Design and comparative analyses of optimal feedback controllers for hybrid electric vehicles
Journal article, 2021

This paper presents an adaptive equivalent consumption minimization strategy (ECMS) and a linear quadratic tracking (LQT) method for optimal power-split control of a combustion engine and an electric machine in a hybrid electric vehicle (HEV). The objective is to deliver demanded torque and minimize fuel consumption and usage of service brakes, subject to constraints on actuator limits and battery state of charge (SOC). First, we derive a function for calculating maximum deliverable torque that is as close as possible to demanded torque and then reduce the number of control inputs to one while minimizing the usage of service brakes in the case of negative demanded torque. Next, we propose modeling SOC constraints by tangent or logarithm functions that provide an interior point to both the ECMS and the LQT. Then, we show that the resulting objective functions are convex, and we propose sub-optimal analytic solutions for the optimization problem by applying their second order approximation about a given reference. We also consider robustness of the controllers to measurement noise using a simple model of noise. Simulation results of the two controllers are compared, and their effectiveness is discussed.

Hybrid electric vehicles

State of charge

hybrid electric vehicle (HEV)


Linear quadratic tracking (LQT)


adaptive power-split control


equivalent consumption minimization strategy (ECMS)

Mechanical power transmission

Electronic countermeasures


Maryam Razi

Chalmers, Electrical Engineering, Systems and control, Mechatronics

Nikolce Murgovski

Chalmers, Electrical Engineering, Systems and control, Mechatronics

Tomas McKelvey

Chalmers, Electrical Engineering, Signal Processing and Biomedical Engineering, Signal Processing

Torsten Wik

Chalmers, Electrical Engineering, Systems and control, Automatic Control

IEEE Transactions on Vehicular Technology

0018-9545 (ISSN)

Vol. In Press

Driving Forces

Sustainable development

Areas of Advance


Subject Categories

Control Engineering

Signal Processing

Other Electrical Engineering, Electronic Engineering, Information Engineering



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