Cascade Control Of A Tubular Chemical Reactor Using Nonlinear Part Of Primary Controller

The paper deals with the cascade control of a tubular chemical reactor. The control is performed in the primary and secondary control-loops. A gain of the primary discrete nonlinear P controller consists of two parts. The first nonlinear part is determined on the basis of simulated or measured steady-state characteristics of the reactor, the second part is selectable. The controller in the secondary control-loop is an adaptive controller. The proposed method is verified by control simulations on a nonlinear model of the reactor with an exothermic reaction. INTRODUCTION The cascade control belongs to useful control methods for many technological processes. It may be applied in such cases when at least two output variables can be measured and only one input variable is available to the control. Principles and examples of the use of cascade control can be found e.g. in (Smuts 2011; King 2010; Seborg et al. 1989). Chemical reactors are typical processes suitable for the use of cascade control. In cases of non-isothermal reactions, concentrations of the reaction products mostly depend on a temperature of the reactant. Further, it is known that while the reactant temperature can be measured almost continuously, concentrations are usually measured in longer time intervals. Then, the application of the cascade control method can lead to good results. In this paper, the procedure for control design of a tubular chemical reactor is presented. Tubular chemical reactors (TCRs) are units frequently used in chemical industry inclusive of manufacturing and processing of polymers and some others. From the system theory point of view, TCRs belong to the class of nonlinear distributed parameter systems. Their mathematical models are described by sets of nonlinear partial differential equations (PDEs). The methods of modelling and simulation of such processes are described e.g. in (Corriou 2004; Ingham et al. 1994). Detailed analysis of the specific TCR is carried out for example in (Dostál et al. 2008). In this paper, the TCR control strategy is based on the fact that a concentration of the main component of the reaction taking place in the reactor depends on the output reactant temperature. Moreover, the procedure assumes that the output reactant temperature is measured continuously. Then, in the cascade controlloop, the concentration of a main product of the reaction is considered as the primary controlled variable, and, the output reactant temperature as the secondary controlled variable. The coolant flow rate represents a common control input. The primary controller determining the set point for the secondary (inner) control-loop is derived as a proportional controller with a nonlinear part obtained from the steady-state characteristics of the reactor and with a selectable part. Since the controlled process is nonlinear, a continuous-time adaptive controller is used as the secondary controller. The procedure for the adaptive control design in the inner control-loop is based on approximation of a nonlinear model of the TCR by a continuous-time external linear model (CT ELM) with recursively estimated parameters. In the process of the parameter estimation, a corresponding delta model is used, see, e.g. (Garnier and Wang 2008; Mukhopadhyay et al. 1992; Stericker and Sinha 1993; Bobál et al. 2005). The resulting CT controller is derived on the basis of the polynomial method, see, e.g. (Kučera 1993; Mikleš and Fikar 2004; Dostál et al. 2007). The control is tested by simulations on nonlinear model of the TCR with a consecutive exothermic reaction. MODEL OF TCR An ideal plug-flow tubular chemical reactor with a simple exothermic consecutive reaction 1 2 k k A B C → → in the liquid phase and with the countercurrent cooling is considered. Heat losses and heat conduction along the metal walls of tubes are assumed to be negligible, but dynamics of the metal walls of tubes are significant. All densities, heat capacities, and heat transfer coefficients are assumed to be constant. Under above assumptions, the reactor model is described by five PDEs in the form 1 A A r A c c v k c t z ∂ ∂ + = − ∂ ∂ (1) 1 2 B B r A B c c v k c k c t z ∂ ∂ + = − ∂ ∂ (2) Proceedings 30th European Conference on Modelling and Simulation ©ECMS Thorsten Claus, Frank Herrmann, Michael Manitz, Oliver Rose (Editors) ISBN: 978-0-9932440-2-5 / ISBN: 978-0-9932440-3-2 (CD)