Machine-tool axes for high-speed machining make great demands on the mechanical system, the actuators, and the numerical control. They require a high stiffness, a high bandwidth, and a precise motion at maximum speed. Linear motors as direct drives for machine-tool axes provide the basis to fulfil these requirements. They eliminate the gear-related problems of rotary drives with lead-screw transmission (from rotary to linear motion). In research and industrial projects, linear drives are already successfully implemented for machine-tool axes. From the point of view of control, the accurate and low-noise estimation of the axis speed is a key issue. Due to the high bandwidths required, high sampling frequencies are employed. The estimation of the drive speed by differentiation of the measured position is sensitive to position quantization at high sampling frequencies. All position-based speed estimation methods involve a trade-off between delay and quantization noise on the estimated speed. Delay limits the achievable control bandwidth. Noise leads to audible control noise and might excite structural resonances. It limits the maximum values of the feedback gains and thus also limits the bandwidth. Given a certain position resolution, a substantial reduction of quantization effects is only possible at the expense of a reduction of the stiffness. A further increase in position resolution limits the maximum axis speed with today's position encoders. This is not desired and other solutions have to be found. A survey of different sensors for linear-axis control describes the state of the art. As a result, the use of acceleration measurement in addition to the position measurement for high-precision speed estimation is proposed. The commonly used aerospace methods of combining position with acceleration to obtain a high-precision speed estimate (complementary filters, Kalman filters) raise design and realisation problems for linear-axis applications. Therefore, we propose a novel method of accelerometer-enhanced speed estimation (AESE). This method lowers the demands on the position resolutions considerably. Generally speaking, the low frequency components are extracted from the position measurement and the high frequency components from the acceleration signal by observing the two measurements over a certain time period in the past. This solution is not sensitive to accelerometer measurement noise. Its design consists in the choice of one design parameter, the observation period length. The design is very easy, as the resulting speed quality is not very sensitive to this parameter. An analysis of the closed-loop system demonstrates that, by the use of accelerometer-enhanced speed estimation, the position quantization influence on the speed feedback path is equalised to the one of the position feedback path. Therefore, high controller bandwidths and thus high sampling frequencies are possible without noise on the speed signal. On-line identification algorithms for the accelerometer gain and offset parameter, which are proposed in this dissertation, simplify commissioning of the system with the additional accelerometers. They are based on the proposed AESE-method. Low-cost inertial accelerometers are used for the experimental validation of the proposed algorithms on real linear-drive axes. They demonstrate that the AESE-algorithm provides an accurate, low-noise speed estimate with a delay in the range of the delay of the direct position differentiation over one sampling period. Altogether, the proposed AESE-method is well-suited for an industrial application because of the high quality of the obtained speed signal, the simple design, the low cost, the low measurement-noise sensitivity, and the on-line parameter identification.