Feedback regularization and control of nonlinear differential‐algebraic‐equation systems

The feedback control of nonlinear high‐index differential‐algebraic‐equation systems for which the underlying algebraic constraints among the system variables involve the manipulated inputs is addressed in this work. A state‐space realization of such systems cannot be derived independently of the controller design. In view of this fact, a two‐step methodology is proposed for the control of such systems. The first step involves the derivation of a dynamic state‐feedback compensator such that in the resulting system, the underlying constraints are independent of the new inputs. In the second step, a state‐space realization of the feedback modified system is derived and used as the basis for a state‐feedback controller synthesis. Application of the developed control methodology is demonstrated on an interconnection of a two‐phase exothermic reactor and a condenser.