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Due to rising energy requirements, the use of low-weight materials is becoming more important, especially in aerospace and automotive engineering. Because of their high strength-to-weight ratio, carbon fiber reinforced plastics (CFRP) are increasingly replacing metals. These materials are usually machined by milling operations. Their main problems are high tool wear, thermal damage, and surface integrity. This paper presents a machine concept and control strategy to substitute milling with laser cutting. Because a high, constant-trajectory velocity is required during laser cutting operations, a highly dynamic machine tool is needed. Conventional machine tools requiring large workspaces are inertial and therefore unsuitable for this task. Thus, a portal machine concept was investigated with an additional laser scanner and lightweight moving components. To increase path accuracy, two control strategies were implemented and analyzed in a multi-body simulation. One approach is to use a frequency-separating filter, while the second is based on estimation of tool center point positioning error using a Kalman filter. An acceleration sensor located near the tool center point (TCP) or the drive current signal can be used as input for the Kalman filter. Both input signals are investigated and compared in this paper. Results presented in this paper show that with these control strategies, highly dynamic trajectories can be realized with high precision.