Dynamic Real-time Optimization Research Articles

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.

Real-time Dynamic Optimization of Batch Crystallization Processes

An on-line optimization strategy is developed and applied to a semi-industrial crystallization process. The seeded fed-batch crystallizer is represented by a nonlinear moment model. An optimal control problem pertinent to maximization of the batch crystal yield is solved using the sequential optimization approach. As the dynamic optimizer requires knowledge of the states of the system, an extended Luenberger-type observer is designed to estimate the unmeasured state variable, i.e. solute concentration. Real-time implementations of the proposed strategy reveal the effectiveness of closed-loop optimal control of the crystallizer. The superior performance of the closed-loop implementation to that of the open-loop implementation is attributed to the distinct role of the observer in the feedback control structure that not only accounts for plant-model mismatch by state adaptation, but also enables disturbance handling. Experimental results also demonstrate that the application of the proposed optimal control strategy leads to a substantial increase in the crystal volume fraction at the end of the batch, while the reproducibility of batches with respect to the product crystal size distribution is sustained.

An Efficient Strategy for Real-Time Dynamic Optimization based on Parametric Sensitivities

The optimal operation of chemical processes is challenged by frequent transitions and by the influence of process or model uncertainties. Under uncertainties, it is necessary to quickly update the optimal trajectories in order to avoid the violation of constraints and the deterioration of the economic performance of the process. Although an economically optimal operation can be ensured by online dynamic optimization, the high computational load of dynamic optimization associated with nonlinear and complex models is often prohibitive in real-time applications. To reduce the computational time required for online computation of the optimal trajectories in the neighborhood of the optimal solution under uncertainty, different strategies have been explored recently. If the operation is affected by small perturbations, efficient techniques for updating the nominal trajectories based on parametric sensitivities are applied, which do not require the solution of the rigorous optimization problem. However for larger perturbations, the linear 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. In this work, the sensitivity-based approach of Kadam and Marquardt (2004) is extended with a fast computational method for second-order derivatives based on composite adjoints. The application of the method to a simulated semi-batch reactor demonstrates that fast and optimal trajectory updates can be obtained.

Real-time process optimization based on grey-box neural models

This paper investigates the feasibility of using grey-box neural models (GNM) in Real Time Optimization (RTO). These models are based on a suitable combination of fundamental conservation laws and neural networks, being used in at least two different ways: to complement available phenomenological knowledge with empirical information, or to reduce dimensionality of complex rigorous physical models. We have observed that the benefits of using these simple adaptable models are counteracted by some difficulties associated with the solution of the optimization problem. Nonlinear Programming (NLP) algorithms failed in finding the global optimum due to the fact that neural networks can introduce multimodal objective functions. One alternative considered to solve this problem was the use of some kind of evolutionary algorithms, like Genetic Algorithms (GA). Although these algorithms produced better results in terms of finding the appropriate region, they took long periods of time to reach the global optimum. It was found that a combination of genetic and nonlinear programming algorithms can be use to fast obtain the optimum solution. The proposed approach was applied to the Williams-Otto reactor, considering three different GNM models of increasing complexity. Results demonstrated that the use of GNM models and mixed GA/NLP optimization algorithms is a promissory approach for solving dynamic RTO problems.

Real-time dynamic optimization of batch systems

In this paper a methodology for designing and implementing a real-time optimizing controller for batch processes is proposed. The controller is used to optimize a user-defined cost function subject to a parameterization of the input trajectories, a nominal model of the process and general state and input constraints. An interior point method with penalty function is used to incorporate constraints into a modified cost functional, and a Lyapunov based extremum seeking approach is used to compute the trajectory parameters. The technique is applicable to general nonlinear systems. A precise statement of the numerical implementation of the optimization routine is provided. It is shown how one can take into account the effect of sampling and discretization of the parameter update law in practical situations. A simulation example demonstrates the applicability of the technique.

Real-Time Dynamic Optimization of Controllable Linear Systems

A real-time optimization controller is developed to steer a linear time-varying control system to closed-loop trajectories that optimize a cost functional of interest. When advantage is taken of the differential flatness of the linear systems, a basis function approach is used to parameterize the open-loop trajectories of the system and to approximate the optimal solution of the finite time optimal control problem. An adaptive optimization method is used to formulate the real-time optimization scheme. The problem is posed as a real-time optimal trajectory generation problem in which the approximate optimal trajectories are computed using an extremum-seeking approach. The control algorithm provides tracking of the approximate optimal trajectories. Two optimal control problems are considered to demonstrate the application of the technique. It is shown that the technique can be successfully implemented in real time.

Real-time dynamic optimization of nonlinear systems: A flatness-based approach

In this paper, a real-time optimizing controller is developed to steer a differentially flat nonlinear control system to closed-loop trajectories that optimize a cost functional of interest. An interior-point optimization method with penalty function is used to formulate a real-time optimization scheme. The problem is posed as a real-time optimal trajectory generation problem in which the optimal trajectories are computed using an adaptive extremum-seeking approach. Simulation examples are used to demonstrate the application of the technique to various finite time dynamic optimization problems that arise in batch process control.

