Despite the energy penalty and solvent regeneration cost, carbon capture using amine-based absorption/stripping systems is one of the most used technologies for CO2 removal of post-combustion processes, mainly due to its high capture efficiency. This work presents a complex control strategy for a post-combustion carbon capture plant that aims to minimize the effect of disturbances and maintain the desired performance of the CO2 capture system. It is based on a comprehensive mathematical model for the plant considered to have, in addition to the absorption/stripping columns, a buffer tank and heat exchangers designed to ensure energy efficiency and to determine the flexible, smooth, and robust operation of the plant. The buffer tank is provided with 3 control loops that have the purpose of adjusting the parameters of the absorber inlet solvent solution, such as downstream disturbances that are, to a less extent, recirculated back into the system from the desorber. Using a model predictive control algorithm, an additional control system was designed with the aim to maintain the carbon capture rate of the plant at the setpoint value of 85 % and to keep the reboiler liquid temperature at 395 K setpoint. The control performance results are shown for the hybrid control approach that includes the MPC controller. Results show that the control approach can simultaneously control the targeted variables while efficiently coping with the intrinsic and complex input-output interactions. It is able to maintain better the controlled variables at the desired setpoint values, despite the typical flowrate and concentration disturbances of the CO2 influent flue gas flow. This is achieved with reduced offset and minimal peak deviations from the setpoints. The mean absolute error values of the controllers are maintained below 7 %, and the carbon capture rate is maintained above 78 % at all times. The energy performance index is maintained at values below 3.5 MJ/kgCO2.