A Robust Model Predictive Control for efficient thermal management of internal combustion engines

Highlights: • A Robust Model Predictive Control for ICE thermal management was developed. • The proposed control is effective in decreasing the warm-up time. • The control system reduces coolant flow rate under fully warmed conditions. • The control strategy operates the cooling system around onset of nucleate boiling. • Little on-line computational effort is required. - Abstract: Optimal thermal management of modern internal combustion engines (ICE) is one of the key factors for reducing fuel consumption and CO₂ emissions. These are measured by using standardized driving cycles, like the New European Driving Cycle (NEDC), during which the engine does not reach thermal steady state; engine efficiency and emissions are therefore penalized. Several techniques for improving ICE thermal efficiency were proposed, which range from the use of empirical look-up tables to pulsed pump operation. A systematic approach to the problem is however still missing and this paper aims to bridge this gap. The paper proposes a Robust Model Predictive Control of the coolant flow rate, which makes use of a zero-dimensional model of the cooling system of an ICE. The control methodology incorporates explicitly the model uncertainties and achieves the synthesis of a state-feedback control law that minimizes the "worst case" objective function while taking into account the system constraints, as proposed by Kothare et al. (1996). The proposed control strategy is to adjust the coolant flow rate by means of an electric pump, in order to bring the cooling system to operate around the onset of nucleate boiling: across it during warm-up and above it (nucleate or saturated boiling) under fully warmed conditions. The computationally heavy optimization is carried out off-line, while during the operation of the engine the control parameters are simply picked-up on-line from look-up tables. Owing to the little computational effort required, the resulting control strategy is suitable for implementation in the ECU of a modern engine. The control strategy was validated by means of experimental tests under several operating conditions, involving both warm-up and fully warmed engine thermal states. The tests were carried out with a small displacement Spark-Ignition Engine which was equipped with an electric coolant pump, directly driven by the control algorithm. Results show that the controller is robust in terms of disturbance rejections, it respects the defined system constraints and is also very fast in terms of response to the perturbations. The experimental tests proved that the proposed control is effective in decreasing the warm-up time and in reducing the coolant flow rate under fully warmed conditions as compared to a standard configuration with pump speed proportional to engine speed. The adoption of these cooling control strategies will, therefore, result in lower fuel consumption and reduced CO₂ emissions.