CLOSED LOOP DYNAMIC OPTIMIZATION OF PRODUCTION PLANTS

Realtime economical optimization of production plants has traditionally relied on steady state process models. Because real plants are normally in transient states, such models could be adapted to measurements only occasionally. Neste Jacobs Oy has developed a new closed loop dynamic realtime optimization (DRTO) technology, which optimizes the plants also during transient states. The technology permits optimization practically in realtime, which contributes to quickly reaching optimum. The DRTO application example is in the Ethylene Plant of Borealis Polymers Oy, Porvoo, Finland. The DRTO is in continuous use since 2004 and the experience has been outstanding.

DYNAMIC REAL-TIME OPTIMIZATION OF A FCC CONVERTER UNIT

Fluidized-bed Catalytic Cracking (FCC) is a process subject to frequent variations in the operating conditions and changes in the feed quality and feed rate, due to the attempts to maximize LPG and gasoline. This fact makes the FCC converter unit an excellent opportunity for real-time optimization. The present work aims to apply a dynamic real-time optimization (D-RTO) into a simulation of an industrial FCC converter unit, using a mechanistic dynamic model. The algorithms that solve D-RTO problems need to deal with large-scale problems due to the full or partial system discretization along the optimal trajectory. In this work a simultaneous approach, present in the IPOPT solver, was used to discretize the system and solve the resulting large-scale NLP problem.

Dynamic Optimization of Complex Distributed Process Systems

The dynamic optimization (DO) of complex distributed parameter systems (DPSs), like e.g., reaction–diffusion processes, is a challenging task. Most of the existing numerical approaches imply a large computational effort, therefore precluding its application to demanding applications like real time DO or model predictive control. This work, based on the control vector parameterization (CVP) approach, describes two ways to enhance the efficiency of the resulting nonlinear programming (NLP) problem solution. On the one hand, the convergence properties of the NLP solver are enhanced through the use of exact gradients and projected Hessians (H.p). On the other hand, simulation efficiency is improved through the use of reduced order descriptions of the DPSs. The capabilities and possibilities of these two enhancements are illustrated with a number of complex distributed case studies.

An introduction to a dynamic plant-wide optimization strategy for an integrated plant

In this paper, we develop a dynamic real-time optimization (RTO) strategy for an integrated plant. The steady-state assumption in conventional RTOs severely limits frequency of optimization and precludes the use of dynamic degrees of freedom available in the plant (e.g. storage capacities), resulting in suboptimal economic performances. Other approaches that attempt to synchronize the frequency of the plant-level optimization to that of the local-unit-level model predictive controllers can be sensitive to local disturbances and model uncertainty in high-frequency parts of plant dynamics. We reason that a logical middle ground is to perform a dynamic optimization but at a rate significantly lower than the model predictive controllers in order to keep the modeling and computational requirements at a reasonable level for the optimization. We discuss the obtaining of a reduced-order model for a chosen optimization frequency and the interfacing of the real-time optimizer with unit controllers. Two examples are given to compare the various approaches.

Destroying VOCs

Dynamic real-time optimization (DRTO) is an extension of the traditional steady-state RTO paradigm to account for process dynamics in the RTO calculations. This paper presents methods for approximating closed-loop dynamic predictions within DRTO calculations for processes regulated under constrained model predictive control (MPC). Three approximation approaches are formulated and analyzed – hybrid, bilevel and input clipping formulations. The hybrid formulation involves application of rigorous closed-loop prediction over a limited DRTO horizon, followed by open-loop optimal control. In the bilevel formulation, only a single MPC optimization subproblem is embedded, whereas the input clipping approach is formulated using an unconstrained MPC algorithm with an input saturation mechanism applied over the DRTO horizon. The relative performance of the proposed approximation approaches is illustrated through two case study applications, the second of which involves economically optimal polymer grade transitions. Excellent closed-loop approximation is achieved without significant loss of prediction accuracy.

Dynamic optimization of the Tennessee Eastman process using the OptControlCentre

This study focuses on the performance of large-scale nonlinear programming (NLP) solvers for the dynamic optimization in real-time of large processes. The matlab-based OptControlCentre (OCC) is coupled with large-scale optimization tools and developed for on-line, real-time dynamic optimization. To demonstrate these new developments, we consider the on-line, real-time dynamic optimization of the Tennessee Eastman (TE) challenge process in a nonlinear model predictive control (NMPC) framework. The example captures the behavior of a typical industrial process and consists of a two phase reactor, where an exothermic reaction occurs, along with a flash, a stripper, a compressor and a mixer. The process is nonlinear and open loop unstable; without control it reaches shutdown limits within an hour, even for very small disturbances. The system is represented through a first principles model with about 200 differential algebraic equations (DAEs). As a result, the NMPC formulation of this system presents some interesting features for dynamic optimization approaches. This study compares two state-of-the-art NLP solvers, SNOPT and IPOPT, for dynamic optimization on a number of challenging control scenarios, and illustrates some of the advantages of IPOPT for dynamic optimization.