In the rapidly evolving field of electric vehicle (EV) infrastructure, mobile charging robots represent a cutting-edge application of robot technology, offering flexible and on-demand charging services. These robots leverage advanced power electronics to efficiently manage energy transfer, with the dual-active-bridge (DAB) DC-DC converter playing a pivotal role due to its isolation, bidirectional power flow, and high power density. However, challenges such as poor dynamic performance under disturbances and high current stress in traditional modulation schemes like single phase shift (SPS) can hinder the reliability of robot technology systems. To address this, we propose a hybrid control strategy combining sliding mode control (SMC) and proportional-integral (PI) control under dual phase shift (DPS) modulation, optimized for current stress reduction using the Karush-Kuhn-Tucker (KKT) algorithm. This approach enhances the robustness and efficiency of robot technology in mobile charging applications, ensuring stable operation across varying loads and conditions.
The DAB converter topology consists of two full-bridge circuits (H1 and H2), a high-frequency isolation transformer, a resonant inductor, and filtering capacitors, as illustrated in the system diagram. Key parameters include input voltage $U_{in}$, output voltage $U_{out}$, transformer turns ratio $n$, switching frequency $f_s$, and resonant inductance $L$. The modulation involves two phase-shift angles: the inner phase-shift angle $D_a$ between switches in the same bridge, and the outer phase-shift angle $D_b$ between bridges, controlling power direction. For power flow from H1 to H2, $0 < D_b < 1$. The voltage conversion ratio is defined as $k = U_{in} / (n U_{out})$, with $k \geq 1$ assumed for analysis. Under DPS modulation, the converter operates in two modes: Mode 1 where $0 \leq D_a \leq D_b \leq 1$, and Mode 2 where $0 \leq D_b \leq D_a \leq 1$. This study focuses on Mode 1, with the operating waveform divided into intervals based on $t_0 = 0$, $t_1 = D_a T_{1/2}$, $t_2 = D_b T_{1/2}$, $t_3 = (D_a + D_b) T_{1/2}$, and $t_4 = T_{1/2}$, where $T_{1/2} = 1/(2f_s)$.
The inductor current $I_L$ during the first half-cycle is derived as follows:
$$I_L(t_0) = \frac{n U_{out}}{4 f_s L} \left[ (1 – k) + 2D_a (k – 1) \right],$$
$$I_L(t_1) = \frac{n U_{out}}{4 f_s L} \left[ k(1 – 2D_a) + 2D_b (k – 1) \right],$$
$$I_L(t_2) = \frac{n U_{out}}{4 f_s L} \left[ k(1 – 2D_b) + 2D_a (k – 1) \right],$$
$$I_L(t_3) = \frac{n U_{out}}{4 f_s L} \left[ (2D_b – 1)k + 2D_a (k – 1) \right].$$
The average power transferred is given by:
$$P_{avg} = \frac{n U_{in} U_{out}}{4 f_s L} \left( 2D_b – D_a^2 – D_b^2 \right).$$
Using the base power $P_{max} = \frac{n U_{in} U_{out}}{8 f_s L}$ and base current $I_{max} = \frac{P_{max}}{U_{in}} = \frac{n U_{out}}{8 f_s L}$, the normalized power and current stress are:
$$P^* = \frac{P_{avg}}{P_{max}} = 2D_b – D_a^2 – D_b^2,$$
$$I^* = \frac{I_L}{I_{max}} = 2 \left[ (1 – k) + 2D_a (k – 1) \right].$$
These equations form the basis for optimizing current stress in robot technology applications.
To minimize current stress for a given power $P^*$, we apply the KKT algorithm, treating current stress as the objective function with power as an equality constraint and $0 \leq D_a \leq D_b \leq 1$ as inequality constraints. The Lagrangian is formulated as:
$$\mathcal{L}(D_a, D_b, \lambda, \mu) = I^* + \lambda (P^* – P_{ref}) + \sum \mu_j g_j(D_a, D_b),$$
where $P_{ref}$ is the reference power, $\lambda$ is the Lagrange multiplier, and $\mu_j$ are slack variables. Solving the KKT conditions yields optimal phase-shift angles that depend on $k$ and $P^*$. For instance, when $0 \leq P^* < 1/2$ and $k \geq 1$, the optimal angles are:
$$D_a = \frac{1 – k}{2(k^2 – k + 1)} – \frac{P^*}{2\sqrt{6k^2 – 4k + 4}},$$
$$D_b = \frac{1 – k}{2(k^2 – k + 1)} + \frac{P^*}{2\sqrt{6k^2 – 4k + 4}},$$
with the minimized current stress:
$$I^*_{min} = \frac{1}{2} \left( \sqrt{6k^2 – 4k + 4} – 2k + 2 \right) – \frac{P^*}{\sqrt{6k^2 – 4k + 4}}.$$
Similar分段 optimizations are derived for other power ranges, such as $1/2 \leq P^* < 2/3$ and $P^* \geq 2/3$, ensuring reduced current stress across operating conditions in robot technology systems.
