DOE Webinar Sound Options & Topics
The DOE Webinar provides sound options and discusses FY 2021 Phase I Release 2 Topics. Access to the recorded webinar will be available post-meeting. For unanswered questions, contact the provided points of contact for further clarification or email sbir-sttr@science.doe.gov. Explore the agenda, schedule, and participating DOE programs in the Funding Opportunity Announcements for Phase I Releases 1 and 2.
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Presentation Transcript
Chapter III Frequency response analysis 1. Experimental system characterization 2. Nyquist stability analysis 3. Compensators 4. PID tuning a. PID structure b. Ziegler Nichols 1 c. Ziegler Nichols 2 d. Cohen Coon Automatic Control 211 ASU MN Sabry 2021 III.4 1
PID structure Kp R E C + G KI / s KD s + ++ May not be entirely known Proportional part Kp: High signal for high E; small effect when E 0 High signal if E persists with time; may increase overshoot Integral part KI=Kp/TI: High signal if E increases with time; phases out when E is decreasing Derivative part KD=KpTD: You may deactivate any part PI only is very common Automatic Control 211 ASU MN Sabry 2021 III.4 2
Ziegler Nichols 1 For systems exhibiting NO oscillation for open-loop operation: 1.2 c (t) 1 ) ( ( ) ( ) ( ) t T T t T 1 c t K e delay 0.8 T delay c0 = K u0 0.6 0.4 u T c T u (t) T = = 0 K Tdelay 0 0.2 KT u0 0 delay delay 0 0 2 4 6 8 KP K0 TI TD Type of controller P PI PID 0.9 K0 1.2 K0 Tdelay/0.3 2 Tdelay Tdelay/2 Automatic Control 211 ASU MN Sabry 2021 III.4 3
Ziegler Nichols 2 For systems exhibiting oscillation for closed-loop operation: 8 K = Kcr Adjust controller gain K to obtained sustained oscillation (Neither decay nor grow) K is small K is large 6 4 2 time 0 0 2 4 6 8 10 12 Kcr( 2K0) Pcr ( 4Tdelay) Required gain: Associated period: -2 -4 -6 -8 KP TI TD Type of controller P PI PID (Kcr/2) 0.9 (Kcr/2) 1.2 (Kcr/2) (Pcr/4)/0.3 2 (Pcr/4) (Pcr/4)/2 Automatic Control 211 ASU MN Sabry 2021 III.4 4
Cohen Coon Replaces Ziegler Nichols 1 for large Tdelay: delay T T u T c T T = = 0 = K R 0 KT 0 delay delay KP TI TD Type of controller K R + 01 P 3 K R + 30 3 9 20 + R R + 00.9 delay T PI 12 + + 32 6 13 8 + R R 4 + 16 3 12 R PID delay T delay T K 0 11 2 R Automatic Control 211 ASU MN Sabry 2021 III.4 5
Fine tuning guidelines Effects of increasing a parameter independently* Settling time Small change Increase Steady- state error Parameter Rise time Overshoot Stability Decrease Increase Decrease Degrade KP Decrease Minor change Increase Eliminate No effect in theory Degrade Improve if KDsmall KI Decrease Decrease KD * Kiam Heong Ang; Chong, G.; Yun Li (2005). "PID control system analysis, design, and technology". IEEE Transactions on Control Systems Technology. 13 (4): 559 576. doi:10.1109/TCST.2005.847331. S2CID 921620. Automatic Control 211 ASU MN Sabry 2021 III.4 6
