Fuzzy-Aided P–PI Control for Start-Up Current Overshoot Mitigation in Solid-State Lithium Battery Chargers

Abstract

A battery charger for solid-state lithium battery packs was developed and implemented. The power stage used a phase-shifted full-bridge converter integrated with a current-doubler rectifier and synchronous rectification. Dual voltage and current control loops were employed to enable constant-voltage and constant-current charging modes. To improve the lifespan of the output filter capacitor, the current-doubler rectifier was adopted to effectively reduce output current ripple. During the initial start-up phase, as the charger transitions from constant-voltage to constant-current output mode, the use of proportional–integral control in the voltage and current loop error amplifiers may cause current overshoot during the step-rising phase, primarily due to the integral action. Therefore, this study incorporated fuzzy control, proportional control, and proportional–integral control strategies into the current-loop error amplifier. This approach effectively reduced the current overshoot during the step-rising phase, preventing the charger from mistakenly triggering the overcurrent protection mode. The analysis and design considerations of the proposed circuit topology and control loop are presented. Experimental results agree with theoretical predictions, thereby confirming the validity of the proposed approach.

1. Introduction

In recent years, eco-friendly technologies have become increasingly important in addressing greenhouse gas issues, and clean energy sources are being adopted to reduce greenhouse gas emissions. Currently, popular rechargeable batteries include lead-acid, nickel-metal hydride (Ni-MH), nickel-cadmium (Ni-Cd), and lithium-ion batteries. These batteries are widely employed in various types of electric vehicles, such as forklifts, pallet trucks, stackers, and other mobile equipment. Conventionally, lead-acid batteries have been used to supply driving power for electrified vehicles. However, lead-acid batteries are characterized by their bulky and heavy structure, while Ni-Cd batteries raise environmental concerns due to cadmium contamination. Among the various types of secondary batteries, lithium-ion batteries exhibit the highest power and energy densities, making them ideal candidates to replace other rechargeable batteries in demanding applications, particularly those requiring large-capacity battery packs [1,2,3,4,5].

A solid-state lithium battery utilizes a solid electrolyte instead of the liquid or gel-based electrolytes used in conventional lithium-ion batteries. By employing solid materials such as ceramics, glass, and sulfides as electrolytes, the flammability issues associated with liquid electrolytes are eliminated, thereby reducing the risk of thermal runaway. Moreover, compared to conventional lithium batteries, the solid-state lithium batteries offer several advantages, including faster charging speeds, a wider operating temperature range, higher energy density, longer cycle life, and slower capacity degradation [6,7].

Whether in liquid or solid-state form, lithium-ion batteries are increasingly adopted in portable electronic devices and electric vehicles for both backup power and powertrain applications, due to their high power and energy density. In large-capacity battery packs, a dedicated power supply is required to charge the lithium-ion battery pack efficiently, as rapid full charging is often desired. For this reason, the typical lithium-ion battery chargers operate in two output modes: constant-current (CC) and constant-voltage (CV). Under the low state-of-charge conditions, the battery charger is operated in constant-current mode to supply a uniform charging current, thereby enabling rapid charging. As the battery voltage of the lithium-ion battery pack approaches the predetermined full-charge voltage, the charger transitions to constant-voltage mode, maintaining this voltage while the charging current gradually decreases.

The fuzzy logic is a computational approach designed to manage uncertainty and ambiguity by emulating human reasoning and decision making. It employs a set of fuzzy rules to perform inference and control tasks without relying on precise mathematical models. The fuzzy logic is most commonly applied in fuzzy control systems, which incorporate the processes of fuzzification, fuzzy inference, and defuzzification. Fuzzy logic has found practical applications in various fields, including home appliances, autonomous driving and vehicle controls, industrial automation systems, robotics, and intelligent systems. In [8], fuzzy control was applied to a battery charger, where a fuzzy proportional–integral–derivative control strategy was employed to enhance the control performance of the charger. In addition, the genetic algorithms were used to optimize the membership functions and fuzzy rules of the fuzzy controller. In [9], the fuzzy logic was employed to enhance the charger’s control performance by improving transient response speed and reducing inductor current ripple during steady-state operation.

