Multivariable nonlinear and adaptive control of a distillation column

Abstract

In chemical process control, the processes typically exhibit nonlinear behavior. In spite of this, linear feedback laws often perform quite well as long as the process is being controlled at a fixed operating point. Linear controller designs based on linearized process models are therefore commonly used. The nonlinear process dynamics can be taken into account implicitly by treating them as part of the model uncertainties.If the nonlinearity of the process is too severe for a (single) linear control law to perform satisfactorily, one possibility is to describe the process by a set of different linear models, each valid at a given operating point. One can then derive a different linear feedback law for each operating point and use the feedback law corresponding to the prevailing operating point (Shamma and Athans, 1991). A potential difficulty with this approach is to decide which model and feedback law to use between the given set of operating points. Another possibility is to describe the process by a nonlinear model valid over the whole operating range of interest. The main difficulty with this approach is to find a suitable nonlinear model. Models derived from physical principles are in general much too complex for controller design, and therefore simpler models that capture the nonlinearities are required. If a nonlinear model is available, one can design a nonlinear controller based on this model for the whole operating range (Slotine and Li, 1991). However, it is also possible to use a linear controller whose parameters are updated at each sampling instant on the basis of a linearized form of the nonlinear model.For processes with poorly known or slowly time-varying dynamics, adfptive and self-tuning control are widely accepted approaches ( Astrom and Wittenmark, 1989). When applying adaptive control to nonlinear processes, care should be taken to handle the nonlinearities properly. Adaptive controllers are usually based on linear process models and linear design methods. Although adaptive controllers have the property of adapting their behavior to changing process properties, it is, however, somewhat unsatisfactory to not consider the fact that the process is nonlinear, and to let the adaptive controller retune itself (and the parameters of the linear model) whenever the operating point is changed. As above, possible remedies (including the same problems and difficulties) are to let the algorithm employ several linear process models, each valid at a given operating point, or a nonlinear process model valid over the whole operating range.In this article, multivariable nonlinear and adaptive control is applied to a binary distillation column (Waller et al., 1988). Previous investigations (Waller et al., 1988;Sandelin et al. 1991;Haggblom, 1993) have shown that the process has nonlinear dynamics. Although linear controllers can be used to control the process at any given operating point, it is difficult to control the process satisfactorily over the whole operating range of interest using a fixed linear co...

Realizability of bilinear input/output difference equations: corrections and extensions

“…(1) Such systems with multiplicative controls are common in engineering design and are also used as models of natural phenomena with variable growth rates, see Elliott (2009), Mohler (1991). Furthermore, bilinear structure is often assumed in system identification as a simple approximation of nonlinear dynamics, see for example Strömberg et al (1995), Yu (2000), Dunoyer et al (1996). Unfortunately, the majority of nonlinear i/o equations, including those of bilinear equations, cannot be presented by state equations.…”