On the tuning of predictive controllers: Impact of disturbances, constraints, and feedback structure

Abstract

The impact of problem formulation modifications on predictive controller tuning is investigated. First, the proposed tuning method is shown to adapt to disturbance characteristic changes and thus, takes full economic advantage of the scenario. The second topic concerns point-wise-in-time constraints and the impact of constraint infeasibility. Specifically, we shift the tuning question from selection of nonintuitive weighting matrix parameters to that of a few key parameters and results in a rather intuitive trade-off between expected profit and expected constraint violations. Finally, we show that simple modifications will allow for the consideration of various feedback structures, including computational delay and partial state information. The overall conclusions of the work are that the results of the automated algorithm will help build an intuitive understating of the dynamics of the process and ultimately result in a higher level trade-off between profit and constraint observance.

On the tuning of predictive controllers: Application of generalized Benders decomposition to the ELOC problem

“…Branch and Bound 7 12.17 -GBD (non-convex L * ) 4 5.64 53.7% GBD (convex L * ) 3 2.99 75.4% function are given as linearizations of g, f and h around the OSSOP, as was done in Omell and Chmielewski (2014). Using the branchand-bound approach (which requires the above linearizations), the solution required 5879 iterations and a runtime of 46,459 s. Using the convexified GBD algorithm, only 12 iterations and 23 s were required.…”

“…Consider the two CSTR process of Fig. 5 (see Omell and Chmielewski, 2014 for the process model details and parameters). The dynamic model of this process contains 6 states, 2 manipulated variables, 5 disturbances and 8 constrained outputs.…”

“…In the third installment, (Omell and Chmielewski, 2014) the practical aspects of implementing the constrained ELOC policy on http://dx.doi.org/10.1016/j.compchemeng.2015.06.004 0098-1354/© 2015 Elsevier Ltd. All rights reserved. a chemical process are illustrated.…”

“…In the first installment (Chmielewski and Manthanwar, 2004) of this series on the tuning of predictive controllers, (Chmielewski and Manthanwar, 2004;Omell and Chmielewski, 2014) it was shown that the linear feedback generated by the minimum variance covariance constrained control (MVC 3 ) problem is guaranteed to be in the family of Linear Quadratic Regulator (LQR) feedback policies. In addition, using the inverse optimality results of Chmielewski and Manthanwar (2004), one could generate quadratic objective function weights such that if used within the LQR problem, the resulting controller would be identical to the MVC 3 policy.…”

Control structure selection based on economics: Generalization of the back‐off methodology

“…A large number of alternative methodologies for the solution of the problem of selecting regulatory structures have also been developed. [9][10][11][12][13][14][15][16] The back-off methodology is based on the assumption that the optimal steady state operating point is defined by the intersection of active constraints. This is a well established fact that is critical to the design of successful control systems.…”