End-to-End Deep Neural Network Based Nonlinear Model Predictive Control: Experimental Implementation on Diesel Engine Emission Control

Abstract

In this paper, a deep neural network (DNN)-based nonlinear model predictive controller (NMPC) is demonstrated using real-time experimental implementation. First, the emissions and performance of a 4.5-liter 4-cylinder Cummins diesel engine are modeled using a DNN model with seven hidden layers and 24,148 learnable parameters created by stacking six Fully Connected layers with one long-short term memory (LSTM) layer. This model is then implemented as the plant model in an NMPC. For real-time implementation of the LSTM-NMPC, an open-source package acados with the quadratic programming solver HPIPM (High-Performance Interior-Point Method) is employed. This helps LSTM-NMPC run in real time with an average turnaround time of 62.3 milliseconds. For real-time controller prototyping, a dSPACE MicroAutoBox II rapid prototyping system is used. A Field-Programmable Gate Array is employed to calculate the in-cylinder pressure-based combustion metrics online in real time. The developed controller was tested for both step and smooth load reference changes, which showed accurate tracking performance while enforcing all input and output constraints. To assess the robustness of the controller to data outside the training region, the engine speed is varied from 1200 rpm to 1800 rpm. The experimental results illustrate accurate tracking and disturbance rejection for the out-of-training data region. At 5 bar indicated mean effective pressure and a speed of 1200 rpm, the comparison between the Cummins production controller and the proposed LSTM-NMPC showed a 7.9% fuel consumption reduction, while also decreasing both nitrogen oxides (NOx) and Particle Matter (PM) by up to 18.9% and 40.8%.

Keywords

• deep learning
• deep neural network
• emission reduction
• machine learning
• long-short-term memory
• model predictive control