On this page we present examples where PAROC has been applied to. The aim is to provide an overview over the capabilities of the entire platform as well as each element of it. The examples presented here are:
All these examples were considered using gPROMS and MATLAB®, as well as our own software tools available here.
Diangelakis, N.A.; Manthanwar, A.; Pistikopoulos, E.N. (2014) A Framework for Design and Control Optimisation: Application on a CHP System. Proceedings of the 8th International Conference on Foundations of Computer-Aided Process Design, 34, 765-770.
Diangelakis, N.A.; Panos, C.; Pistikopoulos, E.N. (2014) Design optimization of an internal combustion engine powered CHP system for residential scale application. Computational Management Science, 11(3), 237 - 266.
Pistikopoulos, E.N.; Diangelakis, N.A.; Oberdieck, R.; Papathanasiou, M.M.; Nascu, I.; Sun, M. (2015) PAROC - An integrated framework and software platform for the optimisation and advanced model-based control of process systems. Chemical Engineering Science, 136, 115-138.
Diangelakis, N.A.; Pistikopoulos, E.N. (2015) A Decentralised Multi-parametric Model Predictive Control Study for a Domestic Heat and Power Cogeneration System. In Proceedings of the 12th International Symposium on Process Systems Engineering and 25th European Symposium on Computer Aided Process Engineering, Computer Aided Chemical Engineering 37, 1499-1504.
Diangelakis, N.A.; Avraamidou, S.; Pistikopoulos, E.N. (2015) Decentralized Multiparametric Model Predictive Control for Domestic Combined Heat and Power Systems, Industrial and Engineering Chemistry Research, 55(12), 3313-3326.
Combined heat and power (CHP) systems constitute an upcoming technology that has the potential to replace the conventional processes used so far for the production of usable heat and electricity. The cogeneration of heat and power in a single process increases the system efficiency, while it decreases the operational cost. The use of CHP systems in the domestic/residential sector becomes appealing from (i) an environmental, (ii) economical and (iii) efficiency oriented point of view.
The high-fidelity model was developed in gPROMS and after discretization consists of a complex DAE system featuring 379 equations (15 differential), and 6 degrees of freedom (4 dynamic). Note that this model was validated against the actual system.
Using the system identification toolbox of MATLAB®, an approximate, linear state-space model of the system was obtained. In this specific case, a decentralized approach was taken based on the general concept that the system under consideration has the ability to produce two distinct products, namely heat and power. This procedure results in a 3x3 linear state-space model, which is used in the next step to design the explicit controller.
Using our in-build software ss2qp and the POP toolbox, this linear state-space model is used to derive the explicit controller, removing the need to perform an online optimization.
Via the gPROMS connectivity to MATLAB®, gO:MATLAB, the derived controller is validated against the original, high-fidelity model which in turn was validated against the actual system. Within this validation, we observe that after the settling time the mismatch between the output setpoint and the real output is less than 2%, which is a great result.
Lambert, R., Nascu, I., Pistikopoulos, E.N. (2013) Simultaneous reduced order multiparametric moving horizon estimation and model predictive control. In: Dynamics and Control of Process Systems, IFAC Proceedings volumes. Elsevier, Mumbai, India, pp. 45–50.
Pistikopoulos, E.N.; Diangelakis, N.A.; Oberdieck, R.; Papathanasiou, M.M.; Nascu, I.; Sun, M. (2015) PAROC - An integrated framework and software platform for the optimisation and advanced model-based control of process systems. Chemical Engineering Science, 136, 115-138.
In this simple case study, we consider the simplified model for the binary separation of benzene and toluene is used as the basis for the design of a multiparametric moving horizon estimator and a multiparametric model predictive controller.
The specific column under consideration is a 32 tray distillation model consisting of 32 state equations, 32 equilibrium relations and 3 correlations of the volumetric flows.
The size of the model as well as its nonlinearity make the high-fidelity model unsuitable for the direct use in multi-parametric programming. Hence, model reduction techniques are employed, more specifically non-linear balanced truncation, which is a snapshots based technique. This reduction results in a 2-states model, which provides good validation against the original high-fidelity model.
Similar to the CHP example, the explicit MPC controller is derived. In this section we will hence focus on the derivation of the explicit moving horizon estimator, which provides the values of the states in the presence of noise. While unconstrained optimization techniques such as the Kalman filter have had success, they might provide misleading information about the system as they do not incorporate constraints. This is done in the moving horizion estimation, which is conceptually very closely related to model-predictive control. This allows of the seamless application of multi-parametric programming techniques, and the explicit availablility of the state estimator.
Both the estimator and the controller are validated in the closed-loop fashion through gO:MATLAB, the connection between gPROMS and MATLAB. The maximum offset observed is 2.3%, and the noisy output of the system is adequately handled by the explicit moving horizon estimator.
Tian, Y.*, Pappas, I.*, Burnak, B., Katz, J., Pistikopoulos, E.N. (2020) Simultaneous Design & Control of a Reactive Distillation System - A Parametric Optimization & Control Approach.
In this case study the reactive distillation of methanol and butene is considered. The goal is to perform the simultaneous design and control of the column, where the diameter of the column is considered as an uncertain parameter, while multiparametric model predictive controllers are used to satisfy the operational targets of the process.
The specific column under consideration is a 13 tray distillation model consisting of 52 differential states and 962 algebraic variables, modeled in the gPROMS environment.
The size of the model as well as its nonlinearity make the high-fidelity model unsuitable for the direct use in multi-parametric programming. Hence, MATLAB® System Identification Toolbox™ is utilized to approximate the highly nonlinear process, resulting into a discrete time invariant state space model with 6 states.
The diameter of the distillation column is considered as an uncertain paramter. The multiparametric model predictive controllers are derived by expressing the optimal control actions as explicit functions of the outputs, the diameter of the column, the outputs, the setpoints, and the disturbances of the the process model.
The design-dependent control laws are embedded in the gPROMS environment, where the overall capital and operational cost of the column is minimized subject to the process model and the control laws. The resulting performance demonstrates that the multiparametric model predictive controllers are able to satisfy the operational targets of the process in the presence of disturbances. The dynamic model, the approximate discrete state-space model, and the design-dependent multiparametric model predictive controllers can be downloaded here.
Pistikopoulos, E.N.; Diangelakis, N.A.; Oberdieck, R.; Papathanasiou, M.M.; Nascu, I.; Sun, M. (2015) PAROC - An integrated framework and software platform for the optimisation and advanced model-based control of process systems. Chemical Engineering Science, 136, 115-138.
Papathanasiou, M.M.; Steinebach, F.; Stroehlein, G.; Mueller-Spath, T.; Nascu, I.; Oberdieck, R.; Morbidelli, M.; Mantalaris, A.; Pistikopoulos, E.N. (2015) A control strategy for periodic systems – application to the twin-column MCSGP. In Proceedings of the 12th International Symposium on Process Systems Engineering and 25th European Symposium on Computer Aided Process Engineering, Computer Aided Chemical Engineering 37, 1505-1510.
Papathanasiou, M.M.; Avraamidou, S.; Steinebach, F.; Oberdieck, R.; Mueller-Spaeth, T.; Morbidelli, M.; Mantalaris, A.; Pistikopoulos, E.N. (2016) Advanced Control Strategies for the Multicolumn Countercurrent Solvent Gradient Purification Process (MCSGP). AIChE Journal, in print.
The high operating costs as well as the increased energy consumption of bioprocesses render improvements in their operation vital. In particular there has been an increasing industrial interest to shift biomanufacturing towards continuous operation. To facilitate this we develop advanced computational tools for the optimization and control of such processes. In particular, we considered the Multicolumn Countercurrent Solvent Gradient Purification (MCSGP) process, a periodic, semi-continuous chromatographic separation process.
