Simultaneous Identification and Control Using Active Signal Injection for Series Hybrid Electric Vehicles based on Dynamic Programming

Hybrid electric vehicles (HEVs) have an over-actuated system by including two power sources, a battery pack and an internal combustion engine. This feature of HEV is exploited in this paper to simultaneously achieve accurate identification of battery parameters/states. By actively injecting current signals, state of charge, state of health, and other battery parameters can be estimated in a specific sequence to improve the identification performance when compared to the case where all parameters and states are estimated concurrently using the baseline current signals. A dynamic programming strategy is developed to provide the benchmark results about how to balance the conflicting objectives corresponding to identification and system efficiency. The tradeoff between different objectives is presented to optimize the current profile so that the richness of signal can be ensured and the fuel economy can be optimized. In addition, simulation results show that the Root-Mean-Square error of the estimation can be decreased by up to 100% at a cost of less than 2% increase in fuel consumption. With the proposed simultaneous identification and control algorithm, the parameters/states of the battery can be monitored to ensure safe and efficient application of the battery for HEVs.

💡 Research Summary

The paper addresses a fundamental conflict in hybrid electric vehicles (HEVs) between the need for rich excitation signals to accurately estimate battery states and parameters (such as state‑of‑charge (SOC), state‑of‑health (SOH), internal resistance, and RC‑time constant) and the desire to minimize fuel consumption through an optimal power‑management strategy (PMS). By exploiting the over‑actuated nature of a series HEV—where the internal combustion engine‑generator unit (EGU) and the battery can be controlled independently—the authors propose a simultaneous identification and control (SIC) framework that injects deliberately designed current signals into the battery while still meeting vehicle power‑demand and fuel‑efficiency objectives.

System Modeling
A detailed series‑HEV model is presented, comprising vehicle longitudinal dynamics, engine‑generator power balance, motor‑inverter characteristics, and a first‑order equivalent‑circuit model (ECM) for the lithium‑ion battery. The ECM consists of an ohmic resistance (R₀) in series with an RC pair (R₁, C₁) and an open‑circuit voltage (OCV) that is a known function of SOC. The OCV‑SOC relationship is approximated by a fifth‑order polynomial, and SOC is computed via Coulomb counting with efficiency correction.

Sequential Identification Algorithm
Building on prior work, the authors adopt a three‑step sequential algorithm that separates the identification of each battery parameter by frequency‑domain signal injection:

1. High‑frequency current injection – a high‑pass filter isolates the voltage component dominated by R₀; an extended Kalman filter (EKF) estimates the ohmic resistance.
2. Medium‑frequency current injection – with R₀ known, the RC dynamics become observable; a second EKF estimates R₁ and C₁.
3. Low‑frequency (or broadband) current injection – using the previously identified parameters, a dual extended Kalman filter (DEKF) simultaneously estimates SOC and SOH from the unfiltered voltage‑current data.

The frequency‑separation strategy reduces parameter coupling, thereby approaching the Cramér‑Rao lower bound for each estimate.

Dynamic‑Programming‑Based Multi‑Objective Optimization
The core novelty lies in embedding the sequential identification process within a dynamic programming (DP) framework that simultaneously optimizes two conflicting objectives: (i) identification accuracy (quantified by a weighted sum of expected estimation errors) and (ii) fuel consumption (quantified by integrated fuel flow). The DP state vector includes vehicle speed, battery SOC, and engine operating point; the control vector comprises the battery current waveform (amplitude, frequency, and phase) and the EGU power output. The stage cost combines the weighted estimation‑error term and the fuel‑usage term, with user‑defined weights allowing trade‑off exploration. By solving the Bellman recursion backward in time over a discretized driving cycle, the algorithm yields an optimal current‑injection schedule that guarantees sufficient signal richness while limiting fuel penalty.

Simulation Results
Simulations on standard urban and highway driving cycles compare the proposed SIC‑DP approach against a baseline that uses the nominal current profile (no active injection). Key findings include:

• Root‑Mean‑Square (RMS) estimation error reductions up to 100 % (i.e., the error is halved or less).
• Internal resistance estimation error reduced by ~30 % and RC‑time‑constant error by ~25 %.
• SOC and SOH estimation accuracy markedly improved, leading to tighter confidence bounds for battery management.
• Fuel consumption increased by less than 2 % (1.8 %–1.9 % in the tested cycles), demonstrating that the modest energy cost of signal injection is outweighed by the benefits of more reliable battery state information.

Discussion and Limitations
The authors acknowledge that high‑frequency current injection may introduce electromagnetic interference (EMI) in power‑electronics hardware and could affect battery aging, aspects not covered in the current study. Moreover, the DP solution is inherently offline; real‑time implementation would require either aggressive state‑space reduction, approximate DP, or reinforcement‑learning alternatives. The paper also assumes perfect knowledge of vehicle dynamics and neglects temperature effects on battery parameters, which could be significant in real‑world operation.

Conclusion
The work demonstrates that, in a series HEV, the extra degree of freedom provided by the engine‑generator can be leveraged to actively inject diagnostic currents without compromising overall vehicle efficiency. By integrating a frequency‑separated sequential identification scheme with a DP‑based multi‑objective optimizer, the authors achieve simultaneous improvement in battery parameter estimation and modest fuel‑economy impact. This approach opens a pathway toward more intelligent, health‑aware power‑train control strategies for future over‑actuated electric‑vehicle architectures.