First Principles Model Based Control

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1 European Symposium on Compuer Arded Aided Process Engineering 15 L. Puigjaner and A. Espuña (Ediors) 2005 Elsevier Science B.V. All righs reserved. Firs Principles Model Based Conrol Manuel Rodríguez a*, David Pérez a a Universidad Poliécnica de Madrid José Guiérrez Abascal, 2. Madrid 28006, Spain Absrac Model Based Conrol is an imporan and widely used (mainly MPC) echnique. This paper provides a new conrol archiecure based on he use of physical models. In his preliminary work he archiecure is applied for unconsrained mulivariable conrol. I has been applied on several sandard process unis obaining encouraging resuls. I has some advanages over MPC as i can use non linear rigorous models and i doesn need any idenificaion sep. Keywords: Model Based Conrol, Model Predicive Conrol, Inernal Model Conrol. 1. Inroducion The ineres in Model Predicive Conrol (MPC) sared o increase afer he presenaion of IDCOM (Idenificaion and Command) (Richale, 1978) and DMC (Dynamic Marix Conrol) (Culer, 1979). Afer 25 years MPC has become a widely used echnology in process conrol. Nowadays, a new crude disillaion uni in a refinery is no conceived wih oher conrol scheme bu MPC (and he same happens in many oher processes). The echnology applied is usually based on a previous idenificaion sep (which is of he mos imporance) o ge a linear model of he uni and, hen, on an implemenaion sep (usually more simple and less ime consuming). Alhough a lo of research has been done regarding Nonlinear MPC using differen approaches, differenial equaions, neural nes (Temeng, 1995), Hammersein models (Fruzzei, 1997), Volerra equaions (Maner, 1996), fuzzy models (Sousa, 1997) i is sill an open area where many problems arise. The purpose of his work is he use of firs principles models for model predicive conrol. To achieve his goal, a new archiecure has been developed and esed on some simulaed process unis. The remaining paper is organised as follows: Secion wo describes in deail he new archiecure, how i works and is componens, and explains he sofware implemenaion. Secion hree shows he resuls obained when i is applied o conrol some operaion unis. Finally, secion four presens he conclusions and fuure seps of his work. * Auhor o whom correspondence should be addressed: mrod@diquima.upm.es

2 2. Physical Model Based Conrol Archiecure. The PMBC archiecure is composed of wo modules: he Physical Model Based (PMB) Conroller Module and he PMB Model Module. Figure 1 shows he proposed archiecure: Figure 1. PMBC Archiecure The models used in he componens of he archiecure have been developed wih some degree of error wih respec o he process, as i is impossible o ge a perfec model of a real process. To his purpose, some parameers have been slighly changed. 2.1 PMB Conroller Module This module is he core of he archiecure, i predics he values of he manipulaed variables ha provide he desired performance (se poin change or disurbance rejecion). This module has a model of he uni o conrol. I has a firs principles model comprised of a se of DAEs. This module has he following variables as inpus: The error of he conrolled variables, i can be referred o he conrolled variable direcly or o is derivaive. I is he desired response or he arge curve. Measured disurbances. The oupus of his module are he se of manipulaed variables (which are commonly inpus in a model of he process). If he conrolled variable is a is se poin, he inpu of he module will be he derivaive se o zero or he value se o ha consan (so i remains in ha value). If a disurbance happens, he conroller will produce an oupu o compensae ha disurbance and keep he conrolled variable a he desired se poin value. If a se poin change is desired, he inpu will be an exponenial (sofened sep) in he conrolled variable. If he conrolled variable acs like an inegraor, such as conrolling he level wih an oupu sream, a ramp has o be used insead of a sep. The ime used for he sep or ramp is an adjusable parameer. The ime scale of his module is he simulaion execuion ime of he model in he seleced plaform. I is an adjusable parameer, i can be slowed down o avoid excessive conrol acions ha someimes will provide a worse sysem performance.

3 2.2 PMB Correcor Module This module has a model of he uni o be conrolled. The model is exacly he same as above excep for which are he inpu variables o i. This model is used in he sandard way, so he inpus o i are he disurbances and he inpus o he real process. The oupus of he model are he conrolled and oupu variables of he process. The purpose of his module is o correc, in some way, he predicion made by he Conroller Module. As no model is perfec, he conroller oupu will lead o a conrol acion ha doesn se he conrolled variable o he desired value. This means ha some feedback correcions are necessary. In order o accelerae his procedure, his module compares is oupu wih he acual process oupu and ses a correcion facor o be applied o he conrol acion. So, his module has wo componens: he model componen and he comparison componen. The final oupu of his module, wih he correcion facor, is he conrol acion o be applied o he real process. The ime scale of his module has o be ha of he real process, so i has o be synchronized o i as accurae as possible, in order o be able o compare he same variables Sofware implemenaion The implemenaion has hree componens, he Conroller Module, he Correcor Module and he Process Module. All he componens have been implemened in he same machine, a PC running under Linux OS. The model used in he Conroller and Correcor Modules is no perfec, some changes have been made in several parameers of hem in order o check he proposed archiecure. The models have been developed using he ABACUSS II simulaor (Baron,2003). This sofware allows o embed he simulaion code in oher applicaion. Using he C++ programming language, differen execuables have been generaed for every componen of he archiecure. The informaion flow has been implemened hrough shared memory procedures. 3. Applicaions In his secion he resuls of he applicaion of his archiecure are presened. Se poin and load changes are applied o all he esed unis and he performance of he conroller is evaluaed Sirred ank heaer This uni is a perfecly sirred ank heaer wih a jacke. I has wo inpu sreams and one oupu sream. There are level and emperaure conrol loops. The manipulaed variables are he ank inpu flow and he jacke inpu flow. These wo variables are calculaed in he Conroller Module. This module has as inpus he heaer emperaure and he ank level. To achieve a good conrol on he ank, he following conrol equaions are used: - dh e = ( SPH - PH ) (1) d SPH: Level se - poin, H: level of he model, PH: level of he acual process.

