Formal Methods in Manufacturing

12.3 IMPLEMENTATION ASPECTS AND PERFORMANCE ANALYSIS

In this section, we explore the performance of the MPL system in closed loop with an MPC controller. More specifically, we focus on implementation, stability, feasibility and timing aspects and derive some tuning rules. Consider the standard MPC problem (12.20) through (12.24) for MPL systems (12.8) and (12.9) with

$J_{\text{out}}(k)={\displaystyle \sum _{j=0}^{N_{\text{p}}-1}{\displaystyle \sum _{i=1}^{n_y}\max ({\text{y}}_i(k+j|k)-{\text{r}}_i(k+j),0)={\displaystyle \sum _{i=1}^{n_y{N}_{\text{p}}}\max ({\tilde{\text{y}}}_i(k)-}}}{\tilde{\text{r}}}_i(k),0)$

(12.30)

$J_{\text{in}}(k)={\displaystyle \sum _{j=0}^{N_{\text{p}}-1}{\displaystyle \sum _{i=1}^{n_u}({\text{r}}_i(k+j)-{\text{u}}_i(k+j))={\displaystyle \sum _{i=1}^{n_u{N}_{\text{p}}}({\tilde{\text{r}}}_i(k)-}}}{\tilde{\text{u}}}_i(k))$

(12.31)

For a manufacturing system, cost functions (12.30) and (12.31) correspond to a scheme in which a raw material is fed to the system as late as possible (just-in-time control). Note that this implies that the internal ...