In order to solve servo problems and regulator problems simultaneously for external signals in arbitrarily given function classes, such as step set-point changes and ramp disturbances, the conventional Model Predictive Control algorithm is extended by introducing a filter into the output prediction equation. The necessary and sufficient conditions for eliminating steady-state errors were derived for a stable process and a process with an integrator. The filter design problem resulted in the problem of solving Diophantine equations, the number of which is equivalent to the number of steps of the coincidence horizon. For an integrating process with ramp disturbances, a filter can be designed easily by taking advantage of characteristics of the process. Simulation results demonstrated successful functioning of the proposed control algorithm.