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あきおくまじ
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1 Development of a Predictive Functional Control Tecnique and Practical Applications to Cemical Processes Sumitomo Cemical Co., Ltd. Production & Safety Fundamental Tecnology Center Satoru HASHIZUME We ave developed a practical metodology for te application of Predictive Functional Control (PFC) to certain processes wic conventional Proportional Integral Derivative () controllers ave difficulty in andling. PFC is a variant of te widely-used Model Predictive Control (MPC) tecnology, and is caracterized by its excellent control performance wit a fairly simple calculation algoritm. PFC can be implemented using te standard functionalities of DCS (Distributed Control Systems) and PLC (Programmable Logic s), wic makes it easier tan conventional MPC packages to introduce into and maintain in existing control systems. In tis paper, a general explanation of PFC, as well as illustrative examples of its practical application, will be given. 1) 2) Model Predictive Control : MPCPFC Predictive Functional Control Watt 3) 1940 Proportional Integral Derivative 4) 1936 Taylor Ziegler Nicols 4) DCS Distributed Control System CRT DCS 4) 90% 2015

2 5) 1960 Kalman Single Input Single Output : SISO Multi Input Multi Output : MIMO MPC MPC Ricalet IDCOM Identification and CommandCutler Ramaker DMC Dynamic Matrix Control MPC MPC MPC Que Refining Petrocemicals Cemicals MPC ) MPC 7) MPC MPC 6) RicaletIDCOM MPC PFC IDCOM DMC 9) MIMO 6) PFC 10) MPC Fig. 1 DCS MPC MPC External PC DCS Actual Process Fig. 1 Flow Pressure Level Temperature Quality Optimizer Model Predictive Control General configuration of control systems employing MPC and controllers MPC MPC MPC SISO MPC 2015

3 DCS PFCPFC PFC DCS MPC PFC Fig. 2 DCS Actual Process Fig. 2 P F C Flow Pressure Level Temperature Quality Configuration of a control system employing PFC and controllers PFC MPC 11) P F C P F C Fig. 3 Fig. 4 MPC PFC MPC P ym M MV 1 M 1 DCS Fig. 5 Reference Trajectory Past Future Model Identification Prediction orizon, P Steam Flow Rate (Manipulated Variable : MV) Fig. 3 Model Modeling Temperature of Distillation Column (Model Variable : ym) Basic concept of model identification MV Control orizon, M k 1 k k+1 k+2 k+m 1 k+p Fig. 5 General concept of MPC ym MV Model Predictive Control Fig. 4? Steam Flow Rate (Manipulated Variable : MV) Inverse Model Calculation of appropriate MV Set Point : SP Reference Trajectory Temperature of Distillation Column (Process Variable : ) Basic concept of model predictive control PFC MPCM P Fig

4 Past Future Reference Trajectory (1) (1) ym k+ ym k + 1 = α m ym k + K m β m MV k L m / Δt (1) MV k Coincide point, k k k+ Fig. 6 Basic concept of PFC ym MV Δt α m exp T m β m 1 α m L m = 0 (1 ) ym k + 1 = α m ym k + K m β m MV k (1 ) PFC MPC PFC k k (2)TRBF 95% 3 Δt yr k + 1 = [ SP k k ] 1 exp TRBF (2) Fig. 7PFC K m (= Δ /Δ MV )T m L m 3 1Δ t ym kmv k Δ yr k = yr k+ yr k = yr k+ Δ ym k = ym k+ ym kδ yr k = Δ ym k (1 ) (2) (3) MV k = [ SP k k ] l + βm ym k K m βm Δt βm 1 exp T m 3 Δt l 1 exp TRBF (3) Fig. 7 Δ L m ΔMV T m Process Variable Model Variable Manipulated Variable Actual process response and its approximation by 1 st order + dead time process model (3) Fig. 7 r m(= L m/δ t) ym k rm ym k k r m pred Fig. 8 k ym k ym k rm pred k (4) 2015

