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Internal thermally coupled distillation column (ITCDIC) is a frontier in the energy saving distillation research. It is well known for the complex dynamics, which challenge the establishment of an excellent reduced model for further control strategy design greatly. In this article, a physical approach of the ITCDIC process based on nonlinear wave theory is explored, where it is first discovered that traditional wave theory in conventional distillation columns (CDIC) could not be directly applied in ITCDIC, due to: First, the internal thermal coupling results in mole flow rates varying evidently over each stage, which not only makes the wave modeling of the wave phenomenon in ITCDIC more difficult but also makes wave dynamics greatly different between ITCDIC and CDIC; Second, an interesting wave phenomenon of ITCDIC is discovered that waves located in the rectifying section and stripping section travel under opposite tendencies when the steady state is disturbed by the step change of thermal condition q, one sharpens and the other is likely to spread synchronously, it means the movement of wave profiles in ITCDIC could not be simply described by shock wave velocity, which is usually used in wave modeling of CDIC; more seriously, shapes of the self-sharpening wave profiles in ITCDIC change obviously during the traveling processes, which further reveals that shape influence on wave velocity has to be considered in the wave modeling of ITCDIC. A rigorous wave velocity and a natural wave velocity are derived, respectively, based on which, the detailed analyses of traveling wave characteristics are carried out. A novel wave velocity, based on the profile trial function which has been well developed by Marquardt, is further derived to consider the obvious change of profile shape. And a completed nonlinear wave model of ITCDIC is thereby established by combining the proposed wave velocity with thermal coupling relations and material balance relations. The benzene-toluene system is illustrated as an example, where component concentration prediction and distinct dynamic characteristics are carried out in detail based on the proposed nonlinear wave models. The research results reveal the accuracy and validity of the proposed nonlinear wave model of ITCDIC.

A new model-based control strategy for the internal thermally coupled distillation column (ITCDIC) is presented. Based on the nonlinear wave theory that describes the nonlinear dynamics in the separation processes, a simplified nonlinear wave model is established that concerns both the wave propagation and the profile shape. An advanced controller (WGGMC) is formulated by combining the nonlinear wave model with a generalized generic model control (GGMC). Compared with a conventional generic model controller based on a data-driven model (TGMC), and another wavemodel based generic model controller (WGMC) developed in our previous work, WGGMC exhibits the best performances in both servo control and regulatory control. Furthermore, WGGMC can handle a very-high-purity system of ITC-DIC with top product composition of 0.99999, while the other two controllers fail to work.

Although the internal thermally coupled distillation column (ITCDIC) is much more energy-efficient than the conventional distillation column, the complex dynamics stemming from thermal coupling between the rectifying column and the stripping column have restrained the achievement of control strategies and application in chemical industry. To reduce the difficulties, a novel nonlinear wave model of ITCDIC process is proposed based on the wave theory in the separation processes to simplify the mechanism model of ITCDIC. A nonlinear model predictive control based on the proposed wave model (NWMPC) of the ITCDIC process is further established to handle the multivariable interactions and improve the control performance. A dynamic optimization scheme characterized by an improved control parametrization method is introduced to solve the problem generated by the NWMPC model. An IMC controller is also explored as a comparison research. In the example of a benzene–toluene system, NWMPC presents great advantage over IMC in the servo and regulatory control.