Dynamic Real-time Optimization Research Articles

Integration of set point optimization techniques into nonlinear MPC for improving the operation of WWTPs

Optimization and control strategies are necessary to keep wastewater treatment plants (WWTPs) operating in the best possible conditions, maximizing effluent quality with the minimum consumption of energy. In this work, a benchmarking of different hierarchical control structures for WWTPs that combines static and dynamic real time optimization (RTO) and nonlinear model predictive control (NMPC) is presented. The objective is to evaluate the enhancement of the operation in terms of economics and effluent quality that can be achieved when introducing NMPC technologies in the distinct levels of the multilayer structure. Three multilayer hierarchical structures are evaluated and compared for the N-Removal process considering the short term and long term operation in a rain weather scenario. A reduction in the operation costs of approximately 20% with a satisfactory compromise to effluent quality is achieved with the application of these control schemes.

Assessment of control techniques for the dynamic optimization of (semi-)batch reactors

This work investigates how batch reactors can be optimized to increase the yield of a desired product coupling two appealing techniques for process control and optimization: the nonlinear model predictive control (NMPC) and the dynamic real-time optimization (D-RTO). The overall optimization problem is formulated and applied to calculate the optimal operating parameters of a selected case study and the numerical results are compared to the traditional control/optimization techniques. It has been demonstrated in our previous work (Pahija et al. (2013). Selecting the best control methodology to improve the efficiency of discontinuous reactors. Computer Aided Chemical Engineering, 32, 805–810) that the control strategy can significantly affect optimization results and that the appropriate selection of the control methodology is crucial to obtain the real operational optimum (with some percent of improved yield). In this context, coupling NMPC and D-RTO seems to be the ideal way to improve the process yield. The results presented in this work have been obtained by using gPROMS® and MS C++ with algorithms of BzzMath library.

A software environment for economic NMPC and dynamic real-time optimization of chemical processes

Abstract This paper presents the OptoEcon-Toolbox, a modular software environment for the simulation of chemical and energy processes, and their control using optimizing sampled-data controllers. Key features of this toolbox are modularity, which allows the realization of general multi-layer control architectures, and interfaces to powerful numerical software, which allows the usage of controller and plant surrogate models formulated in different modeling languages such as Modelica or gPROMS. The capability of this toolbox is illustrated in a case study of an industrial copolymerization process.

A Survey on Sensitivity-based Nonlinear Model Predictive Control

This survey explores recent results in the development of optimization algorithms and formulations for moving horizon estimation (MHE), nonlinear model predictive control (NMPC) and dynamic real-time optimization (D-RTO), with extrapolative nonlinear dynamic (e.g., first principle) models. We consider Nonlinear Programming (NLP) and NLP sensitivity as natural tools for formulation and efficient solution of optimization problems for these three tasks. For MHE, we develop a maximum likelihood formulation that directly incorporates nonlinear models, and is seamlessly adapted to updating the arrival costs. This approach is also extended easily to M-estimators, which essentially eliminate biased estimates due to gross errors. For NMPC, we develop formulations that incorporate well-understood stability and robustness properties, even for large, complex plant models. Finally, recent work has extended these capabilities from setpoint tracking objectives to more general stage costs that are economically based, thus leading to a robustly stable strategy for D-RTO. In concert with these problem formulations, the realization of MHE, NMPC and D-RTO requires the application of a fast NLP solver for time-critical, on-line optimization, as well as efficient NLP sensitivity tools that eliminate computational delay, and guarantee stability and robustness. Algorithms that meet these demands are explored and outlined for these tasks. Finally, a number of challenging distillation case studies are presented that demonstrate the effectiveness of these optimization-based strategies.

Hierarchical control of large scale systems: A zone control approach

A methodology for hierarchical control of large scale systems is presented. This approach uses an integration of dynamic real time optimization (DRTO) and model predictive control (MPC) with zone control (coordinator). The dynamic real time optimization problem is solved in the upper layer and addresses the overall economic objective to provide the reference trajectories for the coordinator (middle layer) that calculates hierarchical input variables and output references that are always into the designed zone, this information is taken by the subsystems controllers (lower layer) to generate the input variables that is going to be applied, and that reach the reference that the coordinator generate. This methodology is applied to a complete chemical process composed by three chemical reactors type CSTR (Continuous Stirred Tank Reactor) and three non reactive binary distillation columns.

