<p>This paper presents a compact, hybrid energy storage system (HESS) for power-split hybrid vehicles (PSHVs), composed solely of a lithium-ion battery (BAT) and an ultracapacitor (UC). The control framework integrates (i) an indirect power balance (IPB) law specialized for two sources, enabling fast and well-damped DC-link regulation without exciting the right half-plane (RHP) zero of boost-derived stages and (ii) a nonlinear damped PI (NLPI/PI-NLD) controller that augments classical PI with a fractional-power damping term to achieve chattering-free and finite-time-like convergence. The UC handles high-frequency transients and regenerative events, while the battery supplies mid-frequency energy, with current references coordinating both sources under current and voltage. This work also provides control-oriented averaged models and derives stability guarantees via Lyapunov arguments for the DC-link channel and the PMSM drive (speed/current) cascades. The startup transient of the BU-HESS under step load demand (0–500 V) demonstrates that the proposed PI-NLD controller significantly outperforms the conventional PI by reducing undershoot from 12<InlineEquation ID="IEq1"> <EquationSource Format="TEX">$\%$</EquationSource> <EquationSource Format="MATHML"><math> <mo>%</mo> </math></EquationSource> </InlineEquation> to 3<InlineEquation ID="IEq2"> <EquationSource Format="TEX">$\%$</EquationSource> <EquationSource Format="MATHML"><math> <mo>%</mo> </math></EquationSource> </InlineEquation>, overshoot below 1.5<InlineEquation ID="IEq3"> <EquationSource Format="TEX">$\%$</EquationSource> <EquationSource Format="MATHML"><math> <mo>%</mo> </math></EquationSource> </InlineEquation>, accelerating convergence from 0.25 s to 0.09 s, suppressing voltage oscillations, improving torque delivery, reducing current ripple by 25<InlineEquation ID="IEq4"> <EquationSource Format="TEX">$\%$</EquationSource> <EquationSource Format="MATHML"><math> <mo>%</mo> </math></EquationSource> </InlineEquation>, and providing finite-time-like stabilization for robust and precise power-split operation in PSHVs. The result is a low-complexity controller suitable for real-time automotive platforms that preserves PI simplicity while delivering nonlinear robustness for BAT+UC HESS architectures.</p>

Design and Control of Battery–Ultracapacitor Hybrid Energy Storage System-Based Power-Split Hybrid Vehicle using Nonlinear Damped PI Control Scheme

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发表日期：

2026年2月9日

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Irfan Sami,
Muhammad Salman,
Lutf Ur Rahman,
Fahad Saleh Al-Ismail

摘要

This paper presents a compact, hybrid energy storage system (HESS) for power-split hybrid vehicles (PSHVs), composed solely of a lithium-ion battery (BAT) and an ultracapacitor (UC). The control framework integrates (i) an indirect power balance (IPB) law specialized for two sources, enabling fast and well-damped DC-link regulation without exciting the right half-plane (RHP) zero of boost-derived stages and (ii) a nonlinear damped PI (NLPI/PI-NLD) controller that augments classical PI with a fractional-power damping term to achieve chattering-free and finite-time-like convergence. The UC handles high-frequency transients and regenerative events, while the battery supplies mid-frequency energy, with current references coordinating both sources under current and voltage. This work also provides control-oriented averaged models and derives stability guarantees via Lyapunov arguments for the DC-link channel and the PMSM drive (speed/current) cascades. The startup transient of the BU-HESS under step load demand (0–500 V) demonstrates that the proposed PI-NLD controller significantly outperforms the conventional PI by reducing undershoot from 12 $\%$ $%$ to 3 $\%$ $%$ , overshoot below 1.5 $\%$ $%$ , accelerating convergence from 0.25 s to 0.09 s, suppressing voltage oscillations, improving torque delivery, reducing current ripple by 25 $\%$ $%$ , and providing finite-time-like stabilization for robust and precise power-split operation in PSHVs. The result is a low-complexity controller suitable for real-time automotive platforms that preserves PI simplicity while delivering nonlinear robustness for BAT+UC HESS architectures.