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This paper discusses a real-time implementation of tube model predictive controllers for nonlinear input-affine systems. This is achieved by combining recent theoretical and practical advances on the construction of forward invariant tubes with state-of-the-art algorithms for nonlinear MPC, such as the real-time iteration scheme. The focus of the paper is on presenting these ideas in a tutorial style, using a 10-state quadcopter model as an example. The controller is implemented using the automatic code generation capabilities of ACADO Toolkit. Numerical experiments show that the tube MPC scheme can achieve run-times in the lower millisecond range.