On the role of the necessary conditions of optimality in structuring dynamic real-time optimization schemes

In dynamic optimization problems, the optimal input profiles are typically obtained using models that predict the system behavior. In practice, however, process models are often inaccurate, and on-line model adaptation is required for appropriate prediction and re-optimization. In most dynamic real-time optimization schemes, the available measurements are used to update the plant model, with uncertainty being lumped into selected uncertain plant parameters; furthermore, a piecewise-constant parameterization is used for the input profiles. This paper argues that the knowledge of the necessary conditions of optimality (NCO) can help devise more efficient and more robust real-time optimization schemes. Ideally, the structuring decisions involve the NCO as follows: (i) one measures or estimates the plant NCO, (ii) a NCO-based input parameterization is used, and (iii) model adaptation is performed to meet the plant NCO. The benefit of using the NCO in dynamic real-time optimization is illustrated in simulation through the comparison of various schemes for solving a final-time optimal control problem in the presence of uncertainty.

Multiobjective Nonlinear Model Predictive Control of a Class of Chemical Reactors

Many problems in science and engineering can be posed as multiobjective optimization problems where several objectives must be met simultaneously. Commonly such multiobjective optimization problems are reduced to a single optimization problem by merging all the involved objective functions by using rather subjective weighting functions. This solution procedure can produce suboptimal solutions, and it is not a systematic method since the choice of the weighting functions is up to the designer. Process control is one of the engineering fields where multiobjective optimization control problems frequently emerge because such problems normally involve conflicting objective functions such as economical profit and environmental concerns. Because the optimal value of the conflicting objective functions cannot be simultaneously achieved one has to compute a trade-off solution that best suits, in a given sense, all the objective functions. Moreover, additional requirements, beyond upset rejection and set-point tracking, such as the determination of optimal operating conditions should also be handled by dynamic real time optimal control approaches. In this work we propose a novel multiobjective optimization and control approach able to get target points while simultaneously computing optimal operating conditions. The proposed approach can be applied to nonlinear dynamic systems and does not require the specification of arbitrary weighting functions to handle conflicting multiobjective optimization problems. Several case studies using chemical reactors of varying nonlinear behavior are deployed to illustrate the practical application of the proposed dynamic real time optimization approach.

Solving dynamic optimization infeasibility problems

Dynamic real-time optimization (DRTO) systems sometimes fail when solving intrinsic optimization problems. There are situations where the solution is infeasible due to the initial conditions, constraint changes during operation, or even the presence of conflicts on constraint specifications. By using a goal programming approach, this work proposes a method to solve these infeasibilities by reformulating the differential-algebraic optimization problem as a multi-objective dynamic optimization problem with path constraint relaxations. Three examples were solved exploring the characteristics of such infeasibility problems. The results demonstrate the ability of the proposed method in identifying and relaxing the constraint violations, increasing the robustness of DRTO systems.

Dynamic optimization of a FCC converter unit: numerical analysis

Fluidized-bed Catalytic Cracking (FCC) is a process subject to frequent variations in the operating conditions (including feed quality and feed rate). The production objectives usually are the maximization of LPG and gasoline production. This fact makes the FCC converter unit an excellent opportunity for real-time optimization. The present work aims to apply a dynamic optimization in an industrial FCC converter unit, using a mechanistic dynamic model, and to carry out a numerical analysis of the solution procedure. A simultaneous approach was used to discretize the system of differential-algebraic equations and the resulting large-scale NLP problem was solved using the IPOPT solver. This study also does a short comparison between the results obtained by a potential dynamic real-time optimization (DRTO) against a possible steady-state real-time optimization (RTO) application. The results demonstrate that the application of dynamic real-time optimization of a FCC converter unit can bring significant benefits in production.

A two-layer architecture for economically optimal process control and operation

A two-layer architecture for dynamic real-time optimization (or nonlinear modelpredictive control (NMPC) with an economic objective) is presented, where the solution of the dynamic optimization problem is computed on two time-scales. On the upper layer, a rigorous optimization problem is solved with an economic objective function at a slow time-scale, which captures slow trends in process uncertainties. On the lower layer, a fast neighboring-extremal controller is tracking the trajectory in order to deal with fast disturbances acting on the process. Compared to a single-layer architecture, the two-layer architecture is able to address control systems with complex models leading to high computational load, since the rigorous optimization problem can be solved at a slower rate than the process sampling time. Furthermore, solving a new rigorous optimization problem is not necessary at each sampling time if the process has rather slow dynamics compared to the disturbance dynamics. The two-layer control strategy is illustrated with a simulated case study of an industrial polymerization process.

