Simulation and Robust Control of Continuous Time Circulating Reactor

The aim of presented paper is analysis, mathematical modelling, simulation and control of hydrogenation process. Cyclohexane, as an important base material for polyamide manufacturing, makes by catalytic hydrogenation of benzene. A large number of reaction heat transfers during hydrogenation process. Therefore, benzene and cyclohexane mixture hydrogenation proceed under hydrogen excess. We suppose the hydrogenation mechanism of benzene as a first-order reaction. Matlab-Simulink toolbox was used for robust control simulation with application to the circulating reactor. Robust controllers are obtained via solutions of Diophantine equations in the ring of stable and proper rational functions. Uncertainty and robustness are studied through the infinity norm H∞. For controller design was proposed a scalar parameter m>0 as a tuning knob. INTRODUCTION The behavior of real chemical process is obviously too complex for complete mathematical analysis. We are obliged to use an approximate description which is able to deliver sufficiently accurate results. Cardinal simplifications of the mathematical description can be obtained by the following supposals: the process does not change its properties during the observation period, the relation between input and output variables of the process is linear, all process variables can be measured continuously and have a continuous-time trend. A useful and interesting application of reactor design for chemical engineers can be seen in (Froment and Bischotf 1990), (King and Winterbottom 1998). The treatment of biochemical and polymer reaction engineering is described very extensively in (Nauman 2002). There are emphases on numerical solutions which are needed for most practical problems in chemical reactor design. Sophisticated numerical techniques are rarely necessary. The aim is to make the techniques understandable and easily accessible and allow continued focus on the chemistry and physics of the process. Robust controllers and plant uncertainty became a useful and popular discipline in control theory during the last decade. The necessity of robust control was naturally developed by the situation when the nominal plant (used in control design) differs from the real (perturbed) one. A suitable tool for parameter uncertainty is the infinity norm H∞. Hence, a polynomial description of transfer functions had to be replaced by another one. A convenient description adopted from (Vidyasagar 1995), (Kučera 1993), (Doyle et al 1992) is a factorization approach where transfer functions are expressed as a ratio of two Hurwitz stable and proper rational functions (Rs). Then conditions of robust stability can be easily formulated in algebraic parlance and all controllers are obtained via linear Diophantine equations in an appropriate ring. MODEL DESCRIPTION Benzene and cyclohexane mixture hydrogenation proceed in continuous time circulating reactor under hydrogen excess. The presented mathematical model should respect the following conditions: Reaction mixture is perfectly mixed by circulation. The volume of reaction mixture is constant. All technological parameters in reactor are constant. Heat transfer on the both sides of wall is ideal. The hydrogenation mechanism of benzene is supposed to be a first-order reaction: