Stability Condition for a Class of Finite Memory Integral-Model Predictive Control

In this paper, a new type of model predictive control was discussed and its stability property was studied. An integral model predictive control inspired from the classical PID control was studied to eliminate the adverse effect of the disturbance acting on the plant and the adverse effect of inaccurate internal model. However, it has been shown that integral model predictive control may become unstable if the integral control action constant in model predictive control is not tuned properly; under these conditions, the controlled plant output tends to oscillate with high amplitudes. Therefore, a forgetting term was incorporated to the integral control action so that smooth convergence was achieved. The stability analysis of the integral model predictive control was made and several stability theorems were employed to determine the range of forgetting constants for which the integral model predictive control is stable. As an example problem, a tuned integral model predictive control was used to control the well-known four-tank benchmark problem and its results were compared with the results of a regular model predictive control.