In this study, the battery charger integrated power factor correction (PFC) with a current-doubler rectifier and synchronous rectification. The PFC stage rectified the AC input power into a regulated DC voltage of approximately 400 V and reshaped the input current waveform to closely follow a sinusoidal reference, thereby achieving a near-unity power factor. Moreover, the power stage of the phase-shifted full-bridge (PSFB) converter with a current-doubler rectifier (CDR) and synchronous rectification offered the low switching losses in the power switches and reduced the current ripple on the charger output side [10,11,12]. Furthermore, this study integrated the proportional (P) control, proportional–integral (PI) control, fuzzy logic control, and multiplexer into the current-loop feedback controller of the charger to mitigate the step current overshoot during the startup phase and prevent false triggering of overcurrent protection (OCP).

Only a limited number of studies have effectively addressed and resolved the issue of start-up current overshoot. In [13], the authors have sought to address the current-overshoot-suppression charging method for super-capacitor trams. A cooperative charging protocol was designed to achieve current balancing among chargers, and a set-point modulation method was introduced to smoothly adjust the chargers’ set-points, thereby suppressing current overshoot.

This study builds upon the overshoot mitigation techniques presented in [14,15,16]. The works referenced in [14,15,17,18], as well as the present study, adopt a power stage topology based on a PSFB converter integrated with a current-doubler rectifier. Furthermore, approaches involving the transition from P control to PI control were employed in [14,15,16] to suppress the output current overshoot during the start-up phase of the battery charger. In contrast, this study further enhances the control strategy by integrating fuzzy logic control into the current-loop controller, thereby improving the effectiveness of overshoot mitigation. Additionally, the proposed battery charger was specifically designed to charge solid-state lithium battery packs. Technical comparisons of literatures are list in

Table 1. Technical comparisons of literatures.

Literature	[13]	[17]	[14]	[15]	[18]	[16]	This Study
Application	Charger	Charger	Charger	Charger	Converter	Charger	Charger
Load type	Super-capacitor	Lithium-ion battery	LiFePO4 battery	Liquid-state LiFePO4 battery pack	Resistance load	Battery module	Solid-state lithium battery
Power topology	No mentioned	Full-bridge phase-shifted CDR	PSFB CDR (No resonant inductor)	PSFB CDR (No resonant inductor)	PSFB CDR	No mentioned	PSFB SR CDR
Control	Set-point-modulation cooperative charging method	No mentioned	P transiting to PI	PI and P transiting to PI	No mentioned	P switching to PI	Fuzzy-aided P–PI

.

The charger developed in this study was designed to suppress the current overshoot that occurs during the initial startup phase, specifically when transitioning from constant-voltage to constant-current charging mode. This approach offers the following advantages for solid-state lithium batteries:

• Excessively high charging current can increase interfacial stress or cause localized heat accumulation, potentially leading to reduced reliability and accelerated battery aging.
• Although solid-state lithium batteries have a lower risk of lithium dendrite growth compared to liquid lithium batteries, high voltage and current conditions may still promote dendrite formation. These dendrites can potentially penetrate the solid electrolyte, leading to internal short circuits.
• Liquid and solid-state lithium batteries have different state-of-charge characteristics; therefore, it is not recommended to use traditional lithium battery chargers directly. Instead, a charging strategy should be developed based on the specific characteristics of solid-state batteries, followed by the design and development of a dedicated solid-state lithium battery charger.
• Current overshoot during charging is an undesirable phenomenon that can accelerate the aging of both the circuit component and the battery.

This paper is organized into six sections. Section 2 presents the power stage, focusing on the PSFB converter with a current-doubler rectifier and synchronous rectification. Section 3 describes the control loops for constant-voltage and constant-current charging. Section 4 discusses design considerations for the power stage and the proposed current control loop. Section 5 provides the experimental results. Finally, the conclusions of this study are presented in Section 6.

2. Power Stage

A circuit block diagram of the battery charger proposed in this study is shown in Figure 1. It was composed of the electromagnetic interference (EMI) filter, bridge rectifier, power factor correction stage, PSFB converter, transformer, current-doubler rectifier (CDR), synchronous rectification (SR), filter capacitor, and standby power supply. The standby power supply provided the DC power for driving the cooling fans and the control chips of the proposed control system. Moreover, the input side of the charger was connected to a single-phase (1-ϕ) AC source, while the output side was connected to a solid-state lithium battery pack. Additionally, the output current of the charger was monitored for overcurrent protection to prevent potential damage. The detected current signal was fed into the PSFB controller.

