S UTTE RWORTH I N E M A N N Z Proc. Cont. Vol. 5, No 1, pp. 29-39, 1995 Copyright © 1995 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0959-1524/95 $10.00 + 0.00 Constrained multivariable control of fluid catalytic cracking converters Lincoln F. Lautenschlager Moro* and Darci Odloak t *PETROBRAS, Refinaria de S~o Jose dos Campos, Brazil tEscola Polt#cnica da Universidade de S~o Paulo, Brazil Received 4 January 1993; revised 1 May 1994 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 refer- ence 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 incor- porates 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 formu- lation, to perform steady-state economic optimizations. The calculated variables of the LP are the set- points 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 poten- tial for the application to the real system. Keywords: multivariable control; fluid catalytic cracking converters; DMC algorithm The control of the FCC unit has become one of the challenging problems in process control 1. Even for experienced designers, the development of any sophisti- cated control structure demands a simulation environ- ment tbr tests and pre-tuning of the control algorithm. Usually the development of rigorous nonlinear models is very time consuming and a linear version of the process model is used in the simulation studies. The simulation tool is also useful for the adequacy study of the controller to a non-standard system (for instance an FCC reactor with two or more risers with different feed stockst. For the FCC converter, several dynamic models are presented in the literature I 3. Although the engineer- ing principles of all FCC models are the same, the dynamic effects vary depending on the geometric config- uration of the system. Here we study the dynamics and control of the Kellogg Orthoflow model F reactor/regenerator system. It is not our purpose to describe the complex kinetics of the cracking reactions 4, or the intricate hydrodynamics of the fluidized regener- ator beds. The scope is to include in the model only enough detail to capture the control relevant dynamics, without sacrificing import aspects such as the descrip- tion of non-linearities and interactions. The FCC unit is a typical example of a constrained multivariable process, where various predictive con- trollers have been commercially applied with reported excellent results 57. In the majority of the practical cases, the most profitable operation point lies on the intercep- tion of several FCC constraints. The predictive controllers are capable of including constraints in the formulation of the control law. In the DMC approach 8, constraints can be added to the predicted error equa- tions. The controller calculates the manipulated vari- ables that minimize the errors in a least squares sense. Only equality constraints can be attended to with this strategy. The controller iteratively identifies the active constraints and includes their respective equations in the problem formulation. In the QDMC approach 9,1°, the control problem is formulated as a quadratic programming problem. The cost function is the square of the distance from the predicted to the reference trajectories. Constraints on the controlled and manipu- lated variables can be explicitly included and rigorously attended. In the L D M C 1~, a linear programming problem minimizes the absolute value of the distance between the reference and the predicted trajectories. Constraints can also be explicity considered. The inclusion of constraints in the controller formu- lation can be computer time consuming, particularly for systems of considerable complexity, such as the FCC unit. Another common feature of the predictive controllers concerns the economic optimization that is usually assumed to be performed by an external algo- rithm, probably using average steady-state information. The economic objective of the FCC unit can frequently be translated into very simple operational objectives, as for example, maximum feed flowrate with acceptable 29