A nonlinear approach to the design of gain-scheduled controllers

Gain scheduling is a method widely applied in industrial practice to control processes where large changes of the operating conditions can occur. In its standard implementation, this technique requires to compute a family of steady states covering the operating region of interest and then to design a family of linear feedback controllers ensuring stability and desired output behavior about the selected steady states. In this contribution, a novel approach to design gain-scheduled controllers of nonlinear processes is presented. Parametric continuation and optimization techniques are implemented to compute a parameterized family of steady states covering the output range of interest and, at the same time, fulfilling a prescribed set of control requirements. Then, bifurcation analysis is performed to design a family of linear feedback controllers guaranteeing desired output behavior around the selected steady states and preventing the occurrence of state multiplicity. The method is validated on the problem of controlling a continuous exothermic reactor exhibiting state and input multiplicity.