# Operator-Based Adaptive Tracking Capacity Control in Complex Manufacturing Processes
###### Abstract  
Nowadays, quickly changing customer demands are a big challenge in the manufacturing industry, especially for job shops, which are typical coupling and nonlinear multi-input-multi-output (MIMO) systems. In order to achieve good shop floor performance in the presence of short-term demand fluctuations, a key performance indicator--work in process (WIP)--is required to be effectively controlled in the vicinity of the desired levels. For this purpose, a machinery-oriented capacity adjustment approach via a reconfigurable machine tool (RMT) is employed to flexibly balance capacity and load in the case of a bottleneck. A mathematical model concerning the RMT and WIP was first established in the presence of uncertainty and delays. The operator-based robust right coprime factorization (RRCF) method was adopted to stabilize the uncertain system, and adaptive integral separated proportional-integral (ISPI) tracking controllers were further designed to improve the transient and robustness performance. The performance of the proposed ISPI-RRCF was analyzed and compared with that of a state-of-the-art method in a simulation. The results showed that both control systems could ensure that the WIP was within an allowed bound, while the former had lower overshoots, shorter setting times, and more concentrated distributions facing stochastic demands. This further indicated the effectiveness of the proposed algorithm in the avoidance of serious bottlenecks and unbalanced capacity distributions. operator theory; adaptive tracking capacity control; job shop; reconfigurable machine tool +
Footnote †: journal: Applied Sciences  
In [9], a harmonizing throughput-time capacity adjustment approach via an RMT was proposed to improve productivity while maintaining a certain flexibility in complex job shops. In [10], the WIP of workstations was also controlled by utilizing the flexibility of RMTs in the capacity adjustment of complex manufacturing processes. Although RMTs play a vital role in terms of flexibility and reconfigurability, they are only an enabler for capacity adjustment. Therefore, an effective control method for the usage of RMTs is of crucial importance in the context of Industry 4.0 [11]. Due to its simplicity and wide applicability, the proportional-integral-derivative (PID) algorithm has been applied for single-input-single-output (SISO) systems. [PERSON] and [PERSON] first adopted the PI algorithm in the backlog control of a single-workstation production system [12]. They further extended the application to the capacity control of a multi-workstation production system with disturbances [13]. In [14], the development of a PID method was discussed with respect to its incorporation with other advanced algorithms in practical applications, and the challenges in design and tuning for difficult problems, especially for systems with nonlinearities, coupling, disturbances, and delays (e.g., in a job shop), were also put forward. In contrast to the PID, operator-based robust right coprime factorization (RRCF) is an advanced control method for a class of nonlinear systems that can be appropriately decomposed by using operator theory to design robust controllers via Bezout identity [15]. [PERSON] proposed a new condition for the robust controller design of nonlinear systems with unknown bounded disturbances, which extended the application [16]. Improved RRCF algorithms were proposed to deal with delays, disturbances, and couplings [17; 18]. This method was mathematically demonstrated and applied for a variety of fields, such as a highly nonlinear ionic polymer metal composite with hysteresis [19], a multi-joint manipulator [20], and a coupling multi-tank process [21], which was readily applicable for job shop systems for capacity control via RMTs. In previous work, this method was applied in capacity control. However, the performance still needs to be improved, especially for adaptive tracking control.