A model-based stiction compensation algorithm has been developed based on the H. Zabiri et al. Mixed Integer Quadratic Programming (MIQP) model predictive controller (MPC) algorithm which uses optimization to compensate for backlash in actuators. MIQP-based MPC shows promising result for stiction compensation. However, the backlash compensation formulation alone can remove oscillation caused by stiction dead-band but fails to reduce the offset caused by stiction slip-jump. Several modifications are proposed to solve the offset issue. The MIQP optimization problem constrains were loosened to give more flexibility to the optimizer. Simulation studies were conducted using a 2x2 distillation column model. With loosened constraints, MIQP based MPC reduced the offset at the expense of introducing oscillation into the system.