Robust stabilization of an exothermic CSTR
Systematic methods and tools for managing the complexity
Process Control (T4-8P)
Keywords: chemical reactor, multiple steady states, uncertainty, robust control, static output feedback, LMI
Exothermic reactions are very interesting systems because of their potential safety problems and the possibility of exotic behavior such as multiple steady states. Furthermore, operation of chemical reactors is corrupted by many different uncertainties, which arise from varying or only approximately known parameters. In other cases operating points change. Various types of perturbations also affect chemical reactors. Application of robust control approach can be one of the possibilities how to overcome all these problems influencing controller design for chemical reactors.
The paper presents the possibility to stabilize a continuous-time stirred tank reactor (CSTR) with the exothermic reaction - hydrolysis of propylene oxide to tri-propylene glycol - in an unstable steady state using robust static output feedback control (RSOFC). The CSTR is an uncertain system because of only approximately known parameters, which are reaction rate constant and heat of reaction. Robust controller design uses a linearized model of the CSTR and we suppose that the controlled system is a linear time-invariant polytopic system. Necessary and sufficient conditions for stabilization via static output feedback are given for this system. The problem of RSOFC design is reduced in solution of two matrix inequalities, which are further transformed in two linear matrix inequalities (LMIs) by using the Schur complement formula. These LMIs must be solved for every vertex of a polytopic system. So, we have two sets of LMIs and the stabilizing robust controller can be obtained via non-iterative solution of all LMIs. If the solution of the first set of LMIs is feasible, the polytopic system is simultaneously stabilizable. If the solution of the second set of LMIs is feasible, then the uncertain system is quadratic stable with a guaranteed cost. The design procedure guarantees with sufficient conditions the robust quadratic stability and guaranteed cost.
The designed robust controller is compared with an optimal LQR controller. Simulation results demonstrate the possibility to use robust static output feedback controller for stabilization of an exothermic CSTR with uncertainties in an unstable steady state. They also enable a comparison of the designed robust controller with an optimal LQR controller.
See the full pdf manuscript of the abstract.
Presented Tuesday 18, 13:30 to 15:00, in session Process Control (T4-8P).
