Multiloop Control Systems

Transcription

1 Mltiloop Control Stem. Introdction. The relative gain arra (RG) 3. Pairing inpt-otpt variable 4. Dnamic conideration 5. Mltiloop controller tning 6. Redcing control loop interaction

2 Introdction Mltiloop control approach» Pair inpt and otpt variable together» Deign SISO controller for each inpt/otpt pair» ttempt to minimize interaction beteen controller Challenge» Often not obvio ho to pair variable to minimize control loop interaction» Nmber of poible paring for nn tem = n!» Detning of SISO controller often necear de to interaction

3 Ditillation Colmn Eample Controller otpt D,, P, h D, h Maniplated inpt D,, R, Q D, Q et pairing not obvio Nmber of poible pairing = n! = 5! = 0 Need efficient method to creen poible pairing

4 The Relative Gain Qantifie the change in tead-tate gain beteen an inpt-otpt pair that occr hen other control loop are cloed Provide a meare of tead-tate proce interaction from onl gain information Relative gain beteen inpt j and otpt i ij i i j j i, j [, n]» i j i the open-loop gain ith all other control loop open» i j i the cloed-loop gain ith all other control loop cloed

5 Relative Gain Calclation for Stem Stead-tate model Open-loop gain 0 Cloed-loop gain 0 Relative gain 0 0 0

6 General Relative Gain Calclation Stead-tate model Calclation of H matri Relative gain nn n n n n nn n n T H H H H H tem H ij ij ij

7 The Relative Gain rra (RG) Definition Λ n n nn tem Λ Each ro and colmn of the RG mt m to nit» tem Λ» General nn tem onl need to calclate n- element per ro or colmn

8 Inpt-Otpt Pairing: Cae RG Five poible cae» = : open-loop and cloed-loop gain are identical; pair and» = 0: open-loop gain i zero; do not pair and» 0 < < : cloed-loop gain i larger than the openloop gain; pair and if i cloe to» > : cloed-loop gain i maller than the openloop gain; pair and if i cloe to» < 0: open-loop and cloed-loop gain have oppoite ign; do not pair and

9 Inpt-Otpt Pairing: General Cae RG Λ n n nn ij i i j j Pairing rle» ij = : pair j and i» ij < 0: do not pair j and i» ij = 0: do not pair and» 0 < ij < : pair and if i cloe to» ij > : pair and if i cloe to Caveat» RG i baed onl on tead-tate information and neglect proce dnamic

10 lending Stem Eample Ue and to control and Material balance Open-loop gain Relative gain ) ( ) (

11 lending Stem Eample cont. RG Cae Λ Nobet pairing /, / Pair /, / Pair Λ Λ Λ

12 44 RG Eample RG for ditillation colmn Λ Pairing » = 0.93 pair /» 4 =.54 pair 4 /» 43 = pair 3 / 4» Pair / 3 3 = 3.34

13 Dnamic Conideration: Stabilit mption» Each proce tranfer fnction G pij () i table, rational and proper.» Each controller tranfer fnction G ci () contain integral action.» Each individal control loop i table hen the other n- loop are open. Niederlinki tabilit theorem» me the inpt and otpt are paired a /, /,, n / n» The mltiloop control tem i ntable if: n» Can be applied to different pairing b rearranging ch that the gain of the paired inpt and otpt are on the diagonal» The relt alo provide a fficient condition for tabilit if n = i ii 0

14 Dnamic Conideration: Performance Tranfer fnction matri Pairing baed on RG Pairing baed on time contant: /, / ) ( G e e e e p /, / Pair Λ

15 Mltiloop Controller Tning Control tem deign» Ue RG to pair inpt and otpt variable» Deign SISO controller for each inpt-otpt pair Standard tning procedre» Tne each controller ith other controller in manal» Place all controller in atomatic and detne controller a necear to mitigate interaction Special cae» One otpt i mch more important than the other otpt (e.g. reactor temperatre v. reactor liqid level)» Onl detne controller for leat important otpt o important otpt remain ell controlled

16 Redcing Control Loop Interaction lternative approache» Detne individal SISO controller» Select different maniplated inpt and/or controller otpt» Utilize a mltivariable controller (ee Chapter 0 in tet) lending tem eample Λ