωPM = 8.94 rad/s B- Influence of T: T = 0.05s: -25.6° T = 0.1s: -51.2°

  15. Use of the Bode plot in control Exercise: Drug-induced anasthesia: c) Influence on the step response?

More Related