Darci Odloak

Integrating real-time optimization into the model predictive controller of the FCC system

Abstract In this paper attention has been paid to the establishment of a proper real-time optimization strategy for the FCC unit. The majority of the approaches published in the literature make use of steady-state data. If the plant is highly disturbed updating the optimal operating point may not be easily achieved. In this study procedures are shown on how to overcome this problem and how to make use of the linear model predictive controllers (MPC) extending them to include optimization of the predicted steady-state operational point. Three such optimization strategies are presented that rapidly accommodate measured disturbances while avoiding offsets. The paper also shows results from the industrial implementation of one of these strategies at the refinery of Sao Jose in Brazil. The optimizing controller was integrated into the control package SICON, which was developed by Petrobras. Plant results show that the new controller is able to drive the process smoothly to a more profitable operating point overcoming the performance obtained by the existing advanced controller.

Constrained multivariable control of fluid catalytic cracking converters

Abstract This paper concerns the development of a multivariable controller for the FCC Kellog Orthoflow F reactor/regenerator unit. A nonlinear dynamic model, based on the model of Kurihara, is used as a reference for the design of the control algorithm. This model is compared with the plant data, for open loop changes on the air flow and the regenerated catalyst valve opening. The adopted control algorithm incorporates both the regulatory and optimization functions. The regulatory layer is based on the usual DMC algorithm, while the optimization layer solves a linear programming problem, based on the DMC formulation, to perform steady-state economic optimizations. The calculated variables of the LP are the setpoints to the regulatory layer. The proposed control structure is simulated for a particular set of manipulated and controlled variables of the Kellog FCC converter and the results indicate good potential for the application to the real system.

Multi-model predictive control of an industrial C3/C4 splitter

Abstract In this paper, the application of a linear predictive controller to an industrial distillation column that presents a nonlinear behavior is described. The system is represented by a set of linear approximating models, where each model corresponds to a possible operating point of the system. The control sequence computed by the control algorithm is based on a min–max optimization problem where the controller cost is minimized for the worst process model. The control algorithm makes use of a particular form of the state-space model, which preserves the structure of conventional model predictive control controllers that are based on the step response model. The performance of the proposed controller applied to an industrial system is illustrated with results of the real system at typical plant conditions with the controller performing as a regulator and as an output reference tracker.

Real time optimization (RTO) with model predictive control (MPC)

This paper studies a simplified methodology to integrate the real time optimization (RTO) of a continuous system into the model predictive controller in the one layer strategy. The gradient of the economic objective function is included in the cost function of the controller. Optimal conditions of the process at steady state are searched through the use of a rigorous non-linear process model, while the trajectory to be followed is predicted with the use of a linear dynamic model, obtained through a plant step test. The main advantage of the proposed strategy is that the resulting control/optimization problem can still be solved with a quadratic programming routine at each sampling step. Simulation results show that the approach proposed may be comparable to the strategy that solves the full economic optimization problem inside the MPC controller where the resulting control problem becomes a non-linear programming problem with a much higher computer load.

Industrial implementation of a real-time optimization strategy for maximizing production of LPG in a FCC unit

Abstract This paper describes the implementation of a new non-conventional real-time optimization strategy applied to the maximization of LPG production in a fluid catalytic cracking (FCC) converter in the refinery of Sao Jose dos Campos in Brazil. Focus is given on the difficulties of integrating optimization to existing controllers. The first commissioning tests are described in detail. They show that the benefits from optimization are not restricted to economic values. Implementation of the strategy gives directions on how to change the operating mentality of the plant operators. The implemented optimization strategy is shown to be able to maintain control of the plant even in the loss of several manipulated variables and in the presence of strong disturbances. Furthermore, we show that the optimization strategy is able to drive the process to new operational points.

One-layer real time optimization of LPG production in the FCC unit : Procedure, advantages and disadvantages

This paper summarizes the results of the current stage of the real time optimization (RTO) project of Petrobras in Brazil for optimizing its refineries. Here the maximization of the production of LPG in the FCC converter is considered. The general procedure for applying the RTO using the one-layer approach is outlined. Some difficulties that may arise during the implementation are addressed and the strategy is compared with the more traditional two-layers approach. We also stress the need of using a robust nonlinear programming (NLP) code and all the results presented in the paper were obtained by the MISQPSOL code.

MPC for stable linear systems with model uncertainty

In this paper, we developed a model predictive controller, which is robust to model uncertainty. Systems with stable dynamics are treated. The paper is mainly focused on the output-tracking problem of a system with unknown steady state. The controller is based on a state-space model in which the output is represented as a continuous function of time. Taking advantage of this particular model form, the cost functions is defined in terms of the integral of the output error along an infinite prediction horizon. The model states are assumed perfectly known at each sampling instant (state feedback). The controller is robust for two classes of model uncertainty: the multi-model plant and polytopic input matrix. Simulations examples demonstrate that the approach can be useful for practical application.

An infinite horizon model predictive control for stable and integrating processes

Abstract This paper deals with the linear model predictive control (MPC) with infinite prediction horizon (IHMPC) that is nominally stable. The study is focused on the output-tracking problem of systems with stable and integrating modes and unmeasured disturbances. To produce a bounded system response along the infinite prediction horizon, the effect of the integrating modes must be zeroed. The integrating mode zeroing constraint may turn the control problem infeasible, particularly when the system is affected by large disturbances. This work contributes in two ways to the problem of implementing IHMPC. The first contribution refers to the softening of some hard constraints associated with the integrating modes, while nominal stability is preserved. Another contribution is related to the strategy followed to deal with the infinite horizon and the removal of the matrix Lyapunov equation from the controller optimization problem. A real industrial example where the application of the controller has been studied is used to illustrate the advantages of the proposed strategy.

Output feedback MPC with guaranteed robust stability

Abstract This paper focuses on the issues of robust stability of model predictive control (MPC). The control problem is formulated as linear matrix inequalities (LMI) optimization problem. A suboptimal solution for the output feedback control problem is proposed. The size of the resulting MP controller is reduced by using a suitable state-space representation of the process. Guaranteed stability conditions for the output feedback MPC are enforced via a Lyapunov type constraint. An iterative algorithm is developed resulting in a pair of coupled LMI optimization problems which provide a robustly stable output feedback gain. Model uncertainties are considered via a polytopic set of process models. The methodology is illustrated with the simulation of the control problem of two chemical processes. The results show that the proposed strategy eliminates the need to detune the MP controller improving the performance for most of the cases considered.

A stable model predictive control for integrating processes

Abstract This paper proposes a stable model predictive control for systems with stable and integrating poles. The method presented here extends the method of [Rodrigues, M. A., & Odloak, D. (2003a). An infinite horizon model predictive control for stable and integrating processes. Computers and Chemical Engineering, 27, 1113–1128] to provide nominal stability for a set of process conditions, which is larger than in previous methods. The main effort is to eliminate the conflict between the constraints in the system inputs, which are usually included in the MPC, and the constraints created by zeroing the integrating modes of the system at the end of the control horizon. This problem has hindered the practical application of nominally stable infinite horizon MPC in industry. The improved controller is obtained through a modified control objective that includes additional decision variables to increase the set of feasible solutions to the control problem. The hard constraints associated with the integrating modes are softened and the resulting control problem is feasible to a much larger class of unknown disturbances and set point changes. Two methods are proposed to obtain stability: by imposing the contraction of the norm of the vector of slack variables associated with the integrating modes and by separating the control problem in two sub-problems. The methods are illustrated with the application of the proposed approach to two integrating examples of the literature.