Effect of Model-Plant Mismatch on Model Predictive Control and Mismatch Threshold Determination

The performance of model predictive control is highly affected by model-plant mismatch. Existing model-plant mismatch detection, isolation and estimation techniques do not take into account the threshold of significant mismatch, preventing clear analysis of the implications of mismatch. This study investigates the relationship between model-plant mismatch and plant performance in a multiple input multiple output system and determines the thresholds of mismatch. The approach uses a closed loop system with the Wood and Berry distillation model controlled by MPC simulated with varying degrees of parametric mismatch. The threshold values above which the MPC performance is unacceptable are determined from the Integral Error- MPM graph by specifying the base Integral Error. The values for positive mismatches are 27%, 19% 40% and 31% for the four gains, 27%, 40% 40% and 32% for the time constants and 21%, 9%, 6% and 14% for the time delays respectively. The values for negative mismatches are 22%, 22% 38% and 16% for the four gains, 20%, 20% 31% and 20% for the time constants and 40%, 10%, 6% and 11% for the time delays respectively. Time delay mismatch yields the most significant effect on the MPC performance. Gain mismatch causes significant impact on the MPC performance when the mismatch increases the condition number otherwise its impact is lower than the effect of time delay mismatch. The effect of mismatch in time constant becomes significant when the plant time constant increases, otherwise, it is minimal. Simultaneous mismatches in two transfer functions are pronounced when the mismatches affect the same output.