Paroc - a Unified Framework Towards the Optimal Design, Operational Operation and Model-Based Control of Process Systems
AIChE Spring Meeting and Global Congress on Process Safety
2015
2015 AIChE Spring Meeting and 11th Global Congress on Process Safety
Manufacturing for the 21st Century
Optimization and Control in Smart Manufacturing
Tuesday, April 28, 2015 - 3:30pm to 4:00pm
PAROC - A unified framework towards the optimal design,
operational operation and model-based control of
process systems Efstratios N. Pistikopoulosa,b, Richard Oberdiecka,
Nikolaos A. Diangelakisa, Maria M. Papathanasioua, Ioana Nascua a Department of Chemical Engineering, Centre for Process Systems
Engineering, Imperial College London, London, United Kingdom. b Artie MrFerrin Department of Chemical
Engineering, Texas A&M University, College Station TX, United States. The
presence of uncertainty in process systems is one of the key reasons for
deviation from set operation policies. The realization of these uncertainties on
different time scales such as in a control, scheduling or design level require
the development of an integrated, comprehensive approach. Thus, in this
contribution we present PAROC (PARametric
Optimization and Control), a novel unified framework for the design,
operational optimization and advanced model-based control of process systems,
which decomposes this challenging problem into a series of steps [4] (see
Figure 1).
step comprises of the formulation of a high-fidelity dynamic model of the original
process, as well as its validation using various techniques such as parameter estimation
and sensitivity analysis. While the
high-fidelity model is in general applicable to design purposes, its complexity
may render its use for the development of receding horizon policies
computationally impractical. Thus, in the second step, the validated
high-fidelity model is reduced in complexity and size using advanced model approximation
tools, while compromising the accuracy of the original model as little as possible
[10, 19, 8]. This approach results in a discretized state-space
model, which is used for the development of receding horizon policies such as control
laws and scheduling policies [1, 15, 16, 6]. At this
step, based on the discretized state-space model, the problem of devising a suitable
receding horizon policy is formulated as a constrained optimization problem. Within
our framework, this problem is solved offline employing multi-parametric programming,
where the states of the system are treated as parameters and the constrained
optimization problem is solved as a function thereof [15, 17]. Due to the
parameter-dependence of the constraints, different solutions might be optimal
in different neighbourhoods of the parameter space. This results in the
partition of the parameter space into different regions, associated with a
corresponding optimal solution which is a function of the parameters. As a
result we obtain the receding horizon policies explicitly as a function of the
states of the system[1],
and reduce the computational effort of their evaluation to a point location in
the parameter space and an affine function evaluation. However,
when solving the receding horizon policies it is assumed that the values of the
state vector are exactly known. As this might not be the case, e.g. due to noise,
it is necessary to infer the state information from the available output
measurements using a state estimator. While a long existing model-based
technique for unconstrained state estimation is the Kalman
filter, the use of constrained estimation techniques such as the moving horizon
estimator (MHE) can lead to significant improvements of the result by adding
system knowledge [9, 18, 3]. MHE is an method that
obtains the estimates by solving a constrained optimization problem given a
horizon of past measurements. Thus similarly to the problem of receding horizon
policies, the presented framework solves the MHE problem in a multi-parametric
fashion, where the past and current measurements and inputs and the initial
guess for the estimated states are the parameters of the problem [20, 11]. As a last
step, the obtained receding horizon policies are validated ?in-silico? using the original high-fidelity model, thus
closing the loop. In particular in the case of multiple objectives such as
minimization of error, safe operation and economically optimal performance, the
possibility of performing ?in-silico? tests of a
developed control strategy allows for the fine-tuning and optimal design of the
control strategy. In order
to apply the afore-described framework, we also present software solutions for
the different aspects of the framework. Due to its modeling and dynamic optimization
capabilities, we employ PSE?s gPROMS® ModelBuilder to formulate and validate the high-fidelity
model of the process. Similarly, due to its wide-spread use and numerous
in-build functions, the steps of model approximation as well as formulation and
solution of multi-parametric programming problems is performed in MATLAB® using
state-of the art software [5, 21, 12] based on the POP® toolbox [14]. Lastly,
the solution of the multi-parametric programming problem is integrated into gPROMS® using a specifically designed dynamic link library.
