This thesis deals with model predictive control principally Based Predictive Control (MPC). The first part describes the principle of predictive control, cost function, the choice of a constraints in regulation and the choice of weights. In the next section is an analysis system: a system with non-minimal phase (control water turbine), oscillating systems (trolley frame control) and system with a time-delay . In all of these systems is performed classical feedback control using PID control and concurrently regulation with the MPC. MPC is selected as the solution fy Mathworks Model Predictive Control Toolbox and Simulink. The results are then analyzed using the criteria of quality control.