The hybrid control strategy employs a voltage outer loop with SMC and a current inner loop with PI control. Defining the voltage error as $e = U_{ref} – U_{out}$, the sliding surface is designed as:
$$s = k_1 e + \dot{e},$$
where $k_1 > 0$ is a gain. To reduce chattering, an exponential reaching law with a hyperbolic tangent function is used:
$$\dot{s} = -k_2 s – k_3 \tanh(s),$$
with $k_2$ and $k_3$ as positive gains. The system dynamics are derived from the output voltage equation:
$$\frac{d U_{out}}{dt} = \frac{1}{C} I(t) – \frac{1}{RC} U_{out}(t).$$
The error dynamics become:
$$\dot{e} = -\dot{U}_{out}, \quad \ddot{e} = -\frac{1}{C} \dot{I}(t) + \frac{1}{RC} \dot{U}_{out}(t).$$
Setting $\dot{s} = 0$, the control law for the inductor current reference is:
$$I_{ref} = C k_1 \dot{e} + C k_2 \int s \, dt + C k_3 \int \tanh(s) \, dt + \frac{C}{R} U_{out}.$$
This hybrid approach combines the fast response of SMC with the steady-state accuracy of PI control, enhancing the resilience of robot technology in mobile charging scenarios.
Simulation results validate the proposed strategy using parameters typical for robot technology applications. The main circuit parameters are summarized in Table 1.
| Parameter | Value |
|---|---|
| Input Voltage $U_{in}$ | 450 V |
| Output Voltage $U_{out}$ | 300 V |
| Resonant Inductance $L$ | 75 μH |
| Transformer Turns Ratio $n$ | 3:2 |
| Switching Frequency $f_s$ | 20 kHz |
| Input/Output Capacitance $C_a$, $C_b$ | 600 μF |
Control parameters for the inner PI loop and outer SMC are listed in Table 2.
| Control Strategy | Parameter | Value |
|---|---|---|
| Inner PI Loop | $k_P$, $k_I$ | 0.01, 1.20 |
| Outer PI Loop (Traditional) | $k_P$, $k_I$ | 0.6, 60.0 |
| Sliding Mode Control | $k_1$, $k_2$, $k_3$ | 11.1, 1666, 6000 |
Under startup conditions with $U_{in} = 450\,V$, $U_{out} = 250\,V$, and $R = 10\,\Omega$, the proposed hybrid control reduces startup time from 13 ms (traditional DPS) to 4 ms, a 69.2% improvement, demonstrating enhanced dynamic performance for robot technology. For load transients from $R = 10\,\Omega$ to $20\,\Omega$, the voltage deviation decreases by 83.3% (from 24 V to 4 V), and settling time shortens by 30% (from 20 ms to 14 ms). Current stress optimization is evaluated across power levels: at full load ($P^* = 10\,kW$, $R = 6\,\Omega$), current stress drops by 37.3% from 67 A to 42 A; at half-load ($R = 10\,\Omega$), it reduces by 10% from 30 A to 27 A; and at light load ($R = 20\,\Omega$), it decreases by 5.4% from 18.5 A to 17.5 A. These improvements underscore the benefits for robot technology, including extended component lifespan, higher reliability, and energy efficiency.
In conclusion, the integration of current stress optimization with sliding mode PI hybrid control in DAB converters significantly advances mobile charging robot technology. By leveraging KKT-based optimization and robust control techniques, the system achieves faster response, reduced current stress, and improved stability, ensuring reliable operation in diverse charging scenarios. This approach highlights the potential of robot technology to transform EV infrastructure through innovative power management solutions.