This paper develops a new approach to soft constrained model predictive control (MPC) for real-time trajectory tracking. The presented method does not rely on solving an iterative optimization algorithm at each sampling instance. In fact, the optimal control input is directly computed via an inner product of two vectors. This enables the computation of an optimal control input in real-time rather than having to use a suboptimal solution as is the case in most current real-time MPC approaches. The computational complexity of the presented method is linear w.r.t. the prediction horizon, state and input dimension, which makes it ideal for fast sampled, large systems. The functionality of the new approach is demonstrated in a laboratory setup of an underactuated, cranelike system. Furthermore, its performance is compared with a suboptimal MPC based on an active-set method with warmstart (ASM-MPC). It is shown that the new method is of the order of 10 5 times faster than the ASM-MPC, while achieving similar and in some cases even better tracking accuracy.