Distributed Nonlinear Control of a Plug-flow Reactor Under Saturation

This paper deals with the saturated control problem of a class of distributed systems which can be modelled by first-order hyperbolic partial differential equations (PDE). The objective is designing a distributed-parameter state feedback with guaranteed performance for this class of systems, using the Lyapunov stability theory and polynomial sum-of-squares (SOS) programming. For this, a polynomial parameter varying (PPV) model is employed to exactly represent the nonlinear PDE system in a local region of the state space and then, based on it, a PPV state-feedback law is designed guaranteeing exponential stability and actuator saturation in such region. The approach is illustrated here through the standard example of a nonisothermal plug-flow reactor.