control theory
Download
Skip this Video
Download Presentation
Control Theory

Loading in 2 Seconds...

play fullscreen
1 / 18

Control Theory - PowerPoint PPT Presentation


  • 98 Views
  • Uploaded on

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

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Control Theory' - zada


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.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
control theory

ControlTheory

Bode StabilityCriterion

other view on stability of cl
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.

two important measures
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

= ?

phase margin
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]

given the previous bode plot of the open loop
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]

on the phase margin
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

the estimated overshoot is
The estimated overshoot is
  • ca. 15%
  • ca. 30%
  • ca. 45%
  • ca. 60%

[Default]

[MC Any]

[MC All]

we can now state that the disadvantage of the i action is
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]

we can use the stability criterion to design controllers as well
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%?
group task ii
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?
slide16
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

slide17
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°

slide18
Use of the Bode plot in control

Exercise: Drug-induced anasthesia:

c) Influence on the step response?

ad