The high-fidelity model comprises a 5x3 single-column configuration consisting of the modifier concentration, the flow rate and the component concentrations in the feed stream as inputs, while the output set includes the concentrations of the three mixture components. The dynamics are thereby described by partial differential and algebraic equations (PDAEs).
Using the system identification tool from MATLAB®, a reduced, lienarized version of the model is derived, consisting of three SISO systems. These systems are now used to formulate and solve the explicit MPC problem.
Using our in-build software, the explicit controller for this system was derived.
Using gO:MATLAB, the in-build connection between gPROMS and MATLAB, the designed controllers are validated against the high-fidelity model. A very good agreement between the monitored output and the setpoint is observed. Additionally, note that the derived controller results in a periodic profile although the linearized model provided does not enforce it.
Burnak, B; Katz, J.; Diangelakis, N. A.; Pistikopoulos, E. N. "Simultaneous Process Scheduling and Control: A Multiparametric Programming Based Approach", Industrial & Engineering Chemistry Research 2018, 57 (11), 3963-3976.
This material is based upon work supported by the National Science Foundation under Grant Number 1705423. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.
Multipurpose chemical processes are designed to meet the demands for multiple products or multiple grades of one product. Operability and profitability of these processes rely heavily on the decision making strategies in different time scales, including scheduling (long term) and control (short term) decisions. In this example, we present a methodology to integrate the scheduling and control decisions via a multi-scale application of the PAROC framework on a three product CSTR.
The high fidelity model comprises a CSTR and three product storage tanks, each of which is filled if and only if the product purity in the reactor is above a threshold. The objective is to minimize the inventory costs, while satisying a continuous time varying demand scenario by determining the production sequence, target production rate, and optimal reactant composition at the reactor feed.
Using MATLAB® System Identification Toolbox™, we derive linear, discrete time state space models for the open loop system. The approximate models can be downloaded from here.
Based on the identified model, we derive an explicit control law via the POP Toolbox. The explicit control expressions can be downloaded from here.
Embedding the explicit control law in the high fidelity model, we derive new appoximate models to represent the closed loop dynamics of the system. The approximate models can be downloaded from here.
The approximate model that recognizes the closed loop dynamics is used to derive a (i) multiparametric scheduler, and (ii) a surrogate model that bridges the gap between the scheduler and the controller. The parametric solution map of the scheduler and the surrogate model can be downloaded from here.
Katz, J.; Burnak, B.; Pistikopoulos, E. N. "The Impact of Model Approximation in Multiparametric Model Predictive Control".
This material is based upon work supported by the National Science Foundation under Grant Number 1705423. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.
Determining if approximate models used in the formulation of multiparametric model predictive controllers are acceptable a priori is a non trivial task. Two examples are presented that are used as a benchmark for several error metrics used to ascertain the effectiveness of the developed mpMPCs based on different approximate models.
The high fidelity models comprise a tank and CSTR, where the interest is to track a given setpoint.
Using MATLAB® System Identification Toolbox™, we derive linear, discrete time state space models for the open loop system that represent the high fidelity model.
Based on the identified model, we derive an explicit control law via the POP Toolbox. The explicit control expressions can be downloaded from here.
The developed explicit controllers are then validated against the developed high fidelity model.
Burnak, B.; Katz, J.; Pistikopoulos, E. N. "A Novel Space Exploration Algorithm via for Multiparametric Programming via Delaunay Triangulation".
This material is based upon work supported by the National Science Foundation under Grant Number 1705423. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.
A novel parameter space exploration algorithm is presented for the solution of classes of multiparametric programming problems, where Delaunay triangulation is utilized for the identification of the optimal partitions of the parameter space.
An example problem of the proposed approach is presented here along with the solution. The problems used in this computational study can be downloaded here.