The effect of prediction horizons in MPC for first order linear systems

Model Predictive Control (MPC) algorithms are computationally intensive optimization based control techniques. Their complexity significantly increases when the cost function prediction horizon increases. This problem is more pronounced when applying this techniques to systems having fast dynamics, in this case the prediction horizon length is limited by the calculation power of the processor. The use of long prediction horizons should provide healthier results than single prediction horizon yet prediction horizon equal to one are widely used for the control of electrical system and are achieving beneficial results. This paper proves mathematically that in some special cases of MPC applied to first order systems the use of a prediction horizon equal to one is similar to the use of a prediction horizon greater than one. An MPC algorithm is then applied for the control of the current of an RL load driven by an H-Bridge, multiple prediction horizon are used and results are compared.