Model Predictive Control for Bread Oven Temperature Regulation: Thermal Modeling, Constraint Handling and Performance Evaluation Against PID Control

temperature. This is because PID control reacts directly to the instantaneous error, producing an aggressive control action that rapidly drives the system toward the setpoint. IJEMT Table 6: Performance Comparison between MPC and PID Controllers S/N Controller Rise Time (s) Settling Time (s) Overshoot (%) 1 MPC 300 527 0.00 2 PID 180 420 6.50 In terms of settling time, the PID controller also appears to perform better numerically, with a value of 420 s compared to 527 s for MPC. This suggests that the PID controller reaches the steady-state region faster. However, it is important to note that this faster settling is achieved despite the presence of oscillations and overshoot, which may not be acceptable in sensitive thermal processes. The MPC controller, although slower, provides a more gradual and controlled convergence to the setpoint without oscillatory behavior. A critical distinction between the two controllers was observed in the percentage overshoot. The MPC controller achieves zero overshoot (0.00%), meaning that the oven temperature never exceeds the desired setpoint. In contrast, the PID controller exhibits an overshoot of approximately 6.50%, indicating that the temperature rises above the reference value before settling. This behavior is undesirable in bread oven applications, as excessive temperature can lead to over-baking, degradation of product quality, and increased energy consumption. Figure 12 presents the tracking error comparison of the MPC and PID controllers. Immediately after each setpoint change, both controllers produce large positive errors because the oven temperature initially lags behind the new reference value. However, the MPC error decreases smoothly and monotonically toward zero, indicating a stable and well-damped correction process. In contrast, the PID error reduces more rapidly at first, but this faster correction is accompanied by oscillatory behavior around the zero-error line due to overshoot and subsequent compensation. This shows that, although the PID controller reacts more aggressively, its error response is less stable than that of the MPC controller. Figure 12: Tracking Error Comparison of MPC and PID Controllers IJEMT Figure 13 presents the multi-run convergence overlay of the MPC and PID controllers for repeated simulations under the same step change in reference temperature. The results show that the MPC controller exhibits highly consistent convergence behavior across all runs. In each simulation, the oven temperature follows a smooth and monotonic trajectory toward the reference value, with negligible variation between runs. This consistency is primarily due to the optimization-based nature of MPC, where control actions are computed by solving a constrained optimization problem at each sampling instant. As a result, the controller produces nearly identical control inputs and system responses for the same operating conditions, leading to deterministic and repeatable convergence. In contrast, the PID controller demonstrates less consistent convergence characteristics across multiple runs. Although the general trend of the response remains similar, noticeable variations are observed in overshoot magnitude, oscillation amplitude, and settling time. These variations arise from the sensitivity of PID control to tuning parameters, initial conditions, and disturbance effects. Small changes in system conditions or numerical settings can lead to different transient responses, resulting in non-uniform convergence behavior. This makes PID less predictable compared to MPC in repeated simulations. Another important observation is that the MPC controller maintains stable convergence without oscillation in all runs. The temperature approaches the setpoint in a well-damped manner, and the convergence path remains smooth even under disturbances or constraints. On the other hand, the PID controller often exhibits oscillatory convergence, where the temperature fluctuates around the setpoint before settling. In multiple runs, the extent of these oscillations may vary, indicating that the PID controller does not guarantee uniform damping performance under all conditions. Figure 13: Convergence Overlay of MPC and PID Controllers 4. Conclusion This paper presented the development and evaluation of a MPC-based temperature regulation system for a bread oven using a physics-based thermal model derived from the fundamental mechanisms of conduction, convection, and radiation. Simulation results demonstrated that the proposed MPC controller achieved accurate temperature tracking with zero overshoot, smooth control action, effective disturbance rejection, robust handling of ambient temperature variations, and reliable performance under actuator constraints. Comparative analysis further showed that, although the conventional PID controller provided a faster initial response, it exhibited overshoot, IJEMT oscillations, and less coordinated control behavior, whereas the MPC controller consistently delivered superior stability, robustness, and convergence characteristics. Therefore, the presented MPC framework provide an effective and practical solution for intelligent bread oven temperature regulation and can be applied to industrial baking systems and other thermal processing applications requiring precise, reliable, and energy-efficient temperature control. IJEMT References [1] Abdelbasset, M., Chang, V. and Mohamed, R. (2021). 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