Passivity-based multivariable control for the stabilization of continuous styrene polymerization reactor / Nguyen Thanh Sang - Nguyen, Thanh Sang (2017)
Chemical process systems, and among them free-radical polymerization (FRP) systems, belong to complex nonlinear dynamical systems and usually exhibit highly nonlinear characteristics owing to the reaction kinetics and the constitutive equations caused by transport phenomena, heat and mass transfer. Consequently, this may make the process operated under multiple steady states behavior and therefore fairly difficult to operate and stabilize the systems at the middle steady state with acceptable quality and process performance. In this context, this work proposes an advanced nonlinear control strategy based on the passivity theory and passivity-based control (PBC) (also, briefly speaking, passivity-based approach (PBA)) for the stabilization of a class of FRP processes taking place in a continuous stirred tank reactor (CSTR) at a desired set-point (including openloop- unstable steady state). More precisely, it is worth noting that the PBA has been recognized as a useful and systematic tool for nonlinear control design due to its potential applications for the stabilization of mechanical and electromechanical systems. Recently, the PBA has been extended and utilized to stabilize a process system. Due to the ubiquity of process systems in biochemical, biotechnology and materials processing industries, an extensive attention has been paid and remains to this kind of systems for the purpose of control design. As a contribution to this active research area, in this work, we adopt the PBA to stabilize FRP systems subject to multiple steady states behavior at a desired equilibrium point (including open-loop-unstable steady state). The polystyrene production process in CSTR is used as an case study to illustrate the theoretical developments in this work. Essentially, the present work has four main sections as follows. Firstly, the theoretical development of PBA established by the basis of feedback passivation is extended to stabilize exponentially a class of general MIMO nonlinear systems. Secondly, before applying this control design method for the polystyrene production process in a CSTR iii which is considered as a case study, the dynamical behaviors of this system are analyzed by using two different approaches where the first one is built by the tools of system theory and the second one is associated with principle of heat balance to determine the desired set-point. Thirdly, once the control problem of the nonlinear chemical process is stated, the PBC is applied to design the feedback laws for the exponential stabilization of the polymerization process at the desired equilibrium point. Finally, the numerical simulations show the effectiveness of this control design method as well as evaluate the effects of the uncertain operating and physical parameters caused by noise and/or disturbance in order to test the robustness of closed-loop system. Additionally, the control performance of closed-loop system under control of the proposed feedback laws is also compared with that under control of a proportional-integral (PI) control in terms of the merit scores of errors including ISE, IAE and ITAE.