System poles and zeros sensitivity for dynamic process controllability

A new approach for the calculation of the sensitivity of the system dynamics as described by system poles and transmission zeros with respect to variations in operating conditions, system design changes and exogenous disturbances is presented. System poles are retrieved from the eigenvalues of the linearized state space representation of the nonlinear process model. Transmission zeros are obtained from the generalized eigenvalues of the input-output state space representation. The set of poles and transmission zeros as well as the steady state response of the process system are path-followed for multiple variations in model parameters and operating conditions within an optimal disturbance rejection framework. A predictor-corrector continuation technique is employed for the solution of the parameterized nonlinear set of optimality conditions for the disturbance rejection problem that further enables the identification of active set changes and feasible region limits. The sensitivity of the system dynamics acts as the guideline for the screening of process designs and control structures that exhibit unfavorable sensitivity in the dynamic characteristics and impose limits in the achievable performance of the control system.