White Paper. OptiRamp Model-Based Multivariable Predictive Control. Advanced Methodology for Intelligent Control Actions

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1 Whte Paper OptRamp Model-Based Multvarable Predctve Control Advanced Methodology for Intellgent Control Actons Vadm Shapro Dmtry Khots, Ph.D. Statstcs & Control, Inc., (S&C) propretary nformaton. All rghts reserved.

2 OptRamp Model-Based Multvarable Predctve Control Whte Paper Table of Contents Introducton... 2 PC vs. PID Control Comparson... 3 PC Concept... 4 PC Transfer Functons... 5 PC Algorthm... 7 About Statstcs & Control, Inc Introducton The OptRamp Model-Based Multvarable Predctve Control (PC) Submodule s a software functon wthn the OptRamp Advanced Dspatch Control System (ADCS), Operator Tranng Smulator (OTS), and Dynamc Smulaton (DS) sutes that s desgned to control proccesses wth multple nterdependent nput and output sgnals. Ths state-of-the-art tool complements the Statstcs & Control, Inc., (S&C) market offerng as t encompasses a 360 degree vew of the process by ncorporatng predctve models, real-tme optmzaton, and control to maxmze plant performance whle mantanng a favorable cost euaton. Exstng sngle-dmenson control methods, such as the PID controller, have shown nstablty n regulatng hghly volatle processes as well as an nablty to accomodate the complex nonlnear nteractons wthn process varables. PC overcomes both of these challenges by ntegratng mathematcal process models nto the plant control structure, where control varable set ponts are proactvely mantaned by ssung predctve control decsons gven a fxed set of ambent condtons. Furthermore, havng a process model of the entre plant allows PC to make global control actons that beneft the overall process and that account for each process obect s constrants, whch sets PC apart from the PID controller envronment. The OptRamp Model-Based PC Submodule drectly nteracts wth the OptRamp Real-Tme Optmzaton (RTO) Submodule to ensure the most proftable and optmal operaton. RTO generates transfer functons (dscussed later n ths whte paper) for the PC that represent a dynamc relatonshp between nput and output sgnals. The ultmate goal of the OptRamp Model-Based PC Submodule s to calculate desrable values of manpulated varables (s) to ensure that targets for controlled varables (CVs) are reached and account for chosen optmzaton crtera. PC acheves ths goal by examnng past changes n s and dsturbance varables (DVs), such as ambent condtons, and by usng modeled relatonshps between all process varables produced by the OptRamp Modelng Submodule to ascertan the mpact that past changes n s and DVs had on controlled varables, accountng for process delay tmes. PC s also eupped wth an operator nterface that allows users to montor processes wthn the submodule as well as control actons trendng and forecasted controlled varable behavor based on a predefned tme horzon. Copyrght 20, S&C propretary nformaton. All rghts reserved. 2

3 OptRamp Model-Based Multvarable Predctve Control Whte Paper PC vs. PID Control Comparson The proportonal ntegral dervatve (PID) controller s one of the most prolferated control methods n the control system ndustry. The basc prncple of PID controller work s to measure the dfference between the controlled varable value (output) and ts set pont (called the error) and to adust the manpulated varable (nput) to mnmze ths error. Dependng on the desred outcome, the error can be adusted proportonately (for boundary results), ntegrally (for gradual results), or usng error dervatves to damp resultng oscllatons. Adustng PID coeffcents s both an art and a scence for optmal PID tunng and control. Once optmal parameters are found, the man advantages of mplementng a PID controller are ts speed and robustness. The man dsadvantages are susceptblty to oscllaton n hghly volatle process condtons (for example, when set ponts are suddenly changed) as well as a complete lack of knowledge of the rest of the process. Usng a PID controller can be thought of as drvng a car by only usng the rear-vew mrror. It s a reactve control method; the conseuences of control actons reman unknown untl a new control acton s reured to adust for prevous errors. The OptRamp Model-Based PC Submodule s a proactve control method. In the drvng example, usng ths submodule can be thought of as lookng forward and beng able to antcpate future turns based on current and past actons. Fgure shows the advantage of usng PC over a standard PID controller, where the controlled varable (flow) drop and eventual recovery s avoded gven certan ambent dsturbances by proactvely changng manpulated varable values to accommodate for smooth process operaton. Feedback Control Acton Model Based Feed forward Control Acton Fuel Flow No control acton Steam Flow Dsturbance Dsturbance Dsturbance Flow ncrease caused by fuel Control Acton Dsturbance Flow ncrease caused by fuel Control Acton Generator Steam Flow No Flow Change Steam Flow 2 Target Target flow SP Flow drop Flow drop and recovery No target flow varaton Manual Control- Exstng Operatng Mode PID Control Model Based Control Tme Fgure. PC vs. PID controller Copyrght 20, S&C propretary nformaton. All rghts reserved. 3

