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This paper considers trajectory planning with given design constraints and design of a feedforward controller for single-axis motion control. A motivation is given for using fourth-order feedforward with fourth-order trajectories. An algorithm is given for calculating higher-order trajectories with bounds on all considered derivatives for point-to-point moves. It is shown that these trajectories are time-optimal in the most relevant cases. All required equations for fourth-order trajectory planning are derived. Implementation, discretization and quantization effects are considered. Simulations and hardware-in-the-loop experiments show superior effectiveness of fourth-order feedforward in comparison with lower-order feedforward.