The dynamic study of the Supercritical Carbon Dioxide (SCO2) Brayton cycle has received extensive attention from the industry in recent years. While various dynamic operating conditions occur intermittently within the system, some commonly used control methods are unable to adapt effectively to those situations. In this study, a dynamic model of the SCO2 Brayton cycle coupled with a printed circuit heat exchanger with embedded PCM, a storage tank, and a proportional-integral-derivative (PID) controller was developed and validated with the model, and then the control effects of the various control models were compared in terms of their control effectiveness under three typical variable operating conditions (periodic temperature fluctuation, load reduction and recovery, and reduced flow rate). In addition, the stability assessment of the SCO2 Brayton cycle was modeled. Compared to the basic SCO2 Brayton cycle, the PCM-PCHE reduces the amplitude of the total efficiency fluctuations by 44.8 %, and the integrated layout covering the printed circuit heat exchanger with embedded PCM, storage tank, and PID controller shows the best stability. Controlling the extraction ratio with a PID controller contributes more to the stability of the SCO2 Brayton cycle than controlling the condensate flow rate with a PID controller. In contrast, the printed circuit heat exchanger with an embedded PCM contributes more to the stability of the SCO2 Brayton cycle concerning the storage tank. Overall, the total control layout reduced the instability by about 40 % compared to the initial recompression layout, indicating that the PCM, storage tank, and PID controller greatly improved the stability of the SCO2 Brayton cycle.