5 ym k ym k rm Past Future ym k ym k rm ym TRBF/3 IMC Internal Model Control PFC k rm k 1 k k+rm Fig. 8 MV k = (1 ) (4) PFC TRBF TRBF PFC k SP k k MPC (4) Δ ydm k Δ yr k = Δ ym k + Δ ydm k (5) MV k = Concept of dead time compensation [ SP k pred k ] l + βm ym k K m βm pred k = k + ( ym k ym k rm ) [ SP k k ] l + βm ym k Δymd k K m βm (4) (5) PFC Fig. 9 1%/%300sec 150sec 300sec0%1% PFC PFC TRBF 300sec SP, [%] PFC TRBF MIMO MPC Fig. 2MPC Fig. 9 PFC SP (IMC) [sec] Comparison of control performance by PFC and (tuned wit IMC metod) PFC Fig. 10Initialize α m β m AUTO PFC Calculate bumpless (1 ) Calculate ym k (4) Calculate MV k 2015

6 START Initialize PFC TI Vapor Reflux AUTO? N Calculate bumpless Feed FC Y Calculate ym k steam BTM i N i = i + 1 TI : Temperature Indicator FC : Flow Rate to be controlled by controller Y Calculate MV k i = 1 Fig. 11 Scematic diagram of a distillation column and its control structure N Ceck Bounds Recalculate MV k Y Output MV k Fig. 10 Algoritm flowcart of PFC, ym [%] Δ D m T m ΔMV ym(model) MV MV [%] Fig. 10SFC Sequential Functional CartST Structured Text DCS PFC DCS TRBF Fig. 12 Result of te step response test PFC TRBF Fig DCSPFC DCSPFC MV SP Fig. 11PFC K m(= Δ /Δ MV )T m L m Fig. 12 Temperature [%] Fig. 13 TRBF Temperature of a distillation column controlled by PFC PGC SP 2015

7 PGC PFC Fig. 14 A B A A PGC 35 PFC 80% Fig. 15 PFC Distillation Column A Distillation Column B 1) PFC 12) PFC PFC Fig. 16 TiTr To Qr(6) Manipulated Variable LB A B HB steam FC TC LB A steam LB : Low Boiling point components HB : Hig Boiling point components A : component A B : component B FC : Flow rate to be controlled by controller TC : Temperature to be controlled by PFC PFC Analyzer Process Variable B HB Qr k = C p ρ m V Tr k Tr k 1 Δt Tj k ( Ti k + To k ) /2 UA( Tj k Tr k ) (6) Cp ρv UA k Ti k To ktr k Qr k PFC Fig. 14 Product quality control structure of a distillation column employing PFC Reactant Catalyst Tr TC PFC Manual To TI Component A [%] 12r TC Ti Fig. 15 Control of te product quality of a distillation column Fig. 16 Scematic diagram of a batc reactor and its control structure 2015

PFC Fig. 17 Temperature [%] Fig. 17 PFC+FF Heat Reaction Manual Comparison of te result of temperature control by PFC + FF (Feedforward) and manual operation PFC MPC DCS MPC 1) D.E. Seborg, T.F. Edgar and D.

8 PFC Fig. 17 Temperature [%] Fig. 17 PFC+FF Heat Reaction Manual Comparison of te result of temperature control by PFC + FF (Feedforward) and manual operation PFC MPC DCS MPC 1) D.E. Seborg, T.F. Edgar and D.A. Mellicamp, Process Dynamic and Control Second Edition, WILEY (2003). 2),,, 64 (), 166 (2012). 3),, (1990), p.22. 4), 11, (2008). 5),, 2010-@, 32 (2010). 6) S.J. Qin and T.A. Badgwell, Control Engineering Practice, 11, 733 (2003). 7),, 143 (2009). 8) J. Ricalet and D. O Donovan, Predictive Functional Control, Springer (2009). 9),,,, 10 (15), 132 (2011) 10),,, //, 52 (8), 285 (2008). 11),, 117 (10), 691 (1997). 12),,, 58, (2014). 13),,, 67 (), 117 (2015) PROFILE Satoru HASHIZUME 2015

MPC.dvi

MPC.dvi 1997 1 Copyright c 1997 by Manabu Kano All rights reserved 1 1 3 11 3 12 3 121 3 122 5 13 6 14 6 15 7 2 9 21 9 22 10 221 10 222 11 23 12 24 13 25 14 26 15 27 17 2 1 11 (MPC; Model Predictive Control) 12