## 2 Related Work
### Approaches to Improve the Interaction of Supply Network and Production Planning and Control
#### 2.2.2 Closed-Loop Control  
Closed-loop control, also referred to as feedback control, is a process in which the controlled variable \(x\) is continuously or sequentially measured, compared to the reference variable \(w\) and influenced by the manipulated variable \(y\) to adapt it to the reference variable [38; 39]. One or several disturbance variables \(z\) can also be implemented. The objective of the controlling element is, within the controlled system, even with the occurrence of disturbances, to adapt the controlled variable to the reference variable. A characteristic of closed-loop control is the closed-loop action sequence with continuous self-influencing of the controlled variable in the action path of the control loop [39]. A distinction can be made between continuous feedback control and sampling control as well as between non-adaptive and adaptive control [39].  
Adaptive control is necessary to couple systems directly and to adapt models to changing conditions. Therefore, the principle of closed-loop control has been successfully used for many years in manufacturing processes and has also received a great deal of attention in PPC [9; 40; 41]. Here, the principle of the control loop is transferred to elements of the PPC to achieve a continuous adaptation of manufacturing (cf. Figure 2).  
An overview and classification of existing approaches for control loops in PPC is given by [PERSON] et al. [42]. This classification is supplemented by an industry standard concept for model-based process control [40]. Table 1 shows a characteristic concept for each category.  
According to [42], categories one to three are closely related by the manufacturing system's load as their controlled variable. The load can be determined by controlling order releases and, therefore, the inventory (1), or by capacity adjustments (2), or by a more complex setup of multiple controlled and manipulated variables (3). Since categories four and five build on a terminated production plan, their control activities are only performed in case of deviations. The controller type can be distinguished between rescheduling the entire production plan (4) and knowledge-based and predefined procedures to react in  
\begin{table}
\begin{tabular}{l l} \hline
**Category According to [42]** & **Characteristic Representative** \\ \hline (1) Control of Inventory & [PERSON] [44] \\ (2) Control of Capacity & [PERSON] [45] \\ (3) Control of Load & [PERSON] et al. [46] \\ (4) Control by Rescheduling & [PERSON] [47] \\ (5) Knowledge-based Control & [PERSON] et al. [48] \\ (6) Model-based Control & [PERSON] et al. [49] \\ \hline \end{tabular}
\end{table}
Table 1: Classification of control loops in manufacturing (adapted from [43]).  
Figure 2: Transferring the principle of closed-loop control to manufacturing (adapted from [41]).  
the current manufacturing situation (5). The categories are complemented by an approach from discrete, model-based process control (6).  
These concepts focus primarily on the internal optimization of manufacturing and not on the integration with the supply network. Company-external events from the supply network are consequently not considered. The concepts are also designed adaptively for known parameters only and not as learning systems. The degree of automation is mainly less and only a few concepts intensively consider multi-dimensional parameters as manipulated variables [43].