4 dto d - e = K ( SPT - PT) (2) SPT: Temperaure se - poin, To: jacke emperaure of he model, P: emperaure of he acual process. The jacke emperaure is used as he forcing equaion of conrol insead of he ank emperaure because he use of he laer poses a 2 - index problem. Due o his problem, he gain beween he wo variables needs o be added o he conrol equaion. In his model some parameers are changed abou 5% wih respec o he acual process. Figure 2 shows he conrol of he uni in he presence of a flow disurbance and a level se poin change. Tou Tou Level Jacke Flow Flow in Flow in Level Jacke Flow Flow disurbance Figure 2. Heaer response afer a flow disurbance on he lef. Heaer response afer a level se poin change on he righ. In hese ess boh loops are affeced as he emperaure changes wih a change in any of he sream flows Coninuous Sirred Tank Reacor (CSTR) This uni has he same equaions as he heaer bu a firs order reacion, following he Arrhenius expression, is added. In his case, he same wo loops (level and emperaure) are conrolled. Bu, in his case, he level is conrolled wih he oupu sream, which means ha he conrol acion has o be changed. An exponenial (sep) canno be used and a ramp is used insead. The following equaion shows he level conrol acion implemened:

5 dh SPH - PH = (3) d The emperaure conrol equaion is he same as in he heaer applicaion. Figure 3 shows he performance of he sysem in he presence of concenraion and emperaure disurbances. In his model, he parameer ha is changed wih respec o he acual process is he Arrhenius pre-exponenial consan in 5%. T ou T ou Conc. ou Conc. ou Conc. disurbance T disurbance Jacke Flow Jacke Flow Figure 3. CSTR response afer a concenraion disurbance on he lef. CSTR response afer a emperaure disurbance on he righ Disillaion Column This uni is a binary disillaion uni. I assumes equimolal overflow, 20 heoreical rays, simple liquid ray hydraulics and consan relaive volailiy (ideal mixures) for he vapour - liquid equilibrium in every sage. Feed eners above 10h ray (feed sage). Toal overhead condenser and parial reboiler. The implemenaion of his uni for a coninuous es is no finished a he ime of his paper. The only implemenaion available is jus he firs conrol acion o be applied o he process. The model in his iniial implemenaion is assumed perfec (his means ha jus a single conrol acion ges he conrolled variable o he desired value). The conrol equaions used are similar o he ones presened in he previous applicaions. Nex figure shows ha his conrol archiecure can be applied o he disillaion column as well. 4. Conclusions This paper has presened a new archiecure for model based conrol. Regarding he obained resuls, his physical model based conrol seems o be a usable echnology for

6 Disillae Flow Booms Flow Vapor Flow Reflux Flow Booms composiion Feed composiion Figure 4. Disillaion column performance wih a composiion disurbance and a booms composiion se poin change. any process uni. This new approach has some clear advanages over he ones used currenly in he indusry. I uses a firs-principles model ha is suied o any operaing region, so, i is a non-linear MPC. I doesn need any idenificaion sep which is very resource consuming for any process uni. Alhough he resuls presened are promising, a lo of work sill has o be done o esablish he availabiliy of his echnology. Firs of all, he iniial approach aken is for unconsrained predicive conrol, addiional seps aking ino accoun consrains (like valve range, ) have o be made. New issues have o be sudied as dead-ime, sabiliy, The nex sep in his work will be o es his archiecure wih a real sysem. References Baron, P.I, 2003 hp://yoric.mi.edu/abacuss Culer, C. R. and Ramaker B. L.,1979. Dynamic marix conrol a compuer conrol algorihm. AIChE 86h Naional Meeing. Houson,TX. Fruzzei e al., Nonlinear conrol using Hammersein models. J. Proc. Conrol, 7, n1, 31-4 Maner e al, Nonlinear model predicive conrol of a simulaed mulivariable polymerisaion reacor using second order Volerra models. Richale, J., Raul, A., Tesud, J. L., and Papon, J.,1978. Model predicive heurisic conrol: applicaions o indusrial processes. Auomaica, 14(5), Sousa e al, Fuzzy predicive conrol applied o an air condiioning sysem. Conrol Engineering Pracice, 5. n10, Temeg e al, Model predicive conrol of an indusrial packed bed reacor using neural neworks. J. Proc. Conrol, 5, n1, Acknowledgemens The projec is sponsored by Repsol-YPF foundaion.

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