# Change Control Design in Product Supply Chain System Based on Radial Basis Function Neural Network
## 4 Simulation Analysis
The solid line represents the production and control signals of the plant providing raw material \(x_{1}(t)\), and the dashed line represents the signals of the plant providing the final product \(x_{2}(t)\). It is evident that, due to disturbances, inventory fluctuations are more pronounced, the time required to stabilize is longer, and there is a relatively higher degree of overshooting compared to the LQR and RBFNN control methods discussed in this paper. In addition to the classical PID control method in the control of product supply chain systems, sliding mode control is also widely used due to its strong anti-disturbance ability and robustness to uncertainty [33]. Therefore, in this experiment, we took sliding mode control as one of the comparison methods. In the experimental design, we still considered the dynamic characteristics of the system under the influence of the bullwhip effect. In the case that inappropriate inventory management and production scheduling trigger state fluctuations, sliding mode control tries to achieve stable control of a system and mitigate the influence of the bullwhip effect by designing a sliding mode surface and the corresponding control law. Figure 5:0 Production controlsignals for two product plants. In Figure 15, when the system is operating normally and is affected by external perturbations and the bullwhip effect, although sliding mode control achieves a fast response by switching control strategies, its response speed is unstable. High-frequency switching can cause discontinuities in the controller output, triggering inventory fluctuations and adversely affecting production control stability. This is particularly unfavorable for semiconductor production because the discontinuity in control output caused by sliding mode control can further aggravate inventory fluctuations, which can lead to the under- or over-supply of raw materials or semi-finished products, directly affecting the rhythmic balance of the production line. At the same time, the unstable supply of raw materials may make part of the equipment work in a non-ideal state, leading to a decline in processing  
Figure 5:1 Production control signals for two product plants. Figure 5:2 Inventory of two plant systems under PID control. accuracy, which in turn reduces product yield, extends the production cycle, and even affects the timeliness of delivery. Therefore, the high-frequency-switching characteristics of sliding mode control can significantly impact the stability and efficiency of semiconductor production systems. Although sliding mode control can effectively suppress the bullwhip effect and stabilize the system quickly, its high-frequency switching is prone to chattering. Chattering can cause additional losses and have adverse effects on system performance. Moreover, large fluctuations during stabilization can affect the balanced allocation of internal resources and degrade system performance. Finally, we compared the performance of different control methods and quantitatively analyzed the system inventories using Tables 1 and 2. As shown in the results, the LQR-RBF method consistently outperforms the other methods in key performance metrics. For both system inventories, LQR-RBF achieves the shortest settling time, significantly surpassing PID control and sliding mode control. Moreover, LQR-RBF results in the lowest overshoot, further demonstrating its superior performance in controlling system dynamics. The mean squared error (MSE) also confirms the effectiveness of LQR-RBF. Meanwhile, sliding mode control affects inventory accuracy due to the chattering phenomenon, leading to large fluctuations in inventory, which in turn triggers abnormal out-of-stock or over-replenishment situations. On the other hand, PID control has a slow response and is prone to causing disruptions and waste of supply chain resources.