(282c) Paroc - a Unified Framework Towards the Optimal Design, Operational Operation and Model-Based Control of Process Systems

Authors: 
Pistikopoulos, E. N., Texas A&M Energy Institute, Texas A&M University
Oberdieck, R., Texas A&M University
Diangelakis, N. A., Imperial College
Papathanasiou, M. M., Imperial College London
Nascu, I., Texas A&M University

The presence of uncertainty in process
systems is one of the key reasons for deviation from set operation policies,
resulting in suboptimal or even infeasible operation. As these uncertainties
realize themselves on different time scales such as on a control, scheduling or
design level, an integrated, comprehensive approach to consider uncertainty is
required. Thus, in this contribution we demonstrate 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, shown in the
Figure below [1].

The
first step comprises 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 dynamic optimization. This model does not only serve
as the first step in translating a real-world system into a set of equations,
but also as a platform for the validation of any receding horizon policy
developed.

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 infeasible. Thus, in the second step, the validated
high-fidelity model is reduced in complexity and size using system
identification or advanced model reduction techniques, aiming at compromising
the accuracy of the original model as little as possible [2]. This
approach results in a discretized state-space model, which is used in the next
step for the development of receding horizon policies such as control laws and
scheduling policies [3, 4].

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. Due to the parameter-dependence of the constraints, different
solutions might be optimal in different parts of the parameter space. This
results in a partition of the parameter space into different regions, called
critical regions, and each region is associated with a corresponding optimal
solution of the optimization problem as 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 a 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 estimation result by adding system
knowledge [5,
6].
MHE is an estimation 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 [5,
7].

As
a last step, the obtained receding horizon policies are validated 'in-silico'
using the original high-fidelity model, thus closing the loop. This validation
is of crucial importance as iterative experiments on real plants might be too
costly or dangerous to run. 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 [8,
9]
based on the POP® toolbox [10]. Lastly, the solution of the
multi-parametric programming problem is integrated into gPROMS® using a
specifically designed foreign process written in C++. This approach avoids the
use of tools such as gO:MATLAB, and thus enables the use of the dynamic
simulation and optimization capabilities of PSE's gPROMS®.

The
applicability of this novel framework will be demonstrated on a wide range of
problems such as industrial processes [11], bio-medical
[5, 12, 13], cogeneration
heat and power systems [14].

References

1.            Pistikopoulos, E.N., et al., PAROC?An
integrated framework and software platform for the optimisation and advanced
model-based control of process systems.
Chemical Engineering Science, in
print
.

2.            Lambert, R.S.C., P. Rivotti, and
E.N. Pistikopoulos, A Monte-Carlo based model approximation technique for
linear model predictive control of nonlinear systems.
Computers &
Chemical Engineering, 2013. 54: p. 60?67.

3.            Bemporad, A., et al., The explicit
linear quadratic regulator for constrained systems.
Automatica, 2002. 38(1):
p. 3?20.

4.            Kopanos, G.M. 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, 2014. 53(11): p.
4366?4386.

5.            Nascu, I., et al., 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
, 2014, Elsevier. p.
541?546.

6.            Rao, C.V., Moving Horizon
Strategies for the Constrained Monitoring and Control of Nonlinear
Discrete-time Systems
, in Chemical Engineering. 2000, University of
Wisconsin-Madison.

7.            Voelker, A., K. Kouramas, and
E.N. Pistikopoulos, Simultaneous state estimation and model predictive
control by multi-parametric programming.
Computer Aided Chemical
Engineering, 2010. 28(C): p. 607?612.

8.            Dua, V., N.A. Bozinis, and E.N.
Pistikopoulos, A multiparametric programming approach for mixed-integer
quadratic engineering problems.
Computers & Chemical Engineering, 2002.
26(4?5): p. 715?733.

9.            Oberdieck, R., 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, 2014. 59(2-3): p. 527?543.

10.          ParOs, Parametric
Optimization Programming (POP)
. 2004, ParOS.

11.          Papathanasiou, M.M., et al., A
control strategy for periodic systems - application to the twin-column MCSGP.

Computer Aided Chemical Engineering, 2015. Accepted for publication.

12.          Chang, H., et al., Robust
multi-parametric model predictive control for LPV systems with application to
anaesthesia.
Journal of Process Control, 2014. 24(10): p. 1538?1547.

13.          Nascu, I., R. Oberdieck, and
E.N. Pistikopoulos, A framework for hybrid multi-parametric model-predictive
control with application to intravenous anaesthesia.
Computer Aided
Chemical Engineering, 2015. Accepted for publication.

14.          Diangelakis, N.A. and E.N.
Pistikopoulos, A Decentralised Multi-parametric Model Predictive Control
Study for a Domestic Heat and Power Cogeneration System.
Computer Aided
Chemical Engineering, 2015. Accepted for publication.




[1]
In addition, also measured disturbances and output set points are treated as
parameters.