The PSFB converter circuit integrated with a current-doubler filter and synchronous rectification is illustrated in Figure 2. The circuit components was composed of the four power MOSFETs (Q_a-Q_d), blocking capacitor (C_b), transformer (T_r), synchronous rectification (SR) MOSFETs (Q_sr1 and Q_sr2), current-doubler inductors (L_cd1 and L_cd2), filter capacitor (C_o). Moreover, the input power supply to the PSFB converter is denoted as V_i, and the output voltage and current are represented as V_o and I_o, respectively. The calculated formulas for the component values and specifications are referenced from [19] and are described as follows.

It is assumed that two current-doubler inductors have the same value, which can be given by

L_cd1 = L_cd2 = V_o (1 − d_psfb)/(∆i_cd1 f_sw),

(1)

where f_sw is the operating frequency of Q_a-Q_d. The duty cycle ratio is d_psfb, it can be expressed as

d_psfb = (V_o/V_i) (n_p/n_s),

(2)

where n_p denotes the number of primary-side winding turns of the transformer, n_s represents the numbers of secondary-side winding turns of the transformer. Moreover, in (1), ∆i_lcd1 denotes the peak-to-peak current of the inductor L_cd1, and it can be expressed as

∆i_cd1 = ∆i_cd2 = k I_o/2,

(3)

where k represents the percentage of the inductance’s peak-to-peak ripple current relative to the average current.

The root mean square (rms) current flowing through the power MOSFETs (Q_a-Q_d) is given by

$$i_{\mathit{Qad}\left(\mathit{rms}\right)}=\sqrt{0.5} (I_o/2) (n_s/n_p),$$

(4)

The rms current flowing through Q_sr1 and Q_sr2 is given by

$$i_{\mathit{Qsr}\left(\mathit{rms}\right)}=I_o\sqrt{0.25+(d_{\mathit{psfb}}/2)},$$

(5)

The voltage stress of Q_sr1 and Q_sr2 is given by

V_Qsr = V_o/d_psfb,

(6)

The capacitance value of the output capacitor C_o can be expressed as

$$C_o=V_o (1-2 d_{\mathit{psfb}})/(16 {L_{\mathit{cd}}}_1 ∆V_{\mathit{co}} f_{\mathit{sw}}^2),$$

(7)

where ∆V_co represents the voltage ripple across the output capacitor.

3. Control Loop

The circuit block diagram of the control loop for the battery charger is illustrated in Figure 3. It is composed of the current shunt, voltage amplifier, voltage divider, error amplifiers, PSFB controller, and isolated gate driver.

In the voltage and current feedback loops, the error amplifiers are used to control the PSFB converter, as illustrated in Figure 4. The circuit is composed of the amplifiers (EA_v and EA_c), impedance elements (Z_v1, Z_v2, Z_c1, and Z_c2), and a switch S_w.

The voltage signal V_{o_sen} obtained from the voltage divider is proportional to the charger’s output voltage V_o, while the output voltage V_{io_sen} from the voltage amplifier is proportional to the charger’s output current I_o, as shown in Figure 5 [16]. Moreover, V_{ref_vo} serves as the reference command for the charger to operate in constant-voltage charging mode, and V_eav represents the output voltage from the voltage-loop error amplifier. Similarly, V_{ref_io} is the reference command for constant-current charging mode, and V_eac denotes the output voltage of the current-loop error amplifier.

Based on V_eav and V_eac, along with their small-signal perturbations, the input to the PSFB controller adjusts the phase-shifted angle of v_ga-v_gd, thereby enabling the charger to maintain either a constant-voltage or constant-current charging mode. When the charger is operated in constant-voltage charging mode, the switch S_w remains in the off state; conversely, during constant-current mode operation, S_w is turned on.

In Figure 4, the impedance components Z_c1 and Z_c2 can be configured as a resistor–capacitor network to realize PI control, which increases the DC gain and eliminates the steady-state error. Additionally, the system crossover frequency is appropriately set to meet the required phase margin [20,21]. At the initial start-up of the charger, the charger’s output voltage V_o gradually increases due to the soft-start mechanism, initially reaching the constant-voltage output mode before transitioning into constant-current output mode. The corresponding voltage waveforms of the error amplifiers vary over time, as illustrated in Figure 5, where V_ean denotes the voltage at the inverting terminal of the EA_c.