Dynamic Real-time Optimization of Reservoir Production

Water flooding is a common technology of enhanced oil recovery and has been widely used to the world's oil fields. But it is difficult to maintain a uniform displacement of water, which causes the ineffective circulation of injected water. Therefore, the real-time dynamic control strategy is studied to work out development plans scientifically and make better economic profits in this paper. The net present value of crude oil exploitation during a certain period of time is choosen to performance index of the control problem. Hydrodynamic equations of oil, water and gas, which describe the displacement process, are used as governed equations. Meanwhile, the boundary constraints of wells and balance relationship of injection-production are taken into account. Based on the above equations, a control model of oil field development is established. The control vector parameterization method is illustrated in detail to deal with the unconstrained, control constrained and state constrained optimal control problem. Finally, a simulation example is employed to verify the validity of the proposed control algorithm.

Integration of model-predictive scheduling, dynamic real-time optimization and output tracking for a wastewater treatment process

A hierarchical control architecture for the integration of scheduling decisions, dynamic real-time optimization and tracking control is proposed. It is shown how the discrete-continuous problem of simultaneous scheduling and trajectory optimization on a receding horizon can be integrated within the upper control layer of a two-layer architecture. On the upper layer, the optimal plant strategy defined by a sequence of control objectives and optimal control moves is computed on a long time horizon. The lower control layer consists of a state observer and a fast-acting tracking controller which operates on a short time horizon. The properties of this architecture are illustrated by a case study in which a wastewater treatment plant is operated under the influence of external disturbances. Conflicting operational objectives may be valid, depending on the state of the plant and the expected disturbances. By calculating an optimal sequence of operational strategies and control moves on the receding horizon, economically optimal operation of the plant can be achieved.

Odel-Based Optimizing Control and Estimation Using Modelica Model

This paper reports on experiences from case studies in using Modelica/Dymola models interfaced to control and optimization software, as process models in real time process control applications. Possible applications of the integrated models are in state- and parameter estimation and nonlinear model predictive control. It was found that this approach is clearly possible, providing many advantages over modeling in low-level programming languages. However, some eort is required in making the Modelica models accessible to NMPC software. Particular consideration is given to implementation of gradient computation for real-time dynamic optimization, where the dynamic models can be Modelica models. Analytical methods for gradient computation based on sensitivity integration are compared to nite dierence-based

On-line economic optimization of energy systems using weather forecast information

We establish an on-line optimization framework to exploit weather forecast information in the operation of energy systems. We argue that anticipating the weather conditions can lead to more proactive and cost-effective operations. The framework is based on the solution of a stochastic dynamic real-time optimization (D-RTO) problem incorporating forecasts generated from a state-of-the-art weather prediction model. The necessary uncertainty information is extracted from the weather model using an ensemble approach. The accuracy of the forecast trends and uncertainty bounds are validated using real meteorological data. We present a numerical simulation study in a building system to demonstrate the developments.

The energy-efficiency benefits of pump-scheduling optimization for potable water supplies

Water utilities across the developed world have been installing and operating telemetry and SCADA (supervisory control and data acquisition) facilities for at least three decades. They have amassed substantial quantities of historical operational data held in databases called data warehouses. Significant interest exists for extracting the underlying value from this data to support decision making and performance improvement. The water industry uses approximately 3% of total electricity production in developed countries such as the United Kingdom and the United States. Up to 90% of this electrical energy is consumed by pumps. Small improvements in pump efficiency will yield significant reductions in energy consumption with consequential reductions of carbon emissions to the atmosphere. Technologies to initially select a pump to match the expected performance requirements and then maintain optimal performance through periodic refurbishment are well established. Dynamically optimizing the scheduling of pump operation to improve efficiency under changing diurnal and seasonal water demand patterns is far more complex. This paper summarizes 20 years of progress in the development of pump efficiency improvement techniques and focuses on real-time dynamic optimization technologies and data-mining techniques to improve energy efficiency. Case study results from an automated real-time commercial pump-scheduling system, Aquadapt™, are presented.

