To help you quickly start with the modeling and control module of MPT, you can have a look at the following demonstrations.
Representation of linear-time invariant (LTI) dynamic systems
Modeling and simulation of piecewise affine (PWA) systems.
Attaching a finite horizon MPC controller to LTI system.
Closed loop simulation with MPC controller
Design of explicit MPC
Modification of MPC setup by proving a terminal penalty and terminal set constraints.
Continue reading by checking out Demos on Real-Time Implementation.