In this paper, we present a so-called self detection and estimation scheme for the on-line implementation of our Mixed Integer Quadratic Programming (MIQP)-based design of MPC, which addresses simultaneously the actuator saturation and backlash nonlinearity. The estimation scheme is required to determine a set of design parameters required by the MIQP-based MPC for compensating for the backlash effect. The scheme automatically locates the backlash in actuators, and then estimates the size of its dead-band, from the on-line measurements of plant inputs. We illustrate the application of the proposed method to the control of composition and liquid levels in a paper machine head-box system, where the MIQP-based MPC design equipped with the on-line detection and estimation scheme is able to compensate for the backlash effects, and then to regain its nominal performance in the presence of actuator backlash.