The ISOPE approach only outperforms the conventional Two-Phase approach in this case study, when very long-term steady-state behaviour is the chief consideration.
There was a significant difference in the Extended Design Cost for the LAOO and ISOPE approaches, yet little difference between theses two methods in terms of their manipulated variable trajectories (cf.
ISOPE proved faster than the LAOO approach, due to the formers use of a more structurally accurate model; however, the ISOPE approach exhibits longer term oscillations, which are associated with the plant perturbation scheme used by the method.
In the Two-Phase and Roberts' ISOPE approaches the inequality constraints form a natural part of the model-based optimization problem.
In both the ISOPE and LAOO approaches, the reduced gradient is matched.
The ISOPE approach uses steady-state plant experiments.
It can be conclude that: (1) the Two-Phase approach assumes that the plant/model mismatch exists in a form that does not affect the reduced gradient of the optimization problem, as this method has no means to compensate for such a mismatch; (2) the LAOO approach of McFarlane and Bacon (1989) attempts to directly determine the reduced gradient of the plant profit surface through plant experiments; and (3) the ISOPE and QAOO approaches assume specific and different structural forms for the plant/model mismatch in the reduced space and estimate the mismatch using plant experiments.
The parameter estimation problem defined in Equation (4) remains unchanged in ISOPE approach.
The RTO cycle for the ISOPE approach is as in the conventional Two-Phase approach, but has two additional steps that are completed prior to the optimization phase: (1) perturbation step--perturb each independent manipulated variable individually around the current operating point to get derivative matrix [[nabla].
In the ISOPE approach the Karush-Kuhn-Tucker optimality conditions are used to form an augmentation term, which is introduced into the objective function of Equation (5) to compensate for plant/model mismatch: