## 3 Results and Discussion  
During the ohmic heating of the tomato basil sauce, the controller objectives are:  
* Desired transient response to user temperature input: This ensures that the temperature rise within the heating chamber is not too fast or too slow. This goal also places emphases on eliminating temperature over-shoots in order to prevent boiling and pressure build up within the heating chamber. * Desired steady-state response: This objective eliminates steady-state errors at the setpoint temperature. * Robustness: This ensures that the CFOH has a stable and controllable response. Figure 4 shows the temperature response of the CFOH when the tomato basil sauce was heated to a desired reference temperature of 90 \({}^{\circ}\)C using a PID controller. The electrical power supplied by the controller during heating is also shown as recorded by an onboard power meter in the control panel. The performance of the PID controller is shown by the deviation of the output temperature from the setpoint temperature. The trend of the energy efficiency was also shown. As seen in Figure 4, the rapid heating derived from OH was an advantage as the outfeed temperature is close to the setpoint of 90 \({}^{\circ}\)C in less than 2 min of run time. Figure 5 shows the temperature response presented when the MPC controller is used for heating. The MPC controller has a shorter settling time of 90 s compared to that of the PID controller of 117 s, as shown in Table 1.  
The response from applying the AMPC controller is shown in Figure 6. The performance of the AMPC controller in terms of temperature transient time, steady-state error, temperature overshoots, temperature undershoots, and settling time exceed those of both the PID and MPC controllers. The settling time from the AMPC controller was observed to be 76 s--a much shorter time compared to the 117 s and 90 s of PID and MPC, respectively. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Controller** & \begin{tabular}{c} **Settling Time-2\% Criteria** \\ **(s)** \\ \end{tabular} & \
\begin{tabular}{c} **Max. Overshoot** \\ **(\({}^{\circ}\)C)** \\ \end{tabular} &
\begin{tabular}{c} **Max. Undershoots** \\ **(\({}^{\circ}\)C)** \\ \end{tabular} \\ \hline PID & 117 & 91.2 & 88.8 \\ MPC & 90 & 91.2 & 88.8 \\ AMPC & 76 & 91.6 & 89.7 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Performance comparison of the PID, MPC, and AMPC controllers. Figure 4: Temperature response of heating tomato basil sauce with the PID controller. Figure 5: Temperature response of heating tomato basil sauce with the MPC controller. The performances of the PID, MPC, and AMPC controllers are further evaluated in Table 1 below based on the objectives of the controller. According to Table 1, the AMPC controller has the shortest settling time of 76 s, which indicates that the final and setpoint temperature of 90 \({}^{\circ}\)C is reached (with a 2% criterion) the quickest. The PID controller is the slowest to reach the setpoint, at 117 s. The performance of the PID and MPC controllers are similar in terms of the maximum overshoot and maximum undershoot temperature observed. With the AMPC, the maximum overshoot observed was 91.6 \({}^{\circ}\)C, which is higher than that of both MPC and PID. However, the AMPC has a higher maximum temperature undershoot of 89.7 \({}^{\circ}\)C, which indicates that the deviation from the setpoint temperature is the lowest compared to other two implemented controllers. Table 2 shows the root-mean-square error (RMSE) of the temperature response of the PID, MPC, and AMPC controllers when compared to the temperature setpoint of 90 \({}^{\circ}\)C. The RMSE comparison is taken after the first 60 s of heating. From Table 2, the weighted average error between the setpoint temperature and actual temperature for the AMPC is 1.18, which is the lowest compared to the PID and MPC controllers. A low RMSE value of 1.18 indicates a good value when compared to 90 \({}^{\circ}\)C. This indicates less than 2% deviation from the setpoint temperature.