Input constrained funnel control with applications to chemical reactor models

Error feedback control (in the presence of input constraints) is considered for a class of exothermic chemical reactor models. The primary control objective is regulation of a setpoint temperature T^* with prescribed accuracy: given λ>0 (arbitrarily small), ensure that, for every admissible system and reference setpoint, the regulation error e=T-T^* is ultimately smaller than λ (that is, ||e(t)||<λ for all t sufficiently large). The second objective is guaranteed transient performance: the evolution of the regulation error should be contained in a prescribed performance funnel F around the setpoint temperature T^*. A simple error feedback control with input constraints of the form u(t)=sat_[ū,ū](-k(t)[T(t)-T ^*]+u^*), u^* an offset, is introduced which achieves the objective in the presence of disturbances corrupting the measurement. The gain k(t) is a function of the error e(t)=T(t)-T^* and its distance to the funnel boundary. The input constraints ū,ū have to satisfy certain feasibility assumptions in terms of the model data and the operating point T ^*.