MM7. PID Control Design

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1 MM7. PD Control Deign Reading Material: FC: p , DC: p Propertie of PD control 2. uning Method of PD Control 3. Antiwindup echnique 4. A real cae tudy BO9000 0/9/2004 Proce Control

2 . PD Feedback Controller PD Mean: P: Proportional control : ntegral control D: Derivative control u t u t u t e t e τ dτ t t 0 D e t PD Control Sytem Structure: cacade control rt - et PD Controller Plant G yt What are the characteritic of PD control? 0/9/2004 Proce Control 2

3 . Proportional Feedback Control Control Structure ime Domain : Cloed loop Control Sytem rt - et U u t e t Frequency Domain : D E P-Controller: G D G G cl D G G Plant G yt Advantage: a imple controller Diadvantage: Steady tate offet/error problem Diturbance rejection problem 0/9/2004 Proce Control 3 unity p v a feedback lim 0 lim 0 lim 0 G G 2 o o G o y e e e a v p

4 0/9/2004 Proce Control 4 Example: Speed Control of a DC Motor Example: Speed Control of a DC Motor Working mechanim of a DC motor t torque contant i a armature current e electromotive force emf contant Differential equation decription. m e a t e i θ a a t m a e t m m m e a a a a a a t m m m v R R b J implified v i R dt di L i b J : θ θ θ θ θ See FC p.47-49

5 Start Simulink in Matlab... >> imulink Simulink ha become the mot widely ued oftware package in academia and indutry for modelling and imulating dynamic ytem t turn your computer into a lab for modeling and analyzing ytem that imply wouldn't be poible or practical otherwie 0/9/2004 Proce Control 5

6 P-Control for the DC Motor Download motorp.mdl A DC Motor Model : G τ, τ 2 τ τ p, e 2 0., A n order to eliminate the teady-tate offet, introduce integral control!... 0/9/2004 Proce Control 6

7 0/9/2004 Proce Control 7.2 P Feedback Control.2 P Feedback Control Control Structure integral/reet time Cloed loop Control Sytem Advantage: Eliminate teady tate offet/error Good teady diturbance rejection How about the tranient repone? / Plant G Frequency Domain : Domain : ime 0 E U D d e t e t u t t τ τ - rt et yt G G G G G D G D G cl

8 P-Control for the DC Motor Download motorp.mdl 0/9/2004 Proce Control 8

9 0/9/2004 Proce Control 9.3 PD Feedback Control.3 PD Feedback Control Control Structure D Derivative/rate time Cloed loop Control Sytem Advantage: ncreae the damping mprove the tability Good tranient and teady diturbance rejection he mot popular control technique ued in indutry! / i D Plant G 0 E U D et d e t e t u D D t t τ τ - rt et yt 2 2 G G G D G D G D D cl

10 PD-Control for the DC Motor Download motorpd.mdl 0/9/2004 Proce Control 0

11 Effect of contant Diturbance 0/9/2004 Proce Control

12 MM7. PD Control Deign. Propertie of PD control 2. uning Method of PD Control 3. Antiwindup echnique 4. A real cae tudy: BO9000 0/9/2004 Proce Control 2

13 Principle: 2. uning the PD Controller t u t e t e d Det τ τ t0 U D E D Ziegler-Nichol uning Method Quarter decay ratio method: uning by decaying ratio of 0.25 tep repone: Proce reaction curve Slope rate R/τ Lag time L 0/9/2004 Proce Control 3

14 Exercie : Deign a P, P, PD controller for the DC motor example, According to quarter decay m. 0/9/2004 Proce Control 4

15 uning the PD Controller continue... Ziegler-Nichol uning Method Ultimate Senitivity method rt - et Ultimate: u Plant G yt mpule repone Ultimate gain: u Ultimate period: P u 0/9/2004 Proce Control 5

16 MM7. PD Control Deign. Propertie of PD control 2. uning Method of PD Control 3. Antiwindup echnique 0/9/2004 Proce Control 6

17 3. ntegrator Antiwindup Motivation: actuator aturation phenomena integration integrator windup Antiwindup technique: urn off the integral action a oon a the actuator aturate mplement with a dead zone mplement with a nonlinearity 0/9/2004 Proce Control 7

18 Example: DC Motor Control with Saturation Download motorpaturation.mdl motorpantiwind.mdl 0/9/2004 Proce Control 8

19 Download motorpaturation.mdl motorpantiwind.mdl Output repone Control effort 0/9/2004 Proce Control 9

20 Download motorpaturation.mdl motorpantiwind.mdl 0/9/2004 Proce Control 20

21 MM7. PD Control Deign. Propertie of PD control 2. uning Method of PD Control 3. Antiwindup echnique 4. A real cae tudy: BO9000 0/9/2004 Proce Control 2

22 BO9000 Control: BO9000! "#$%"&' "$!!! $#*"&'!" 0/9/2004 Proce Control 22

23 BO9000 Control: Problem "!,-#./#0" "! "$23 4"$ " " "$ 5 "523! ""$ 23! "" 6-%7%04,!$!" " 0/9/2004 Proce Control 23

24 BO9000 Control: Problem!"!!" 0/9/2004 Proce Control 24

25 BO9000 Control: Problem "!" 0/9/2004 Proce Control 25

26 BO9000 Control: Reuirement 0/9/2004 Proce Control 26

27 BO9000 Control: Modelling Sledge direction to CD 6 W ire Sledge direction to CD Sledge Pulley Pulley 2 M otor W ire w ind up around the m otor axel 0/9/2004 Proce Control 27

28 BO9000 Control: Modelling F2 Friction moment for pulley 2 F Friction moment for pulley M he moment of the motor electromagnetic moment FM he friction moment of the motor F FS he friction force of the ledge F 2S he force on the ledge affected by pulley 2 F S he force on the ledge affected by pulley F M he force on pulley affected by the motor F 2M he force on the motor affected by pulley 2 F M2 he force on pulley 2 affected by the motor F M he force on the motor affected by pulley F S he force on pulley affected by the ledge F S2 he force on pulley 2 affected by the ledge he poitive orbital direction F S Sledge F 2S F S F S2 Pulley F Pulley 2 FS F M F 2M F F M Motor F M2 F2 M FM 0/9/2004 Proce Control 28

29 BO9000 Control: Modelling F gx U a - SLa t Ra i M r M M 2 2 r r M 2 M x x x f f C a r M 0/9/2004 Proce Control 29

30 BO9000 Control: PD Controller 0/9/2004 Proce Control 30

31 BO9000 Control: PD Controller 0/9/2004 Proce Control 3

32 BO9000 Control: PD Controller 0/9/2004 Proce Control 32

33 BO9000 Control: PD Controller V 0/9/2004 Proce Control 33

34 BO9000 Control: Root Locu Deign with Antiwindup 0/9/2004 Proce Control 34

35 Exercie : Exercie One Deign a P, P, PD controller for the following DC motor peed control, According to quarter decay method. Exercie 2: Download ZN_tuning_motor.mdl mplement the above ytem with an actuator aturation in imulink model with u max 2, u min -2. Deign an integrator antiwindup trategy for your deigned P controller. 0/9/2004 Proce Control 35

Lecture 4. Chapter 11 Nise. Controller Design via Frequency Response. G. Hovland 2004

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