Offshore wind energy is one of the solutions to meet the growing demand for renewable energy. The offshore wind turbines producing this energy keep increasing in size and, as a result, the monopile foundations are becoming larger and heavier. The traditional jack-up installation vessels have limited crane capacity and many of these vessels are unable to install the XXL monopiles. Therefore, the offshore industry is currently investigating a new installation method using a motion-compensated gripper frame on floating vessel with a dynamic positioning system. The gripper frame is attached to the vessel and encloses the monopile with a ring to keep it vertical during the installation. In addition, the gripper frame compensates for the vessel motions such that the vessel motions do not influence the monopile motions. The purpose of this thesis is to investigate the feasibility of such a motion-compensated gripper frame and to determine what control settings minimise the monopile inclination and the force exerted on the monopile. The system is composed of three main bodies: the vessel, the gripper frame and the monopile. The monopile and PID controller, which controls the amount of force exerted on the monopile to keep it vertical, have been modelled in the frequency domain to gain insight in the effect of changing the control parameters. To model the dynamics of the coupled system an OrcaFlex model has been set-up. The system has been tested for various values of proportional and derivative gain, kP and kD respectively, in various wave conditions. First the perfect control system is tested, where the force to keep the monopile vertical is applied instantly and the vessel motions are fully compensated. However, as the real world is never perfect, the system tested for sensor lag and imperfect motion compensation as well. The results are judged based on three criteria regarding the maximum monopile inclination, actuator force and actuator stroke. Resonance is observed in case a value of kP is selected such that the natural frequency of the monopile and controller matches the wave forcing frequency. Adding derivative gain kD limits the monopile motions and force exerted in this case. To limit the monopile motion the proportional gain should be selected such that resonance is avoided. Two different control settings are investigated and it has been found that a relatively high value of kP of 10,000 kN/m in combination with a kD of 11,000 kNs/m is a suitable setting based on the three criteria. Furthermore, bow quartering waves is the favourable wave direction compared to head waves for the system considered in this thesis, as the force on the monopile is more evenly distributed over the actuator in x- and y-direction. Introducing a sensor lag into the system results in higher monopile motions and forces on the monopile. If the sensor lag exceeds 0.3 s it leads to instability of the monopile for both settings. The effect of not fully compensating the vessel motions is found to be limited due to the fact that these motions are slowly varying. The results of this work contribute to a better understanding of the dynamics of the system in various wave conditions. Furthermore, it provides insight in the effect of sensor lag and imperfect motions compensation, contributing to the design of a motion-compensated gripper frame for the installation of XXL monopiles.