This approach avoids the use of tools such as gO:MATLAB, and thus enables the use of the dynamic
optimization capabilities of PSE?s gPROMS®. This
novel framework has been successfully applied to a wide range of problems such
as fuel cells [13] and bio-medical [2, 11] and bio-pharmaceutical applications.
In this contribution, we focus on its application onto a 32-tray distillation
column, consisting of 32 state equations, 32 equilibrium relations and 3
correlations of the volumetric flows (see Figure 2) [7].
step, gPROMS® is used to formulate a high-fidelity
model based on ordinary differential equations (ODEs). Employing empirical gramians or covariance matrices, the original model is
reduced to a discrete 2-states model, where the output of the system is the
liquid phase composition of the reboiler. The
reduced model is used to formulate the corresponding multi-parametric
programming problem. Additionally, multi-parametric state estimation techniques
are employed to estimate the states of the system as well as the noise. The
multi-parametric programming solution is integrated into gPROMS®
and a close-loop validation is performed, demonstrating the validity of both
the developed controller as well as the state estimator. References [1]Â Â Â Â Â Â Â Â Â A. Bemporad,
M. Morari, V. Dua, and E.N. Pistikopoulos. The explicit linear quadratic regulator for constrained systems.
Automatica, 38(1):3?20, 2002. [2]
        H. Chang, A. Krieger, A. Astolfi, and E.N. Pistikopoulos. Robust multi-parametric model predictive control for lpv systems with application to anaesthesia. Journal
of Process Control, 24(10):1538?1547, 2014. [3] Â Â Â Â Â Â Â Â M.L. Darby and M. Nikolaou. A parametric programming approach to moving-horizon state
estimation. Automatica, 43(5):885?891,
2007. [4]
        N.A. Diangelakis, A.M.
Manthanwar, and E.N. Pistikopoulos. A framework for design and control
optimisation: Application on a chp system. In Proceedings
of the 8th International Conference on Foundations of Computer-Aided Process
Design, volume 34 of Computer Aided Chemical Engineering, pages
765?770. Elsevier, 2014. [5]
        V. Dua,
N.A. Bozinis, and E.N. Pistikopoulos. A multiparametric programming approach for mixed-integer quadratic
engineering problems. Computers & Chemical Engineering, 26(4?5):715?733,
2002. [6]
        G.M. Kopanos and E.N.
Pistikopoulos. Reactive scheduling by a multiparametric
programming rolling horizon framework: A case of a network of combined heat and
power units. Industrial & Engineering Chemistry Research,
53(11):4366?4386, 2014. [7]
        R.S.C. Lambert, I. Nascu, and
E.N. Pistikopoulos. Simultaneous reduced order multiparametric moving
horizon estimation and model predictive control. In Dynamics and Control of
Process Systems, IFAC proceedings volumes, pages 45?50. Elsevier, IFAC,
2013. [8]Â Â Â Â Â Â Â Â Â R.S.C. Lambert, P. Rivotti, and E.N.
Pistikopoulos. A Monte-Carlo based model approximation technique
for linear model predictive control of nonlinear systems. Computers & Chemical
Engineering, 54:60?67, 2013. [9]Â Â Â Â Â Â Â Â Â D. Q. Mayne,
J. B. Rawlings, C. V. Rao, and P.O.M. Scokaert. Constrained model predictive control: Stability and optimality.
Automatica, 36(6):789?814, 2000. [10]Â Â Â Â Â Â Â D.A. Narciso
and E.N. Pistikopoulos. A combined balanced truncation and
multiparametric programming approach for linear model predictive control. In 18th
European Symposium on Computer Aided Process Engineering, volume 25 of Computer
Aided Chemical Engineering, pages 405?410. Elsevier, 2008. [11] Â Â Â Â Â Â I. Nascu, R.S.C. Lambert, and E.N.
