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صفحه 1:
بسم الله الرحمن الرحیم PID Controllers Action, types and tuning Ref 1: Smith & Corripio “Principles and practice of automatic process control”, 3"! ed., Wiley, 2006, Chapter 5 & 7. Ref 2: Yu, Autotuning of PID controllers, 2! ed., Springer, 2006, Chapters 2 &3. Ref 3: Vilanova & Visioli “PID control in the third millennium, Springer, 2012, Chapter 5. Lechrer: ©, @. Pome Pordnunt Daerah oP Dkbed 

صفحه 2:
Action of PID Controllers -d If the action is not correctly selected, the controller will not control * Reverse wien (ereer/deoreer) In feedback control loop, the multiplication of Process fuid Process gain (K,), TS —— Control valve gain (K,), 7 Sensor gain (K,) and 0 Controller gain (K,) must be positive. Reverse action: If K,K,K,>0—7 K,>0 

صفحه 3:
Action of PID Controllers -d © Overt wren (rereerhereer) Ait) gpm Figure 5-3.2 Liquid level control loop. — Direct action: If K,K,K,<0 7 K,<0 To determine the action of a controller, the engineer must know: 1. The process characteristics 2. The fail-safe action of the control valve 

صفحه 4:
Types of PID Controllers -C Classic PID: 0 a ‏كد‎ =m+ K+ % fanate Kr, “40 a dt مرسيط يواعد قلقب ويى ‎Els) TS Range :‏ ‎Parallel PID (Ideal 0.01 to 0.2‏ ‎PID): (0.1)‏ تم بل - لک ويج 1+وم کر ‎Els)‏ ‎Series PID:‏ ‎=x}. 4]| 2‏ 49 = 9( ‎EAs) T,S}\ atpst1 9‏ 

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Types of PID Controllers -C > مسي كا T 1 paraiter =T) +T p TT 35 = D, paralfel 12 Tp, series = * Valid for t/tp=4 

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Tuning of PID 0۵۵۲۵011۵15 ۵ Dore trot OBO tucker ruler ae extol Por 6۳۱ ‏ات0 ۵10 له‎ Okt the mabe tuctert de? Atredy depeuds va pou provess (Type, Order, Parnveters, Ordkeuty, ‏داك‎ civ) Kem Ziegler-Nichols (1942): Recommended ‏وود‎ Df; <0.5 ( ) Ziegler-Nichols K. 1 1 Ku/2 - 0 PI Ku/2.2 ۸ - PID Kull Pyl Py {8 5 

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Tuning of PID 0۵۵۲۵011۵15 ۵ Tyreus-Luyben (1992): Recommended for time- constant dominant processes ( D/r <0. 1) Tyreus—Luyben 18 1 Tt) PI ۲/32 P1045 Derived from Kie™/s PID 12.2 5 ‏63ر2‎ 0 Ciancone-Marlin (1992): Recommended for dead-time dominant processes ( D/r > 2.0) Ciancone-Marlin K. 2 tp PI 1/33 ۹ - Based on Ke” PID 1/33 P/44 — P/8.1 7 * “Series” form of PID 

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Tuning of PID 0۵۵۲۵011۵15 ۵ PID tuning based on IMC (Rivera et al., 0 6( x. 7 tp* ‏ره‎ Remark Kye +22 5 ‏رح‎ ‎ts+1 Kyi. ‏ميد‎ 20.20 Pe +D/2 Kye sot EDD 2 4>0.8D ‏لجوج‎ Kp(A+D/2) 2+0 2120 PI tuning based on IMC (Skogestad, 2003) ‎Method K, 7 2‏ —— فيا اكد كك ‎SIMC K,0+D) mit se) D ‎2773 ame DS D ‎K,@+D) 4G+D) 8‏ تست ‎ ‎ ‎ ‎ ‎ ‎ 

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Model Identification (Open-loop -¢ step test) oer ‘cor | \ 1s Final | Sensor/ * Control + Process ‘Transmit (0, ter ett), % firstorderpludeadime as _K,e™ Ms) 1 Process ‘Gain AG. ——— ——$—<————————— K, =— Am 

صفحه 10:
Model Identification (Open-loop step test) : Fit 1 D=t, 7 Figure 7-2.6a FOPDT model اج | جوا ‎a parameters by fit 1‏ 

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Model Identification (Open-loop step test) : 1۳1 2 ۳-6 | ۱ dey | 0.6324, | ee Figure 7-2.6b FOPDT model ‎parameters by fit 2.‏ 4 لمح ها سوه ‎ 

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Model Identification (Open-loop step test) Fit 3 1 =3(6- ( 2 D=t-+ بط ‎Figure 7-2.6¢ FOPDY model‏ ‎parameters by fit 3.‏ 

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Model Identification (Close-loop ZN) ۰ ‏سییر‎ Tost (OPC) 1. Set the controller gain Kc at a low value, perhaps 0.2. 2. Put the controller in the automatic mode. 3. Make a small change in the set point or load variable and observe the response. If the gain is low, then the response will be sluggish. 4. Increase the gain by a factor of two and make another set point or load change. 5. Repeat step 4 until the loop becomes oscillatory and continuous cycling is observed. The gain at which this, occurs is the ultimate gain Ku , and the period of 

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Model Identification (Relay feedback test) "Roky Predbak Test (Borow & ‏سيوم‎ (OOP) Luyben popularized relay feedback method and called this method “ATV” (autotune variation). mc R Measured Variable Set point 

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03 Model Identification (Relay feedback test) 

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Model Identification (Relay feedback test) " @doanes of Roky Peedbok Test . It identifies process information around the important frequency, the ultimate frequency (where the phase angle is -z). It is a closed-loop test; therefore, the process will not drift away from the nominal operating point. The amplitude of oscillation is under control (by adjusting 2 (. The time required for a relay feedback test is roughly equal to two to four times the ultimate period. If the normalized dead time D /7 is less than 0.28, the ultimate period is smaller than the process time constant. Therefore the relay feedback test is more 

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Model Identification (Relay feedback test) ۰ ‏یی‎ of Roky Porbak Tet <K,e” ۲ +1 Pu/ Time Constant 5 pate A 0.001 0.01 0.1 0.28 3 Dead lime / lime Constant 

صفحه 18:
Model Identification (Close-loop - step test) "| Gkawsuzacke vad Okorgestard, 0 Yuwana and Seborg, 1982, proposed a modification to the Ziegler-Nichols closed-loop experiment. Instead of bringing the system to its limit of stability, one uses a P-controller with a gain that is about half this value, such that the resulting overshoot to a step change in the setpoint is about 30%.This method was modified by Shamsuzzoha and Skogestad, 2010. 

صفحه 19:
Model Identification (Close-loop - step test) K, : Controller gain used in experim +| Ay, : Set point change | ¢, +: First peak time +| 4y,: Maximum output change oy ‏لو ا‎ AY, ‏و5‎ ‏ط‎ 1 D=(0309 0.2095"), A=1.1520V-- 16070V+1 ‏عدم‎ r=2A/B