Since the input impedance of the error amplifier is ideally infinite, $V_{\mathit{ean}}\cong V_{\mathit{io}\_\mathit{sen}}$. As V_ean varies in direct proportion to V_{io_sen} and I_o, the operating principle is described as follows:

• When V_ean < V_{ref_io}, the EA_c output voltage reaches its positive saturation, resulting in V_eac = V_eac(max).
• As I_o increases and reaches the expected constant current I_{o_cc}, the V_ean reaches V_{ref_io}, prompting the current-loop error amplifier to enter its feedback operation. Due to the relatively slow response of the PI-controlled error amplifier, V_eac gradually decreases over a delay period t_d until it reaches the expected control voltage V_{exp_cc} for constant-current charging. This delay results in a current overshoot I_{o_os}, as illustrated in Figure 5.
• This current overshoot I_{o_os} may trigger the charger overcurrent protection; therefore, it must be minimized.

Although a proportional–integral–derivative control can be employed to accelerate the system response, the converters presented in [22,23,24] did not address the suppression of the output current overshoot.

Therefore, this study replaced the PI control in the error amplifier of the charger’s current control loop with a P–PI control approach, and integrated the fuzzy logic control with the multiplexer technology to effectively mitigate the current overshoot caused by step increases during the charger’s start-up phase. The control system block diagram is illustrated in Figure 6. The control system was composed of an error calculation unit (ECU), fuzzy logic unit, P control unit, PI control unit, and multiplexer (MUX). Moreover, the analog voltage signal V_{io_sen} was converted into a digital value by an analog-to-digital converter (ADC), and the digital output of the multiplexer was subsequently converted back into an analog voltage signal V_eac through a digital-to-analog converter (DAC), which was then used to control the PSFB controller. Among them, the expression for the computation performed by the error calculation unit is given by

$$\left\{\begin{array}{c}e\left(t\right)=V_{\mathit{ref}\_\mathit{io}}-V_{\mathit{io}\_\mathit{sen}}\\ ∆e\left(t\right)=e_n\left(t\right)-e_{n-1}\left(t\right)\end{array}\right.$$

(8)

where e(t) represented the instantaneous error, and ∆e(t) denoted the error differential value. e(t) and ∆e(t) served as the input variables for the fuzzy logic system. Based on the predefined rule table and fuzzy sets, the fuzzy logic performed inference on e(t) and ∆e(t) to generate a selection signal that controlled the multiplexer, which determined whether the output from the P control or PI control was used. The selected output was then passed through a digital-to-analog converter to produce an analog voltage V_cea, which is used to control the PSFB controller.

As shown in Figure 6, the operating flowchart of the proposed current loop controller is presented in Figure 7 and is detailed as follows:

• Current acquisition and conversion: The output current I_o was detected by a current shunt, producing an analog signal V_{io_sen} which was then converted into a digital current value via an analog-to-digital converter.
• ECU: The controller established the desired reference current V_{ref_io}, compared it with the actual output current I_o, and calculated the error $e(t)=V_{\mathit{ref}\_\mathit{io}}-V_{\mathit{io}\_\mathit{sen}}$. It then determines the rate of change of the error as $∆e\left(t)=e_n\right(t) -e_{n-1}\left(t\right)$.
• Fuzzy logic unit: Taking $e\left(t\right)$ and $∆e\left(t\right)$ as input, the fuzzy controller inferred which controller should be selected for the current state:

  (1)

  If $e\left(t\right)$ and $∆e\left(t\right)$ were large and changed rapidly, a P control was selected.

  (2)

  If $e\left(t\right)$ and $∆e\left(t\right)$ were small and relatively stable, a PI control was adopted.

• MUX: Based on the control signal S determined by the fuzzy logic unit, the output control action was selected from either the P or PI control accordingly.
• Digital-to-analog converter: The digital P or PI control signal output from the multiplexer was converted into an analog voltage V_eac through a digital-to-analog converter and then fed into the PSFB controller.
• Closed-loop control: The system continuously and dynamically adjusted its output based on this mechanism to regulate charging current, particularly to promptly suppress overshoot induced by the step rising during startup phase.