Pistikopoulos. Simultaneous multi-parametric model predictive
control and state estimation with application to distillation column and
intravenous anaesthesia. In 24th European Symposium on Computer Aided
Process Engineering, volume 33 of Computer Aided Chemical Engineering,
pages 541?546. Elsevier, 2014. [12]
      R. Oberdieck, M. Wittmann-Hohlbein,
and E.N. Pistikopoulos. A branch and bound method for the solution of
multiparametric mixed integer linear programming problems. Journal of Global
Optimization, 59(2-3):527?543, 2014. [13]
      C. Panos, K.I. Kouramas,
M.C. Georgiadis, and E.N. Pistikopoulos. Modelling and explicit model predictive control for pem fuel cell systems. Chemical Engineering
Science, 67(1):15?25, 2012. [14]
      ParOs. Parametric optimization programming (pop), 2004. [15]       E.N. Pistikopoulos. Perspectives
in multiparametric programming and explicit model predictive control. AIChE Journal, 55(8):1918?1925, 2009. [16] Â Â Â Â Â Â E.N. Pistikopoulos. From
multi-parametric programming theory to mpc-on-a-chip multiscale systems applications. Computers &
Chemical Engineering, 47:57?66, 2012. [17]
      E.N. Pistikopoulos, L. Dominguez,
C. Panos, K. Kouramas, and A. Chinchuluun. Theoretical and algorithmic advances in multi-parametric
programming and control. Computational Management Science,
9(2):183?203, 2012. [18] Â Â Â Â Â Â C.V. Rao. Moving
Horizon Strategies for the Constrained Monitoring and Control of Nonlinear Discrete-time
Systems. PhD thesis, University of
Wisconsin-Madison, Wisconsin-Madison, 2000. [19]
      P. Rivotti, R.S.C. Lambert, and
E.N. Pistikopoulos. Combined model
approximation techniques and multiparametric programming for explicit nonlinear
model predictive control. Computers & Chemical Engineering,
42:277?287, 2012. [20]
      A. Voelker,
K. Kouramas, and E.N. Pistikopoulos. Simultaneous state estimation and model predictive control by multi-parametric
programming. Computer Aided Chemical Engineering, 28(C):607?612,
2010. [21]
      M. Wittmann-Hohlbein and E.N.
Pistikopoulos. A two-stage method for the
approximate solution of general multiparametric mixed-integer linear
programming problems. Industrial & Engineering Chemistry Research,
51(23):8095?8107, 2012.
operational operation and model-based control of
process systems Efstratios N. Pistikopoulosa,b, Richard Oberdiecka,
Nikolaos A. Diangelakisa, Maria M. Papathanasioua, Ioana Nascua a Department of Chemical Engineering, Centre for Process Systems
Engineering, Imperial College London, London, United Kingdom. b Artie MrFerrin Department of Chemical
Engineering, Texas A&M University, College Station TX, United States. The
presence of uncertainty in process systems is one of the key reasons for
deviation from set operation policies. The realization of these uncertainties on
different time scales such as in a control, scheduling or design level require
the development of an integrated, comprehensive approach. Thus, in this
contribution we present PAROC (PARametric
Optimization and Control), a novel unified framework for the design,
operational optimization and advanced model-based control of process systems,
which decomposes this challenging problem into a series of steps [4] (see
Figure 1).
Figure
1: The PAROC framework.
