SIMULATION OF ROBUST STABILIZATION OF A CHEMICAL REACTOR Monika Bakoˇ sov´ a, Anna Vasiˇ ckaninov´ a Slovak University of Technology in Bratislava Faculty of Chemical and Food Technology Radlinsk´ eho 9, 812 37 Bratislava, Slovakia Email: {monika.bakosova, anna.vasickaninova}@stuba.sk KEYWORDS CSTR, multiple steady states, stabilization, static output feedback, PID controller. ABSTRACT The paper presents simulation experiments on the con- tinuous stirred tank reactor for hydrolysis of propylene oxide to propylene glycol. The reactor is exothermic one. There are two parameters with only approximately known values in the reactor. These parameters are the reaction rate constant and the reaction enthalpy. The simplified mathematical model of the reactor consists of four nonlinear ordinary differential equations. The steady state analysis shows the reactor has multiple steady states and the open-loop analysis confirms that the reactor is open-loop unstable around one of these steady states. Then the possibility to stabilize the reactor using static output feedback PI and PID controllers is studied. Because of the presence of uncertainty in the continuous stirred tank reactor, the robust static output feedback is designed. Simulations are used for testing the stabilizability of the reactor around its open-loop unstable steady state. INTRODUCTION Continuous stirred tank reactors (CSTRs) are often used plants in chemical industry and especially exothermic CSTRs are very interesting systems from the control viewpoint because of their potential safety problems and the possibility of exotic behaviour such as multiple steady states, see e.g. (Moln´ ar et al., 2002), (Pedersen and Jørgensen, 1999). Furthermore, operation of chemi- cal reactors is corrupted by many different uncertainties. Some of them arise from varying or not exactly known parameters, as e.g. reaction rate constants, reaction en- thalpies and heat transfer coefficients (Antonelli and As- tolfi, 2003). The other control problems are due to the high sensitivity of the state and output variables to in- put changes and process nonlinearites (Alvarez-Ramirez and Femat, 1999). Operating points of reactors change in other cases. In addition, the dynamic characteristics may exhibit a varying sign of the gain in various oper- ating points. All these problems can cause poor perfor- mance or even instability of closed-loop control systems. Conventional control strategies, which are often used for reactor control design, can fail for such complicated sys- tems and their effective control requires application some of advanced methods, as e. g. adaptive control (Vo- jtesek and Dostal, 2008), predictive control (Figueroa et al., 2007), robust control (Alvarez-Ramirez and Femat, 1999), (Gerhard et al., 2004), (Bakoˇ sov´ a et al., 2005), (Tlacuahuac et al., 2005) and others. Robust control has grown as one of the most important areas in modern control design since works by (Doyle and Stein, 1981), (Zames and Francis, 1983) and many others. One of the solved problems is also the prob- lem of robust static output feedback control (RSOFC), which has been till now an important open question in control engineering, see e.g. (Syrmos et al., 1997), (An- tonelli and Astolfi, 2003). Recently, it has been shown that an extremely wide array of robust controller design problems can be reduced to the linear matrix inequalities (LMIs) problem. Especially, the LMIs in semi-definite programming attract a big interest because of their ability to describe non-trivial control design problems integrat- ing various specifications such as robustness, structural and performance constraints, as well as their suitability for efficient numerical processing through various avail- able solvers, see e.g. (Boyd et al., 1994) and references therein. From the system theory viewpoint, CSTRs belong to a class of nonlinear lumped parameter systems. Their mathematical models are described by sets of nonlinear ordinary differential equations (ODEs). The methods of modelling and simulation of such processes are described e. g. in (Ingham et al., 1994). The models are often used for a preliminary analysis of the steady-state, open-loop and closed-loop behaviour of chemical reactors. The paper presents simulation experiments with the CSTR for hydrolysis of propylene oxide to propylene glycol. The reactor is exothermic one. There are two parameters with only approximately known values in the reactor. The steady state analysis shows that the reac- tor has multiple steady states and the open-loop analy- sis confirms that the reactor is open-loop unstable around one of these steady states. Then the possibility to stabi- lize the reactor using robust static output feedback PI and PID controllers is studied by simulations. Proceedings 23rd European Conference on Modelling and Simulation ©ECMS Javier Otamendi, Andrzej Bargiela, José Luis Montes, Luis Miguel Doncel Pedrera (Editors) ISBN: 978-0-9553018-8-9 / ISBN: 978-0-9553018-9-6 (CD)