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Observer-Based High Order Sliding Mode Control of Unity Power Factor in Three-Phase AC/DC Converter for Hybrid Electric Vehicle Applications
Jianxing Liu, Salah Laghrouche, Maxime Wack
TL;DR
HEV AC/DC converters need power-factor correction while avoiding the complexity and cost of extensive sensing. This paper uses a super-twisting sliding-mode observer and controller to estimate currents and load resistance from output-voltage measurements, maintaining power factor close to unity and outperforming conventional PI control in the reported simulations.
Problem
Existing approaches require multiple voltage and current measurements, increasing system complexity, cost, space, and reducing reliability.
Method
A super-twisting sliding-mode observer estimates phase currents and load resistance from measured output voltage, supporting observer-based sliding-mode control.
Results
The proposed observer-based super-twisting sliding-mode control maintains power factor close to unity and performs better than conventional PI control with less overshoot and sensitivity.
Takeaways & Limitations
The approach reduces current-sensor requirements while retaining robustness to changes in load resistance and source-voltage frequency.
Takeaways & Limitations
Measurement accuracy is inherently controlled by the sampling rate.
Abstract
from arXiv · showhide
In this paper, a full-bridge boost power converter topology is studied for power factor control, using output high order sliding mode control. The AC/DC converters are used for charging the battery and super-capacitor in hybrid electric vehicles from the utility. The proposed control forces the input currents to track the desired values, which can controls the output voltage while keeping the power factor close to one. Super-twisting sliding mode observer is employed to estimate the input currents and load resistance only from the measurement of output voltage. Lyapunov analysis shows the asymptotic convergence of the closed loop system to zero. Simulation results show the effectiveness and robustness of the proposed controller.
1 INTRODUCTION
The paper motivates an observer-based nonlinear controller for HEV AC/DC converters because conventional linear and sensor-heavy approaches are slow, condition-sensitive, and costly. It targets battery and super-capacitor charging with unity power factor using output-voltage-based current and load-resistance observation.
- HEV application: Power-factor-corrected utility interfaces support HEV charging by reducing line distortion and maximizing real power from the utility.The AC/DC converter charges the battery and super-capacitor while shaping utility current.
- Control motivation: Linear controllers can respond slowly and perform suboptimally across operating conditions because of slow modulation and duty-cycle/state-variable coupling.The paper contrasts these limitations with nonlinear approaches designed for wider operating ranges.
- Sensing limitations: Existing control and current-reconstruction methods require multiple voltage/current measurements or DC-link sampling every switching cycle, increasing implementation burden.The cited limitations include numerical computations and sampling-rate-dependent measurement accuracy.
- Proposed approach: The proposed design eliminates current sensors by using a super-twisting sliding-mode observer to estimate phase currents and load resistance from measured output voltage.The introduction states that voltage sensors measure the output and source voltages.
- Control objectives: The observer-based super-twisting controller targets unity power factor and ripple-free output voltage while providing fast observation-error convergence.A Lyapunov function is used to establish observer and controller stability, and the method is intended to remain functional under uncertainty and disturbances.
- Evaluation: Simulation results compare the proposed super-twisting sliding-mode controller with conventional PI control to assess performance.The paper reports this comparison in its simulation section but does not provide numerical results in the supplied passages.
2 PROBLEM FORMULATION
The problem formulation models a three-phase voltage-source AC/DC full-bridge boost converter and specifies measurable voltages, switching inputs, and current and output-voltage objectives. The formulation transforms the three-phase system into a rotating d-q frame to express current control as set-point tracking.
- 2.1 System Modeling: The system is a three-phase voltage-source AC/DC full-bridge boost converter connected to an equivalent resistive load.The model includes the converter power circuit and assumes a resistive load R_L.
- 2.1 System Modeling: The d-q model reduces current control to a set-point tracking problem for the transformed variables.The formulation uses this representation as the basis for the subsequent output-feedback super-twisting current controller.
- 2.1 System Modeling: The converter control inputs are discrete switching variables u = [u1 u2 u3]^T with values in {−1, +1}, alongside corresponding inverse controls.The switching states determine conducting and nonconducting elements in each bridge leg.
- 2.1 System Modeling: The model defines parasitic phase resistance, load resistance R_L, phase inductance L, output capacitance C, source voltages, and source angular frequency ω.The source voltages have different magnitudes but the same frequency and phase shift.