step comprises of the formulation of a high-fidelity dynamic model of the original
process, as well as its validation using various techniques such as parameter estimation
and sensitivity analysis. While the
high-fidelity model is in general applicable to design purposes, its complexity
may render its use for the development of receding horizon policies
computationally impractical. Thus, in the second step, the validated
high-fidelity model is reduced in complexity and size using advanced model approximation
tools, while compromising the accuracy of the original model as little as possible
[10, 19, 8]. This approach results in a discretized state-space
model, which is used for the development of receding horizon policies such as control
laws and scheduling policies [1, 15, 16, 6]. At this
step, based on the discretized state-space model, the problem of devising a suitable
receding horizon policy is formulated as a constrained optimization problem. Within
our framework, this problem is solved offline employing multi-parametric programming,
where the states of the system are treated as parameters and the constrained
optimization problem is solved as a function thereof [15, 17]. Due to the
parameter-dependence of the constraints, different solutions might be optimal
in different neighbourhoods of the parameter space. This results in the
partition of the parameter space into different regions, associated with a
corresponding optimal solution which is a function of the parameters. As a
result we obtain the receding horizon policies explicitly as a function of the
states of the system[1],
and reduce the computational effort of their evaluation to a point location in
the parameter space and an affine function evaluation. However,
when solving the receding horizon policies it is assumed that the values of the
state vector are exactly known. As this might not be the case, e.g. due to noise,
it is necessary to infer the state information from the available output
measurements using a state estimator. While a long existing model-based
technique for unconstrained state estimation is the Kalman
filter, the use of constrained estimation techniques such as the moving horizon
estimator (MHE) can lead to significant improvements of the result by adding
system knowledge [9, 18, 3]. MHE is an method that
obtains the estimates by solving a constrained optimization problem given a
horizon of past measurements. Thus similarly to the problem of receding horizon
policies, the presented framework solves the MHE problem in a multi-parametric
fashion, where the past and current measurements and inputs and the initial
guess for the estimated states are the parameters of the problem [20, 11]. As a last
step, the obtained receding horizon policies are validated ?in-silico? using the original high-fidelity model, thus
closing the loop. In particular in the case of multiple objectives such as
minimization of error, safe operation and economically optimal performance, the
possibility of performing ?in-silico? tests of a
developed control strategy allows for the fine-tuning and optimal design of the
control strategy. In order
to apply the afore-described framework, we also present software solutions for
the different aspects of the framework. Due to its modeling and dynamic optimization
capabilities, we employ PSE?s gPROMS® ModelBuilder to formulate and validate the high-fidelity
model of the process. Similarly, due to its wide-spread use and numerous
in-build functions, the steps of model approximation as well as formulation and
solution of multi-parametric programming problems is performed in MATLAB® using
state-of the art software [5, 21, 12] based on the POP® toolbox [14]. Lastly,
the solution of the multi-parametric programming problem is integrated into gPROMS® using a specifically designed dynamic link library.
This approach avoids the use of tools such as gO:MATLAB, and thus enables the use of the dynamic
optimization capabilities of PSE?s gPROMS®. This
novel framework has been successfully applied to a wide range of problems such
as fuel cells [13] and bio-medical [2, 11] and bio-pharmaceutical applications.
In this contribution, we focus on its application onto a 32-tray distillation
column, consisting of 32 state equations, 32 equilibrium relations and 3
correlations of the volumetric flows (see Figure 2) [7].
Figure
2: A schematic representation of a distillation column with 32 trays.
step, gPROMS® is used to formulate a high-fidelity
model based on ordinary differential equations (ODEs). Employing empirical gramians or covariance matrices, the original model is
reduced to a discrete 2-states model, where the output of the system is the
liquid phase composition of the reboiler. The
reduced model is used to formulate the corresponding multi-parametric
programming problem. Additionally, multi-parametric state estimation techniques
are employed to estimate the states of the system as well as the noise. The
multi-parametric programming solution is integrated into gPROMS®
and a close-loop validation is performed, demonstrating the validity of both
the developed controller as well as the state estimator. References [1]Â Â Â Â Â Â Â Â Â A. Bemporad,
M. Morari, V. Dua, and E.N. Pistikopoulos. The explicit linear quadratic regulator for constrained systems.
Automatica, 38(1):3?20, 2002. [2]
        H. Chang, A. Krieger, A. Astolfi, and E.N. Pistikopoulos. Robust multi-parametric model predictive control for lpv systems with application to anaesthesia. Journal
of Process Control, 24(10):1538?1547, 2014. [3] Â Â Â Â Â Â Â Â M.L. Darby and M. Nikolaou. A parametric programming approach to moving-horizon state
estimation. Automatica, 43(5):885?891,
2007. [4]
        N.A. Diangelakis, A.M.
Manthanwar, and E.N. Pistikopoulos. A framework for design and control
optimisation: Application on a chp system. In Proceedings
of the 8th International Conference on Foundations of Computer-Aided Process
Design, volume 34 of Computer Aided Chemical Engineering, pages
765?770. Elsevier, 2014. [5]
        V. Dua,
N.A. Bozinis, and E.N. Pistikopoulos. A multiparametric programming approach for mixed-integer quadratic
engineering problems. Computers & Chemical Engineering, 26(4?5):715?733,
2002. [6]
        G.M. Kopanos and E.N.