4 OptRamp Model-Based Multvarable Predctve Control Whte Paper PC Concept PC algorthms are based on model predctve control (MPC) concepts. Fundamentally, the PC optmzaton routnes use steady-state and dynamc process models to predct how the process wll respond to changes n each of the ndependent varables. It s then able to calculate future moves that wll mantan the operaton at specfed targets. The future s typcally gven by a parametrcally defned horzon N, whch s set dependng on the underlyng process. PC s an teratve process, where control decsons are adusted based on current nformaton at every tme nstance and where the horzon s shfted accordng to a movng wndow methodology. For successful operaton, PC reures three fundamental elements: Process Model produced by the OptRamp Modelng Submodule Transfer Functon produced by the OptRamp RTO Submodule Cost Functon derved wthn the PC tself Both dynamc and steady state process model constructon are descrbed n detal n the OptRamp Modelng Submodule whte paper. The transfer functon descrbes the relatonshp between nput and output system sgnals. The dervaton and the types of transfer functons are dscussed n detal n the PC Transfer Functons secton. Once the nput/output transfer functon s known, t s possble to predct the system s reacton after any dsturbance and at any gven tme. Also, t s possble to compute the manpulated varable value so that the ntegrated (over tme) devaton of CVs from the set pont would be mnmal (Cost Functon). The PC determnes the optmal value for each manpulated varable wth the purpose of upholdng the optmzaton crtera whle smultaneously mantanng the man CVs at a gven level. Euaton () provdes a typcal cost functon. M ( ) 2 2 αy βx, () C = SP y + x = = where y represents CVs, N SP s the correspondng controlled varable set ponts, change n s, and α y and β x are relatve weghts for y and x x s the, respectvely. PC uses RTO to estmate y as a transfer functon of x s and to mnmze the cost functon C. The PC Algorthm secton detals the cost functon setup and optmzaton. PC output s a set of manpulated varable values necessary to mnmze the varance of CVs from ther set ponts whle preservng reured constrants. The output s teratvely recalbrated when new nformaton becomes avalable; thus, PC outputs the best possble scenaro for a specfed horzon and current operatng condtons. Copyrght 20, S&C propretary nformaton. All rghts reserved. 4

5 OptRamp Model-Based Multvarable Predctve Control Whte Paper PC Transfer Functons One of crucal components of PC functonalty s a set of robust and relable transfer functons, whch descrbe the transtonal process from system nput to system output. Gven a tme-dependent nput varable ( t ) and output varable CV ( t ), the transfer functon s shown n euaton (2). { ( )} L{ CV ( t) } H L t = where H s a lnear operator and L ( t ) and ( ) ( t ) and ( ), (2) { } { } CV t, respectvely, as shown n euatons (3) and (4). ( ) { ( )} st ( ) 0 L CV t are the Laplace transforms of F s = L CV t = e t dt (3) ( ) { ( )} st ( ) G s = L CV t = e CV t dt (4) H can be thought of as a rato of { ( )} 0 { } L CV t to ( ) L t. OptRamp RTO emprcally generates nput/output transfer functons usng data obtaned from the smulated open-loop step performed on the current model structure. In case the transtonal process can be characterzed by deal delay (gven by δ ( t ν), where δ s the Drac delta functon and ν s process tme delay), the Laplace transform s gven n euaton (5). s { } ( ) δ ( ν) w s = L t = e ν (5) Then, consderng a frst-order system, the transform functon s gven n euaton (6). ν s ke p W() s = τ s +, (6) p where k p s the process gan andτ p s the process tme constant. Ths transfer functon s llustrated n Fgure 2a. All coeffcents are optmally derved usng genetc algorthms. Overall, the nput/output transfer functons may assume a number of structural forms. Fgure 2b shows a CV = W + W 2 2. Fgure 2c shows a seral structure gven parallel structure gven by [ ] [ ] by CV 2 W W 2[ ] =. For systems wth more than one output, the nput/output transfer functon has the form shown n Fgure 2d. The outputs are related to the nputs va euatons (7) and (8). Copyrght 20, S&C propretary nformaton. All rghts reserved. 5

