Simulation Of Cascade Control Of A Continuous Stirred Tank Reactor

The paper presents simulation results of the cascade control of a continuous stirred tank reactor. The control is performed in primary and secondary control-loops where the primary controlled output of the reactor is the concentration of a desired reaction product, and, the secondary output is the reactant temperature. A common control input is the coolant flow rate. The controller in the primary control-loop is a P-controller with the gain calculated using simulated or measured steady-state characteristics of the reactor. The controller in the secondary control-loop is an adaptive controller. The proposed method is verified by control simulations INTRODUCTION The cascade control method allows the control of processes with a main and secondary controlled variable and with a single control input. The method is especially useful when a main controlled output can be measured only in longer time intervals and with an additional output measurable in shorter time periods. Principles of the cascade control are described e.g. in (Bequette 2006; Mahoney et al. 2006; Seborg et al. 1989; Smuts 2011). Chemical reactors are typical processes suitable for a use of the 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 cascade control description of a continuous stirred tank reactor (CSTR) with results of control simulations is presented. CSTRS are apparatus widely used in chemical industry, biotechnologies, polymer manufacturing, and many others. From the system theory point of view, CSTRs belong to a class of nonlinear systems with mathematical models described by sets of nonlinear differential equations as it can be seen e.g. in (Smith 2005; Corriou 2004). Here, in the cascade control-loop, the concentration of a desired product of reactions is considered as the primary controlled variable, and, the reactant temperature as the secondary controlled variable. The coolant flow rate represents a common control input. The primary control variable is measured in discrete time intervals. The primary controller determining the set point for the secondary (inner) control-loop is a discrete nonlinear proportional controller derived on the basis of steady-state characteristics of the reactor. 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 the nonlinear model of the CSTR by a continuous-time external linear model (CT ELM) with recursively estimated parameters. In the process of parameter estimation, the direct method by (Rao and Unbehauen 2006); Garnier and Wang 2008) is used. The control loop with two feedback adaptive controllers is used, see, e.g. (Dostál et al. 2007). The resulting controllers are derived by the pole placement method, see, e.g. (Grimble 1993; Kučera 1993; Brogan 1991; Franklin et al. 2006). The cascade control is verified by simulations on the nonlinear model of the CSTR. NONLINEAR MODEL OF THE CSTR Consider a CSTR with exothermic reactions according to the scheme 1 k A B → , 2 2 k B C → and with a perfectly mixed cooling jacket. The desired product is the component B. Using usual simplifications, the model of the CSTR is described by four nonlinear differential equations ( ) A r A A f A r d c q r c c dt V = + − (1) ( ) B r B B f B r d c q r c c dt V = + − (2) ( ) ( ) ( ) ( ) h r r r r f r c r p r r r p r A U dT h q T T T T dt c V V c = + − + − ρ ρ (3) ( ) ( ) ( ) c c h cf c r c c c p c dT q A U T T T T dt V V c = − + − ρ (4) where 2 1 1 2 2 A B r k c r k c = = (5) Proceedings 29th European Conference on Modelling and Simulation ©ECMS Valeri M. Mladenov, Petia Georgieva, Grisha Spasov, Galidiya Petrova (Editors) ISBN: 978-0-9932440-0-1 / ISBN: 978-0-9932440-1-8 (CD) and, with in (0) s r r T T = an for concentra for densities volumetric fl exchange su coefficient. S mixture, c superscript s The reaction as where k0 are energies and parameters, i given in Tabl Tab Vr = 1.7 m Vc = 0.64 m ρr = 985 kg m ρc = 998 kg m k10 = 5.616 . k20 = 1.128 . h1 = 4.8 . 10 s Af c = 2.85 k s rf T = 323 K