## 4 Evaluation of Electric Energy Output Quality
### Robustness Analysis  
(1) Uncontrolled rectification  
Under the uncontrolled rectification strategy, the entire circuit uses open-loop control. The output voltage at the load end is entirely determined by the load characteristics, as the three-phase electric power is processed solely by the unidirectional conductivity of diodes. In this paper, an uncontrolled rectification model is established based on the aforementioned analysis of three-phase uncontrolled rectification. Simulation tests are conducted under different load resistance values (10 \(\Omega\), 50 \(\Omega\), 100 \(\Omega\), 150 \(\Omega\), and 200 \(\Omega\)). The test results are shown in Figure 14. Figure 15 shows that the output voltage at the load end increases with growing load resistance, but the rate of increase slows down. Once the resistance reaches a certain level, the output voltage stabilizes and ceases to rise. This is attributed to the limitations of the linear motor's stroke and frequency, which prevent the output voltage from rising indefinitely. Under identical motor parameters, electrical parameters of the main circuit, connection methods, and load characteristics, a load mutation test was performed on the rectification system. The linear motor operated at 50 Hz with an 80 mm mover stroke. The load resistance mutated from 150 \(\Omega\) to 75 \(\Omega\) at 0.5 s. Simulation results are shown in Figure 16. At startup, the load-end output voltage was about 390 V and stabilized in approximately 0.15 s. Upon load mutation, the FPLG system exhibited prolonged fluctuations, taking around 0.4 s to restabilize. The output voltage fluctuated significantly. At 75 \(\Omega\), the output voltage was about 340 V. The uncontrolled rectification scheme caused substantial voltage fluctuations, indicating room for improvement in power quality. Figure 13: Control flowchart of model prediction. Using the uncontrolled rectification strategy can cause serious current disruptions in the three-phase current output from the linear motor. Figure 17 shows the three-phase current data of the linear motor collected during the simulation. In the three-phase rectifier circuit, each phase current on the AC side undergoes two conduction processes within a half-cycle, resulting in discontinuous and continuous phase currents. Under uncontrolled rectification, the current periodic work time ratio is only about 50%, which significantly reduces the motor's output efficiency. Figure 16: Output results of uncontrolled rectification under sudden load changes. Figure 14: Output voltage under different resistance values. Figure 15: Changes in voltage and ripple under different resistance values. 2. Robustness analysis of PWMC rectification and MPSMC rectification results This paper has presented the rectification principle based on MPSMC control, investigated the feasibility of applying the model predictive control strategy to the linear internal combustion power generation system, and established a simulation platform using Matlab/Simulink. Given that the sampling period, control horizon, and prediction horizon all influence control performance, the sampling period was set at 0.0002 s. The simulation results are as follows: A load mutation test was carried out on the MPSMC controller designed in this study while keeping the motor parameters, main--circuit electrical parameters, circuit connections, and load characteristics identical. The load voltage was maintained at 200 V. At 0.5 s, the load resistance was stepped down from 100 \(\Omega\) to 50 \(\Omega\). The simulation results for the load voltage and current waveforms are presented in Figures 18-20. Figure 18 shows that under MPSMC control, the load voltage stabilizes at the reference value in just 35 ms. After a load mutation at 0.5 s, the system responds in only 80 ms, highlighting the controller's robustness. As depicted in Figure 19, the output voltage remains stable near the reference value with a 20 ms system response time and a 7% overshoot, indicating minimal voltage fluctuation.