Abstract
A simulation approach for the assessment of variables interaction and consequent control structure selection of a fluid catalytic cracking unit (FCCU) is presented in this paper. The simulator which was implemented in Matlab draws from an earlier mathematical model of the FCCU, was used as a virtual FCCU for studying the dynamic response of the riser temperature (T rx ), the regenerator temperature (T rg ) and the regenerator flue gas oxygen concentration (O d ) to step changes in air flow rate (F a ), regenerated catalyst flow rate (F rc ), gas oil feed rate (F gr ). The results show strong interaction in FCCU variables, with F a affecting T rg and O d ; F rc affecting T rx, T rg and O d ; F gr affecting T rx , T rg and O d . A linearised state-space model based on the first-principle model was deduced and transformed to a 3x3 input-output model. Three channel interaction measures: Relative Gain Array (RGA), Effective Relative Gain Array (ERGA) and the Normalized Relative Gain Array (RNGA) were applied to the selection of FCCU control structure. All the measures point to a diagonal scheme with the following pairings: (T rx /F gr ), (T rg /F a ) and (O d /F rc ) ,for the decentralized control of the riser temperature, the regenerator temperature and the flue gas oxygen concentration respectively. The suggested control structure offers a high promise of stability, with a Niederlinski index (NI) of 101.79. DOI : 10.7176/CTI/8-03
Highlights
Variable interaction refers to a situation in which a change in the numerical value of an input variable of a process produces a proportional or more than proportional change in more than one output variable, in a simulation study
The quantification of interaction was based on steady state gain and critical frequency variations as prescribed elsewhere16An extension of the Effective Relative Gain Array (ERGA) was and proposed tested by Monshizadeh-Naimi et al.[18 ].The interaction measure which is known as Effective Relative Energy Array (EREA) is, according to the authors, an energy-based compromise between steady-state gain and bandwidth of the system under investigation
With MIMO transfer functions that were drawn from the open literature, the method of Salgado and Cornley[13] was adopted in the evaluation of the controllability and observability gramians as well as the participation matrix A two-step variant of the ERGA was presented in Amit and Babu[20] in which the effective gain of the plant was obtained as scalar product of the steady state gain matrix and the bandwidth matrix
Summary
The riser model was reduced to an ordinary differential equation in time using the approximation that is given in equation (9). Where Trx represent the temperature drop over a displacement of L along the riser. The reduced form of equation (1), equation (2) and equation (6) were transformed to obtain the dynamic linearised model of the form given in equation (13). The state transition matrix, A, the input matrix, B and the disturbance matrix, were obtained by partially differentiating the reduced form of equation (1) , along with (2) and (6) with respect to each element in X,U and D respectively. The elements that constitute equation (17) were implemented in the symbolic math toolbox of. The linear state-space model in compact form becomes: dTrx dt dTrg dt dOd
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