Stabilization of an unstable tubular reactor by nonlinear passive output feedback control

Abstract

The multiple–input multiple–output (MIMO) output feedback (OF) control problem of an exothermic multi-jacket tubular open-loop unstable reactor is addressed. Over its axial length, the reactor has several equally sized cooling jackets. The controller must adjust the jacket temperatures on the basis of per jacket temperature measurements so that the closed-loop system is robustly stable. The problem is solved within a constructive framework, by combining notions and tools from chemical reactor engineering and partial differential equations (PDEs) control systems theory. The result is a MIMO nonlinear OF dynamic control design with (i) a decentralized MIMO passive state feedback (SF) controller implemented with a pointwise observer (PWO), (ii) closed-loop stability conditions in terms of sensor set and control gains, and (iii) efficient late lumping-based on-line implementation. The design is put in perspective with industrial PI and inventory control, and applied to a representative example through numerical simulation with favorable comparison against adaptive controllers.