This paper presents the design of Model Predictive Control (MPC) applied to the Parallel-type Double Inverted Pendulum (PDIP), which is driven by a linear motor. The limited stroke length of the linear motor driving the PDIP and the varying friction distributed on the linear motor track posed a challenge for control design. Therefore, a cascade control structure is considered in this study where the inner loop is formed via state feedback and MPC directs the outer loop to enhance position control of the linear motor. Swing-up control of the PDIP was achieved with energy-based control techniques. Experimental results demonstrated successful swing-up and balancing of the two pendulums in their up-right positions. Compared to the conventional state feedback control, the cascade control structure improved the performance of the position control in the PDIP without the need for a precise friction model.