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Presented in this short document is a description of what is well-known as Advanced Process Control (APC) applied to a small linear three (3) manipulated variable (MV) by two (2) controlled variable (CV) problem. These problems are also known as Model Predictive Control (MPC) (Grimm et. al., 1989) and Moving Horizon Control (MHC). Figure 1 shows the 3 x 2 APC problem configured in our unit-operation-port-state superstructure (UOPSS) (Kelly, 2004, 2005; Zyngier and Kelly, 2012) as an Advanced Planning and Scheduling (APS) problem as opposed to a traditional APC problem.
Although there is a tremendous amount of stability, performance and robustness theory associated with APC which can be directly assumed to APS problems (Mastragostino et. al., 2014), our approach is to show that APC can equally be set into an APS framework except that APS has far less sensitivity technology due to its inherent discrete and nonlinear modeling complexities i.e., especially non-convexities. In order to eliminate the steady-state offset between the actual value and its target, it is well-known to apply bias-updating though other forms of “parameter-feedback” is possible. Typically, APS applications only employ “variable-feedback” i.e., opening or initial inventories, properties, etc. but this alone will not alleviate the steady-state offset as demonstrated by Kelly and Zyngier (2008).