4. Design Considerations

The specifications of the battery charger and the solid-state lithium battery pack are listed in

Table 2. Specifications of the battery charger and pack.

Single-Phase AC Input
Input AC voltage	220 Vrms
Input AC frequency	60 Hz
Phase-Shifted Full-Bridge Converter
Input voltage, Vi	400 V
Output maximum voltage, Vo	28 V
Output current range, Io	0 to 70 A
Solid-State Battery Pack
Charging-end voltage	26.7 V
Discharging-end voltage	18.9 V
SOC-dependent charging voltage	18 V ≅ 0 22 V ≅ 73% 24 V ≅ 86%
Capacity	70 Ah

.

Based on the specifications provided in Table 2, and by substituting n_p = 25, n_s = 7, V_i = 400 V, V_o = 28 V, I_o = 70 A, k = 0.2, and f_sw = 100 kHz into (1)–(7), the following component values are obtained: L_cd1 = L_cd2 = 32.65 μH, i_Qad(rms) = 6.93 A, i_Qsr(rms) = 43.87 A, V_Qsr = 112 V, and C_o = 8.2 μF (1000 μF in practice).

The rule table of fuzzy control defined in this study is listed in

Table 3. Fuzzy control linguistic rule table.

Condition	Detection Rule	Control Method
Start-up phase	≦millisecond	P
Large e(t)	|e(t)| > Error threshold high	P
Large ∆e(t) and small e(t)	|∆e(t)| > Slope threshold high |e(t)| < Error threshold low	PI
Small e(t) and steady-state	|e(t)| < Error threshold low |∆e| < Slope threshold low	PI

. The values of e(t) and ∆e(t) are converted into fuzzy linguistic terms, including the negative big (NB), negative small (NS), zero (ZE), positive small (PS), and positive big (PB). The fuzzy rule table was established using these fuzzy linguistic terms, with the rule weightings indicating the relative preference between P and PI control strategies. In the steady-state region centered around (ZE/ZE), the control strategy tended to favor PI control to improve accuracy and minimize steady-state error. Conversely, in rapidly changing boundary regions such as (NB/NB) and (PB/PB), P control was preferred to avoid integral saturation and suppress current overshoot.

As shown in Figure 6, when e(t) and ∆e(t) were input to the fuzzy logic unit, it generated a control preference degree μ as the output. Based on the μ value, PI control was selected if μ > 0.5, whereas P control was chosen if μ < 0.5. The rule weighting values corresponding to NB, NS, ZE, PS, and PB are listed in

Table 4. Rule weighting value.

∆e(t)	NB	NS	ZE	PS	PB
e(t)
NB	0	0.1	0.2	0.3	0.2
NS	0.1	0.3	0.5	0.4	0.2
ZE	0.2	0.6	1	0.6	0.3
PS	0.3	0.4	0.6	0.4	0.2
PB	0.2	0.3	0.3	0.2	0

.

5. Experimental Results

The experimental waveforms in Figure 8, Figure 9 and Figure 10 were measured using a digital oscilloscope (Model number: HDO4054, LeCroy, Chestnut Ridge, NY, USA). The experimental waveforms of the developed battery charger using conventional PI control and the proposed fuzzy-aided P–PI control are presented in Figure 8 and Figure 9, where V_o represents the charger’s output voltage, I_o denotes the charger’s output current, V_ean indicates the voltage at the inverting terminal of the current-loop error amplifier (EA_c, as shown in Figure 4), and V_eac corresponds to the output voltage of the current-loop error amplifier.

In Figure 8, the battery pack was charged at initial voltages of 18 V and 22 V, respectively. When PI control was employed in the charger’s current feedback loop, a current overshoot I_{o_os} occurred during the start-up phase within delay time t_d, where I_{o_os} exceeded the rated constant current of 25 A before the charger transitioned into the constant-current charging mode at 70 A. The charging voltage corresponding to the SOC is shown in Table 2.

In Figure 9, the battery pack was similarly charged from the initial voltages of 18 V and 22 V, respectively. In Figure 9, the maximum output voltage V_o(max) was 24.5 V during the transient process. Although the maximum output voltage V_o(max) was lower than the final charging voltage of 26.7 V, it remained within the acceptable specification range; therefore, the battery pack was not adversely affected. The charging voltage corresponding to the SOC is shown in Table 2.

