Model predictive control (MPC) schemes employ dynamic models of a process within a receding horizon framework to optimize the behavior of a process. Although MPC has many benefits, a significant drawback is the large computational burden, especially in adaptive and constrained situations. In this paper, a computationally efficient self-tuning/adaptive MPC scheme for a simple industrial process plant with rate and amplitude constraints on the plant input is developed. The scheme has been optimized for real-time implementation on small, low-cost embedded processors. It employs a short (2-step) control horizon with an adjustable prediction horizon, automatically tunes the move suppression (regularization) parameter to achieve well-conditioned control, and presents a new technique for generating the reference trajectory that is robust to changes in the process time delay and in the presence of any inverse response. In addition, the need for a full quadratic programming procedure to handle input constraints is avoided by employing a quasi-analytical solution that optimally fathoms the constraints. Preliminary hardware-in-the-loop (HIL) test results indicate that the resulting scheme performs well and has low implementation overhead.