6 OptRamp Model-Based Multvarable Predctve Control Whte Paper [ ] [ ] CV = W + W 22 2 (7) [ ] [ ] CV 2 = W2 + W 2 2, (8) where W [ ] s the transfer functon correspondng to nput. a) W CV e) DV Wd W W CV b) W2 CV W2 2 W22 c) W CV W2 CV2 2 W2 CV2 W CV DV2 Wd2 W2 Manpulated Varables CV Controlled Varables DV- Measured Dsturbance Varables d) W22 2 W2 CV2 Fgure 2. PC transfer functon structures Processes are nfluenced by external dsturbances, such as changes n ambent condtons and changes n the fuel ualty. To accommodate these effects, the OptRamp RTO Submodule ncorporates process dsturbances nto the model wth the dsturbance transfer functons shown n Fgure 2e. Copyrght 20, S&C propretary nformaton. All rghts reserved. 6

7 OptRamp Model-Based Multvarable Predctve Control Whte Paper PC Algorthm The PC algorthm reures the followng nputs: cost functon and nput/output transfer functons. PC uses an enhanced verson of the cost functon, whch ncorporates weghts for the set pont and manpulated varable change components and uses the least suares method for standard error modfcaton. The PC cost functon s gven n euaton (9). 2 M L R 2 αcv SP, W DV βx = = = φ2 C = φ + M R, (9) where s the th manpulated varable and DV s the th dsturbance varable present n the transfer functon W for every controlled varable CV, wth =,..., L, =,..., M, p=,..., P and =,..., R; φ+ φ = are weghts regulatng the mportance of each component n the cost functon; and α CV represents the relatve weghts of each controlled varable, such that M αcv = and β x are the relatve weghts penalzng large changes n the s so that = R βx =. Also, = ( ) ( ) t + t s the change n the manpulated varable = from tme nstance t to tme nstance t+, where t ( 0,..., N). The constrants n cost functon optmzaton are the boundary condtons for every euaton (0). gven n LL UL, (0) LL s the parametrcally defned lower lmt and where lmt of process varables. UL s the parametrcally defned upper values. The process model adds addtonal constrants, relatng to other To solve ths optmzaton problem, PC uses technues descrbed n the OptRamp RTO Submodule whte paper. For a gven tme horzon N, the soluton s a lst of values gven by set (). { } =,..., ; =,..., M L () Copyrght 20, S&C propretary nformaton. All rghts reserved. 7

8 OptRamp Model-Based Multvarable Predctve Control Whte Paper Once the control acton s taken accordng to the calculated manpulated varables, the horzon s shfted by one tme ncrement and the algorthm s repeated, ensurng that an optmal soluton s acured at any gven tme. Copyrght 20, S&C propretary nformaton. All rghts reserved. 8

9 OptRamp Model-Based Multvarable Predctve Control Whte Paper About Statstcs & Control, Inc. S&C an engneerng consultng and technology company headuartered n West Des Mones, IA solves complex challenges for customers through ts unue technology and ts hghly seasoned team of professonals. The company has a global portfolo spannng the energy, ol and gas, utlty, and dgtal ol feld ndustry sectors. S&C provdes clents wth turbomachnery control solutons that easly ntegrate wth the exstng system as well as OptRamp solutons, whch focus on process and power analytcs to optmze processes and, n turn, reduce costs and ncrease relablty. S&C also provdes consultng, dynamc system studes, modelng, automaton, tranng and OTS, and support servces. Statstcs & Control, Inc. 440 Westown Pkwy, Sute 24 West Des Mones, IA USA Phone: Fax: Copyrght 20, S&C propretary nformaton. All rghts reserved. 9