This research aims to address intricate control challenges in a highly integrated multi-component distillation process within a polyolefin elastomers plant. The studied process incorporates various process intensification techniques into a unified unit, resulting in strong interactivity and presenting unique control challenges. To tackle these challenges, a rigorous mathematical model of the distillation process is established, and index reduction is employed to handle the high-index DAE system. Various control structures and algorithms are utilized to comprehensively assess their feasibility and effectiveness in disturbance rejection, setpoint tracking, and handling inaccurate measurements. The control structures include temperature inferential control, temperature-composition hybrid control, and composition control. The control algorithms encompass PI control, linear model predictive control (LMPC), and nonlinear model predictive control (NMPC). Results indicate that both temperature-composition hybrid control and composition control exhibit comparable and superior performance. This suggests that temperature-composition hybrid control is an effective and cost-efficient configuration for complex distillation systems. The dynamic responses of MPC outperform those of PI control, as evidenced by a reduction in the integral of the absolute error. NMPC exhibits the most outstanding performance in all scenarios, showcasing the smallest maximum deviations and shortest settling times.