Neighboring-extremal updates for nonlinear model-predictive control and dynamic real-time optimization

Nonlinear model-predictive control (NMPC) and dynamic real-time optimization (DRTO) lead to a substantial improvement of the operation of complex nonlinear processes. Whereas the focus in NMPC is primarily on control performance by minimizing the deviation from a given set-point, the objective in DRTO is to achieve a profitable and flexible operation adapted to changing market conditions and process uncertainties by employing an economic optimization criterion. A method for solving dynamic optimization problems based on neighboring-extremal updates suitable for applications in NMPC and DRTO is presented in this paper. If process operation is affected by small perturbations, efficient techniques for updating the nominal trajectories based on parametric sensitivities can be applied [J. Kadam, W. Marquardt, Sensitivity-based solution updates in closed-loop dynamic optimization, in: Proceedings of the DYCOPS 7 Conference, Cambridge, USA, 2004]; these updates do not require the solution of the rigorous optimization problem but rely on first and second-order sensitivities computed by composite adjoints. However for larger perturbations and strong nonlinearities, the fast updates obtained by the neighboring-extremal solutions are not sufficiently accurate, and the solution of the nonlinear optimization problem requires further iterations with updated sensitivities to give a feasible and optimal solution. The application of the method to a simulated semi-batch reactor demonstrates its capabilities. The presented method is discussed in comparison to other methods in the literature.

Closed Loop Dynamic Optimization of a Petroleum Refinery Process

In this paper the requirements set by the modern petroleum oil and petrochemicals industry on dynamic real-time optimization (DRTO) and advanced process control (APC) applications are discussed. The modern processes in the hydrocarbon industry are large, complex and have challenging dynamics. They also produce a wide variety of products from a spectrum of different feedstocks. Some dynamic real-time optimization approaches used by the industry to tackle the characteristics of the processes as well as results attained are presented in the paper.

Dynamic Optimization: Reducing Central Utility Plant Consumption by Over 50 Percent

ABSTRACT This article describes the best practices employed in the systematic upgrade, operation and maintenance of a central utility plant (CUP) and associated energy infrastructure. The CUP provides electrical, heating and cooling services to a 1.4 million square foot super-regional shopping mall in Central Pennsylvania. Since Energy Works' acquisition in late 2003, numerous improvements have been made that include: Selective equipment upgrades Automation of best practices in operation and maintenance Designing and installing an energy management system for real-time dynamic optimization. These improvements not only reduced the plant energy consumption by over 50%; they also reduced the carbon footprint by over 11 million pounds per year. With advanced energy management systems in place, the shopping mall is assured of a healthy, efficient and sustainable energy service.

Large-scale nonlinear programming using IPOPT: An integrating framework for enterprise-wide dynamic optimization

Integration of real-time optimization and control with higher level decision-making (scheduling and planning) is an essential goal for profitable operation in a highly competitive environment. While integrated large-scale optimization models have been formulated for this task, their size and complexity remains a challenge to many available optimization solvers. On the other hand, recent development of powerful, large-scale solvers leads to a reconsideration of these formulations, in particular, through development of efficient large-scale barrier methods for nonlinear programming (NLP). As a result, it is now realistic to solve NLPs on the order of a million variables, for instance, with the IPOPT algorithm. Moreover, the recent NLP sensitivity extension to IPOPT quickly computes approximate solutions of perturbed NLPs. This allows on-line computations to be drastically reduced, even when large nonlinear optimization models are considered. These developments are demonstrated on dynamic real-time optimization strategies that can be used to merge and replace the tasks of (steady-state) real-time optimization and (linear) model predictive control. We consider a recent case study of a low density polyethylene (LDPE) process to illustrate these concepts.

Analytical dynamic model for planar close-chain linkages with alterable length and inertia parameters based on parallel calculation

Analytical dynamic model based on the sub model of links and a parallel algorithm for planar close-chain mechanisms, in which lengths and inertia parameters of links can be changed, is established based on Kane dynamic equation and numeric-symbolic approach. The influence of lengths and mass of driving links on driving force/torque are also studied. The close vector is applied in the kinematical analysis of planar close-chain mechanisms and expressions of velocity and acceleration of links are derived. Real-time code of matrix elements of each sub model, in which lengths and inertia parameters of links as well as generalized coordinates are expressed as symbols, the other variables as numeral, are derived off-line. Then the total driving force/torque of planar close-chain mechanisms are obtained by piled add. An optimization method of real-time code based on the parallel algorithm of sub model of links is proposed. The procedures of dynamic modeling and real-time code optimization can be performed off-line, and parallel calculation structure is adopted, therefore on-line calculation time can be reduced greatly, which is of advantage to real-time control of mechanisms. The examples of dynamic simulation are given for illustration.