J.F. Forbes

Model-based real-time optimization of automotive gasoline blending operations

Abstract Gasoline blending is a key process in the successful operation of most petroleum refineries and real-time optimization (RTO) of gasoline blend recipes has the potential to provide a competitive benefit for oil refiners. The trend toward the use of “running” tanks for blender feedstocks and the recent advances in measurement technology have provided the opportunity for improved blending performance using RTO. This paper provides an improved formulation for the gasoline blend optimization problem that incorporates both the blend horizon and a stochastic model of disturbances into the RTO problem. The proposed approach is illustrated with a blender simulation study.

Regulatory control design for stochastic processes: shaping the probability density function

This paper presents a regulatory controller synthesis technique that makes a pre-selected probability density function (PDF) for the closed-loop (CL) process the target of the design. The proposed design technique, referred to as PDF-shaping, approximately solves the integral equation giving the PDF of the CL process dynamics. The parameterization of the closed-loop process dynamics results in the parameterization of a controller that yields the required closed-loop PDF. Controller synthesis is then a matter of selecting, based on engineering or economic concerns, a target distribution, and then applying the proposed technique to find the approximate closed-loop dynamics. The special case of PDF-shaping using Gram-Charlier PDFs is presented, as well as the general case. Results of this novel approach to controller synthesis are demonstrated with numerical simulations for an example process.

Sensor selection for model-based real-time optimization: relating design of experiments and design cost

Abstract Real-time optimization systems have become a common tool, in the continuous manufacturing industries, for improving process performance. Typically, these are on-line, steady-state, model-based optimization systems, whose effectiveness depends on a large number of design decisions. The work presented here addresses one of these design decisions and proposes a systematic approach to the selection of sensors to be used by the RTO system. This paper develops a sensor system selection metric based on a trade-off between two approaches to the design of experiments, which is shown to be consistent with the design cost approach of Forbes and Marlin [Computers Chem Eng 20 (1996) 7/7]. The resulting design metric is incorporated into a systematic procedure for RTO sensor selection problem. Finally, the proposed RTO sensor selection procedure is illustrated with a case study using the Williams–Otto [AIEE Trans 79 (1960), 458] plant.

Robust characteristic-based MPC of a fixed-bed reactor

In this work a model predictive control methodology is applied to a set of hyperbolic partial differential equations (PDEs) which models a chemical fixed-bed reactor. Initially, the model of the fixed-bed reactor is linearized and by the method of characteristics is transformed into the set of ODEs which is explored within the model predictive controller synthesis. We consider uncertainties present in the reactor model which are taken into account by the construction of the polytopic family of plants and subsequent robust model predictive controller synthesis which ensures input and state constraints satisfaction. The proposed robust control problem formulation and the performance of the controller have been evaluated by simulations.

Linear quadratic optimal boundary control of a diffusion-convection-reaction system

Abstract In this work, the boundary control of a distributed parameter system (DPS) modeled by parabolic partial differential equations with spatially varying coefficients is studied. An infinite dimensional state space setting is formulated and an exact transformation of the boundary actuation is realized to obtain an evolutionary model. The evolutionary model is used for subsequent linear quadratic regulator synthesis which incorporates the spatially varying coefficients of the underlying set of the PDEs. The formulated LQR controller is applied to the nonlinear model of the system and its performance is studied.

Model updating in the presence of stochastic feedstock disturbances for real-time optimization of blending operations

Real-time optimization based control systems are used for blending operations in many industries. Typically, in blending of automotive gasoline, these systems use linear programming with bias update of blending models. This paper considers the performance of such systems in terms of profit level and shows that the blender control performance can be increased very significantly by eliminating or reducing plant/model mismatch. Further, a new control approach that optimizes over the entire blend, rather than at a point in time, is presented and the benefits of adopting this new approach are illustrated. The paper concludes with a brief discussion of observability issues which must be considered to ensure the success of the proposed control scheme.

Optimal control of a time-varying catalytic fixed bed reactor with catalyst deactivation

The paper deals with the linear-quadratic control problem for a time-varying partial differential equation model of a catalytic fixed-bed reactor. The classical Riccati equation approach, for time-varying infinite-dimensional systems, is extended to cover the two-time scale property of the fixed-bed reactor. Dynamical properties of the linearized model are analyzed by using the concept of evolution systems. An optimal LQ-feedback is computed via the solution of a matrix Riccati partial differential equation. Numerical simulations are performed to show the performance of the designed controller on the fixed-bed reactor.

Performance Assessment of Nonlinear State Filters

Abstract Nonlinear state filters of different approximations and capabilities have been developed in the last decade. The quality of different nonlinear filters, in terms of the mean squared error (MSE) of the estimates, depends on the approximations used in the filtering algorithm; however, there are no known methods for effectively evaluating the relative performance of these filters. A new method which measures the performance of different state filters against the theoretical posterior Cramer-Rao lower bound (PCRLB) is proposed. The complex high-dimensional integrals in PCRLB are approximated using sequential Monte-Carlo (SMC) methods. Efficacy of the proposed method is illustrated through a simulation example.

MODEL PREDICTIVE CONTROL OF A CATALYTIC FLOW REVERSAL REACTOR WITH HEAT EXTRACTION

Abstract This paper presents the formulation of a controller for a Catalytic Flow Reversal Reactor (CFRR) with heat extraction. The controller is based on the Model Predictive Control (MPC) concept. The MPC scheme uses a model that assumes plug flow and neglects radial gradients in the reactor but accounts for the two phases within the reactor. The prediction of the future output behavior from the model is obtained by using the Method of Characteristics as proposed by Shang et al. (2004) for convection dominated distributed parameter systems. The formulated controller is applied to a CFRR unit for the catalytic oxidation of fugitive lean methane mixtures. The objective of the control algorithm is to maintain stable reactor operation, while extracting the maximum amount of useful energy by hot gas removal from the mid-section of the reactor. Simulations are used to show the performance of the designed controller.

LQ-control of a flow reversal reactor for the catalytic combustion of fugitive methane emissions

This paper deals with linear-quadratic control problem for a catalytic flow reversal reactor using an infinite dimensional Hilbert space representation of the system. A LQ-controller is developed on the basis of the catalytic reactor with unidirectional flow. The controller is formulated to keep the distribution of the temperature along the axis of the reactor at stationary state by using the fluid flow velocity. We study the application of the controller on the catalytic reactor with reverse flow operation. We take advantage of the two-time scale characteristic of catalytic tubular reactors to develop a controller that requires only the measurement of the temperature along the axis of the reactor. Using the infinite dimensional state space, a state LQ-feedback operator is computed via the solution of a Riccati differential equation. The developed controller is tested numerically for the catalytic combustion of lean methane emissions in CFRR unit and implemented for a reactor configuration at the CANMET Energy Technology Centre Varennes, Quebec, Canada, and currently experimental tests are underway.