Booms of modern mobile concrete pumps are vulnerable to elastic vibrations due to the light-weight construction. Although these vibrations can be effectively damped with appropriate controllers, the residual movement of the tool center point (TCP) during the pumping process is still uncomfortable for the workers guiding the end hose. In this paper, it is shown that this movement can be compensated with a position controller in combination with a damping controller. In practice, the required measurement of the absolute height of the TCP with respect to the ground is, however, difficult. Therefore, a strategy for the determination of the height of the TCP based on the kinematic description of the boom is proposed. For this purpose, the measurement of the inclination of each boom segment with inertial sensors in combination with an observer concept is presented which circumvents the disadvantages of tilt sensors. It is shown that a complementary filter design utilizing an additional inertial sensor placed on the TCP allows for the practical implementation of a PD-controller based on the inverse differential kinematics of the rigid-body approximation of the boom. This effectively compensates the vertical movement of the TCP. The estimation and control concepts are evaluated by extensive simulation studies on a validated mathematical model of a mobile concrete pump.