However, with the implementation of the proposed fuzzy-aided P–PI control in the charger’s current control loop, I_{o_os} was significantly reduced from 25 A to 5 A prior to the transition into the constant-current charging mode at 70 A. Compared to conventional PI control, this result clearly demonstrates the effectiveness of the proposed control strategy in mitigating current overshoot during the start-up phase.

The performance of the developed battery charger using PI control and the proposed fuzzy-aided P–PI control in the current control loop was compared as follows:

• PI control: The current overshoot was 25 A/70 A = 35.71%, with a steady-state error of less than 0.5%.
• Fuzzy-aided P–PI control: The current overshoot was 5 A/70 A = 7.14%, with a steady-state error of less than 0.5%.

Therefore, the proposed fuzzy-aided P–PI control strategy effectively reduces the start-up current overshoot while maintaining high control accuracy in steady-state operation.

P and PI control are widely adopted and effective strategies in many control systems, particularly in stable and linear applications. However, in systems characterized by strong nonlinearity, parameter uncertainties, or significant external disturbances, traditional PI or PID controllers often require extensive tuning, iterative adjustments, and trial-and-error processes to achieve an acceptable trade-off between stability and performance. These limitations can diminish development efficiency and restrict the flexibility of the control strategy in practical implementations. The adoption of fuzzy control is not intended to increase the complexity of control design, but rather to overcome the fundamental limitations encountered by traditional controllers when dealing with complex or poorly defined systems.

Fuzzy control offers several advantages, including independence from precise mathematical models, robustness to parameter variations, and the capacity to incorporate expert knowledge and rule-based logic. These characteristics enable fuzzy controllers to outperform conventional PI controllers in a wide range of applications. The practical effectiveness of fuzzy control can be validated through numerical simulations, performance metrics—such as integral of absolute error (IAE), integral of squared error (ISE), and integral of time-weighted absolute error (ITAE)—as well as experimental verification. These methods provide an objective framework for evaluating control strategies in terms of steady-state error, response time, overshoot, and overall system stability under specific performance requirements. Therefore, the adoption of fuzzy control should be based on a comprehensive understanding of the system’s dynamic behavior and real-world application demands, rather than being driven solely by the goal of simplifying controller design. This study posits that, if computational and experimental results demonstrate that fuzzy control can significantly enhance performance under defined conditions, then its integration into the controller is not only reasonable, but also academically sound, engineering-justifiable, and forward-looking.

The input AC current, which closely approximated a sinusoidal waveform and was in phase with the input AC voltage, is shown in Figure 10. Under the conditions of V_o = 24 V and I_{o_cc} = 70 A, the root mean square values of the input AC voltage and current were v_ac = 220 V_rms and i_ac = 9.1 A_rms, respectively. Therefore, the power factor was approximately unity. The charging voltage corresponding to the SOC is shown in Table 2.

Using the fast Fourier transform function of the digital oscillator (Model number: SDS2104X Plus, Siglent Tech. Corp., Solon, OH, USA), the total harmonic distortions (THDs) of v_ac and i_ac were analyzed, as shown in Figure 11. The THD of the AC input voltage was primarily concentrated in the fundamental component H_v1. In contrast, the AC input current exhibited significant components at the fundamental, third, fifth, and seventh harmonics (H_c1, H_c3, H_c5, and H_c7), with corresponding amplitudes of 9.1 A_rms, 0.86 A_rms, 0.34 A_rms, and 0.07 A_rms, respectively. By employing an EMI filter, the high-order harmonics can be effectively attenuated to comply with various safety standards.

Figure 12 shows the prototype of the battery charger and the experimental platform, including the input AC source, the charger prototype, and the solid-state lithium battery pack.

6. Conclusions

A battery charger for solid-state lithium batteries was developed and implemented in this study. The proposed power stage was based on a phase-shifted full-bridge converter integrated with a current-doubler rectifier and synchronous rectification. To achieve constant-voltage and constant-current charging modes, both voltage and current control loops were employed. In the current control loop, the fuzzy inference was integrated with proportional and proportional–integral control strategies to realize segmented optimal control, effectively addressing both start-up current overshoot and steady-state error. The proposed fuzzy-aided P–PI control strategy significantly mitigated output current overshoot during the charger’s start-up phase while maintaining high control accuracy during steady-state operation.