Steady-state optimization of chemical processes with guaranteed robust stability and controllability under parametric uncertainty and disturbances

• We discussed the robust stability and controllability in a optimization problem.
• Robust stability guarantees for parametric uncertainty and disturbances.
• Robust controllability guarantees for parametric uncertainty.
• We illustrated the method with three different examples of chemical processes.

A new methodology is proposed for the steady-state optimal design of chemical processes under parametric uncertainty and disturbances. The methodology allows the integration of uniform constraints for robust controllability and stability in an optimization problem by using the Routh–Hurwitz test and zero dynamics based method. The underlying mathematical problem is difficult to solve because it involves infinite stability and controllability constraints. We developed an algorithm where an infinite number of constraints can be implemented as several relaxation problems that are solved iteratively. Additionally, the dynamic simulation results under parametric uncertainty and disturbances are also used to estimate the bound of the state perturbations rather than assumptions based on experience, which may lead to overly conservative or non-implementable design. To illustrate the methodology, three different examples are presented and robustly stable and controllable designs are obtained.