Optimal tuning of model predictive controllers for organic Rankine cycle systems recovering waste heat from heavy-duty vehicles

The organic Rankine cycle power system is an emerging technology, which is able to recover the waste heat from the diesel engine of heavy-duty trucks and thus increase the overall engine efficiency. One of the major technical challenges for the integration of the organic Rankine cycle unit on-board trucks are the broad and rapid fluctuations of the available waste heat, caused by the unsteady driving conditions of the truck. Model predictive control has shown to be a powerful tool to ensure safe operation and optimal performance of the organic Rankine cycle unit on-board trucks. This paper presents a novel systematic method for the tuning of model predictive controllers based on a multi-objective optimization routine using a fourth-order reduced linear model. The objectives of the optimization are the settling time due to a step change of the exhaust gas mass flow rate and the cumulative controller effort due to measurement noise. The results suggest that a trade-off exists between the two objectives. Among the controller design parameters, the input rate weight has the largest influence on the controller performance. Interestingly, the simplified optimization procedure based on the reduced-order linear model of the organic Rankine cycle unit can provide key information about the controller performance based on a more complex nonlinear model of the organic Rankine cycle unit when subjected to a realistic waste heat profile. The results indicate that the settling time due to a step change of the exhaust gas mass flow rate is a good indicator of the absolute mean square tracking error over the profile, and it should not exceed 15 s for an absolute mean square tracking error below 2 K. On the other hand, the cumulative controller effort due to measurement noise is strongly correlated to the cumulative controller effort over the profile, and it should stay below 0.5 %/s for a cumulative controller effort over the whole profile below 2 %/s. The presented method is a powerful tool to help the control designer to find the optimal design parameters of model predictive controllers in a systematic way, in contrast to the time-consuming, experience-based trial and error methods.