Pistikopoulos. Reactive scheduling by a multiparametric
programming rolling horizon framework: A case of a network of combined heat and
power units. Industrial & Engineering Chemistry Research,
53(11):4366?4386, 2014. [7]
        R.S.C. Lambert, I. Nascu, and
E.N. Pistikopoulos. Simultaneous reduced order multiparametric moving
horizon estimation and model predictive control. In Dynamics and Control of
Process Systems, IFAC proceedings volumes, pages 45?50. Elsevier, IFAC,
2013. [8]Â Â Â Â Â Â Â Â Â R.S.C. Lambert, P. Rivotti, and E.N.
Pistikopoulos. A Monte-Carlo based model approximation technique
for linear model predictive control of nonlinear systems. Computers & Chemical
Engineering, 54:60?67, 2013. [9]Â Â Â Â Â Â Â Â Â D. Q. Mayne,
J. B. Rawlings, C. V. Rao, and P.O.M. Scokaert. Constrained model predictive control: Stability and optimality.
Automatica, 36(6):789?814, 2000. [10]Â Â Â Â Â Â Â D.A. Narciso
and E.N. Pistikopoulos. A combined balanced truncation and
multiparametric programming approach for linear model predictive control. In 18th
European Symposium on Computer Aided Process Engineering, volume 25 of Computer
Aided Chemical Engineering, pages 405?410. Elsevier, 2008. [11] Â Â Â Â Â Â I. Nascu, R.S.C. Lambert, and E.N.
Pistikopoulos. Simultaneous multi-parametric model predictive
control and state estimation with application to distillation column and
intravenous anaesthesia. In 24th European Symposium on Computer Aided
Process Engineering, volume 33 of Computer Aided Chemical Engineering,
pages 541?546. Elsevier, 2014. [12]
      R. Oberdieck, M. Wittmann-Hohlbein,
and E.N. Pistikopoulos. A branch and bound method for the solution of
multiparametric mixed integer linear programming problems. Journal of Global
Optimization, 59(2-3):527?543, 2014. [13]
      C. Panos, K.I. Kouramas,
M.C. Georgiadis, and E.N. Pistikopoulos. Modelling and explicit model predictive control for pem fuel cell systems. Chemical Engineering
Science, 67(1):15?25, 2012. [14]
      ParOs. Parametric optimization programming (pop), 2004. [15]       E.N. Pistikopoulos. Perspectives
in multiparametric programming and explicit model predictive control. AIChE Journal, 55(8):1918?1925, 2009. [16] Â Â Â Â Â Â E.N. Pistikopoulos. From
multi-parametric programming theory to mpc-on-a-chip multiscale systems applications. Computers &
Chemical Engineering, 47:57?66, 2012. [17]
      E.N. Pistikopoulos, L. Dominguez,
C. Panos, K. Kouramas, and A. Chinchuluun. Theoretical and algorithmic advances in multi-parametric
programming and control. Computational Management Science,
9(2):183?203, 2012. [18] Â Â Â Â Â Â C.V. Rao. Moving
Horizon Strategies for the Constrained Monitoring and Control of Nonlinear Discrete-time
Systems. PhD thesis, University of
Wisconsin-Madison, Wisconsin-Madison, 2000. [19]
      P. Rivotti, R.S.C. Lambert, and
E.N. Pistikopoulos. Combined model
approximation techniques and multiparametric programming for explicit nonlinear
model predictive control. Computers & Chemical Engineering,
42:277?287, 2012. [20]
      A. Voelker,
K. Kouramas, and E.N. Pistikopoulos. Simultaneous state estimation and model predictive control by multi-parametric
programming. Computer Aided Chemical Engineering, 28(C):607?612,
2010. [21]
      M. Wittmann-Hohlbein and E.N.
Pistikopoulos. A two-stage method for the
approximate solution of general multiparametric mixed-integer linear
programming problems. Industrial & Engineering Chemistry Research,
51(23):8095?8107, 2012.