Ind. Eng. Chem. Res. 1997, 36, 5531-5536
5531
Comparison of Nonlinear Controllers for Distillation Startup and Operation† Chimmiri Venkateswarlu and Kota Gangiah* Process Dynamics and Control Group, Chemical Engineering Sciences, Indian Institute of Chemical Technology, Hyderabad 500 007, India
A control algorithm which has been acclaimed as the best algorithm for startup control and also operation control of a real system may not be the best algorithm for a different real system. Therefore, a nonlinear internal model control (NIMC) strategy supported by an on-line deterministic estimator is presented for startup control and also operation control of a continuous distillation column. The performance of the NIMC strategy is evaluated by comparing with globally linearizing control (GLC) and generic model control (GMC) strategies. The results show that NIMC, GLC, and GMC have exhibited nearly the same performance for startup and operation control of a continuous distillation column. NIMC strategy is recommended for startup and operation control of a continuous distillation column due to easier tuning of one controller parameter and best transition from total reflux to steady-state operation. Introduction Startup of chemical processes especially the continuous distillation is a challenging control problem which involves complex heat- and mass-transfer operations and encounters a wide range of operating conditions during startup period. The commonly used strategy in industry is to switch on to a conventional PI controller to maintain the desired tray temperature. The dynamic behavior of distillation columns during startup has been studied and analyzed by Ruiz et al. (1988) by simulation studies. The highly nonlinear transition from total reflux to specified reflux in the presence of several disturbances is to be effected optimally and conventional controllers are usually less effective. Yasuoka et al. (1987) proposed a semiempirical characteristic function for determining the optimal switching time from total reflux to steady-state operation. The characteristic function is to be calculated using the on-line composition and temperature measurements of the column. The optimal switching time is determined as the time corresponding to the minimum of the characteristic function. This strategy lacks robustness. A model-based controller, viz., the globally linearizing control (GLC) framework, using a nonlinear transformation that transforms a nonlinear input/ output system into a linear input/output system is proposed by Kravaris and Chung (1987). The generic model control (GMC) introduced by Lee and Sullivan (1988) allows the implementation of a nonlinear process model directly into the controller structure. Further, Henson and Seborg (1991) proposed a nonlinear internal model control (NIMC) approach which is different from the GMC of Lee and Sullivan (1988) and Kravaris and Chung (1987). Barolo et al. (1993, 1994) presented a simple model for control of distillation by grouping a number of component dynamic balance equations into one dynamic equation, in which the controlled variable is considered as the inventory of multiple tray temperatures. First, Barolo et al. (1993) applied the GMC-based strategy for startup of a binary distillation column. Further, the * To whom correspondence should be addressed. E-mail:
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GLC-based strategy was applied by Barolo et al. (1994) for startup and operation control of a distillation column. In this study, a nonlinear internal model control (NIMC) based strategy supported by an on-line estimator is presented for startup and operation control of a distillation column. The performance of the proposed strategy is evaluated by applying it to a continuous distillation column separating a methanol-water mixture. Further, comparison of the NIMC-based strategy is made with the GMC-based strategy of Barolo et al. (1993) and also with the GLC-based strategy of Barolo et al. (1994). Control Algorithms Description The general form of a control affine single-input single-output (SISO) system with a state-space description is
x˘ ) f(x) + g(x) u
(1)
y ) h(x)
(2)
where x is a vector of n states, u is the manipulated input, y is the measured output, f(x) and g(x) are vector functions, and h(x) is a scalar function. The relative order r of a system described by eqs 1 and 2 is defined by the following equations:
LgLkf h(x) ) 0;
k
