Session: 04-01: Modelling, Control and Design of Hybrid Powertrains

Paper Number: 164406

164406 - Feedback Linearization Control for Enhanced Load Transient Performance in an Off-Road Diesel Engine With E-Booster 

Abstract: 

In this paper, a multiple-input multiple-output (MIMO) nonlinear control law-based feedback linearization controller is proposed to enhance load transient performance in a 4.5L off-road diesel engine with an e-booster (electrically driven compressor). The incorporation of e-booster operation during load-transients mitigates the drop in the air-to-fuel ratio (AFR), thereby reducing smoke emissions. The air/charge subsystem of a diesel engine is inherently strongly coupled and highly nonlinear, due to the thermodynamic relationship between pressure and flow rate. Consequently, conventional single-input single-output (SISO) control strategies are challenging to apply across varying engine speed/load conditions and become even more complex with the integration of additional degrees of freedom, such as e-booster control during transients.

The simulated four-cylinder diesel engine used in this study is equipped with a single-stage fixed-geometry turbocharger, an exhaust gas recirculation valve (EGRV), an exhaust throttle valve (ETV) positioned downstream of the turbine, and an e-booster upstream of the compressor. It is modeled in the high-fidelity engine simulation software GT-Power, and meticulously calibrated with baseline experimental data to ensure accurate performance representation. The proposed nonlinear-MIMO controller is designed based on a reduced six-order mean-value model of the simulated diesel engine to track the desired engine outputs—AFR, engine speed, and diluent-air-ratio (DAR - representative of EGR percentage), by controlling the inputs: EGRV, ETV, fuel injection quantity, and e-booster speed. The nonlinear feedback linearization control law compensates for nonlinearities and eliminates coupling interactions between inputs and outputs. The nonlinear MIMO controller is then coupled with a PI controller to guarantee transient performance and robustness. Additionally, the proposed control strategy is compatible with existing engine sensors and sensing systems, facilitating practical implementation.

The nonlinear-MIMO controller was simulated during a load transient test from 100 Nm to 500 Nm in 0.3 seconds at constant engine speeds of 1200, 1600, and 1800 rpm, representing real-world scenarios in off-road applications such as construction and mining. The results were compared against the baseline engine controller (with no e-booster), where actuators were controlled by an ECU look-up table. For a fair comparison, the proposed nonlinear MIMO controller was also evaluated against two controllers developed for an engine setup with an e-booster: (1) a SISO controller—a robust H_∞ controller on e-booster speed, with other engine actuators controlled by the baseline ECU map, and (2) a linear-MIMO controller—a robust H_∞ controller developed using a linearized engine plant model (@1800 rpm-300 Nm operating condition) to track AFR, engine speed, and DAR. The performance criteria of the controllers during this load transient test were (a) lower engine speed droop and overshoot, with faster settling time, (b) closely tracking the DAR profile with a faster settling time at high-load steady-state conditions, and (c) lower AFR droop. These performance criteria are directly linked to better transient performance and improved NOx-smoke emissions in diesel engines for off-road applications, which is critical for meeting stringent emission standards and ensuring customer satisfaction.

The nonlinear-MIMO controller reduced engine speed droop by 48% and achieved steady-state 1 second faster than the baseline controller at an engine speed of 1800 rpm. Additionally, at 1800 rpm, it demonstrated more accurate tracking of the DAR profile during load-transients and settled 0.5 seconds earlier at high load compared to the baseline. The study reveals that the nonlinear-MIMO controller consistently outperformed both the SISO and linear-MIMO controllers in AFR regulation, DAR tracking, and engine speed recovery across all tested engine speeds (1200, 1600, and 1800 rpm). In contrast, the robust linear-MIMO controller failed to perform effectively at 1200 rpm, as it was developed based on a linearized model at 1800 rpm, limiting its applicability. This demonstrates that the proposed nonlinear-MIMO controller offers better robustness and stability across varying engine speeds.

Presenting Author: Raghav Kakani Purdue University

Presenting Author Biography: Raghav Kakani is a PhD student in Mechanical Engineering at Purdue University, specializing in powertrain optimization and vehicle automation for off-road applications. His research focuses on enhancing gas-exchange management, advanced engine controls, and autonomous vehicle systems to improve the efficiency, safety, and regulatory compliance of heavy-duty off-road vehicles. Raghav holds a dual degree (Bachelor’s and Master’s) in Mechanical Engineering from the Indian Institute of Technology Madras, where he graduated in 2021.

Authors:

Raghav Kakani Purdue University
Adil Manzoor Shaikh Purdue University
Shubham Ashta Daimler Truck
Nicholas Vang University of Wisconsin–Madison
Jaal Ghandhi University of Wisconsin-Madison
David Rothamer University of Wisconsin-Madison
Gregory Shaver Purdue University