- 2.1 System Modeling: The three-phase variables are transformed into a synchronously rotating d-q frame using Park’s transformation.In this frame, the source-voltage components satisfy U_gd = 0 and U_gq = E.
- 2.2 Control Objectives: The measured quantities are the phase voltage U_g and output voltage U_0.This is the stated measurement assumption for the control formulation.
- 2.2 Control Objectives: The input phase currents must be in phase with their corresponding source voltages to obtain unity power factor.The current-control objective is later expressed as driving the sliding variables s_d and s_q to zero.
- 2.2 Control Objectives: The output-voltage objective is to drive the DC component toward U_0* while attenuating its AC component to a specified level.The formulation therefore combines voltage regulation with current-shape control.
3 OBSERVER-BASED SLIDING MODE CONTROLLER DESIGN
The controller combines a sliding-mode current observer with output-feedback super-twisting control, using output-voltage measurement to regulate converter currents and voltage. Observability and Lyapunov analyses support convergence of observation and tracking errors.
- Observer-based control structure: Observer-based control replaces plant states with observer states, reducing the number of required measurements.The control structure contains a sliding-mode current observer and a controller system.
- Super-twisting observer design: The nonlinear system is analyzed for observability before constructing the super-twisting observer.The design proceeds through observability analysis followed by ST observer construction.
- Observability analysis: The input currents i_d and i_q can be observed from output-voltage measurement when the control-input norm is nonzero.With singular inputs u_d = 0 and u_q = 0, the reduced system instead has detectability property.
- Observer convergence: The super-twisting observer achieves finite-time convergence of output-voltage observation errors and exponential stability of the reduced error dynamics.The reduced dynamics converge faster than the corresponding open-loop dynamics under the stated gain conditions.
- Reference-current and current-control design: The desired d–q currents are selected through input-output power balance, with i_d set to zero to guarantee unity power factor.Tracking the reference current regulates the output voltage to the desired value U* while the current controller targets zero sliding variables.
4 ST PARAMETER OBSERVER DESIGN AND POWER FACTOR ESTIMATION
The paper designs a super-twisting parameter observer to estimate load resistance and evaluates power factor from estimated phase-current and source-voltage characteristics. The estimation separates displacement and harmonic distortion effects.
- Load resistance estimation: The load resistance R_L is assumed to vary around its nominal value R_0 and is estimated using super-twisting observer dynamics.R_0 denotes the nominal load resistance.
- Load resistance estimation: The observer uses output-voltage error dynamics and boundedness assumptions to obtain the load-resistance estimate during sliding motion.The first derivative of the perturbation term Ψ_RL is assumed bounded.
- Power factor estimation: Three-phase power factor is calculated from the estimated single-phase power factors.The overall value is formed as a product of the three phase-current power-factor values.
- Power factor definition: Unity power factor corresponds to no harmonic distortion and no phase shift between input current and source voltage.The power-factor definition separates harmonic distortion PF_h from displacement PF_d.
- Power factor definition: RMS quantities distinguish the fundamental current component from the total current in the harmonic-distortion calculation.The period T is used to calculate the root-mean-square quantities.
- Power factor estimation: The single-phase estimator uses Fourier analysis for fundamental current–voltage phase displacement and harmonic analysis for input-current total harmonic distortion.The structure is implemented in MATLAB/SIMULINK.
5 SIMULATION RESULTS
Simulations compare observer-based super-twisting sliding mode control with linear PI control under varying load conditions. The proposed controller regulates output voltage, reduces input-current harmonics, and maintains power factor above 97%.
- The simulations vary load resistance and frequency at 1.0 s and 1.5 s to test controller performance under changing conditions.
- Both controllers eliminate phase shift between input current and source voltage, but PI control produces higher harmonics than ST SMC.
- Observer-based ST SMC regulates the converter output voltage to the desired level under load variation.
- Compared with ST SMC, PI control shows greater fluctuation around the DC level and higher voltage overshoot.
- PI control is less robust to load variation because its gains kp and ki depend on load resistance RL.
- Power factor values remain above 97% for observer-based ST SMC, while PI control gives lower values with more oscillations.
6 CONCLUSIONS
The observer-based super-twisting sliding mode controller reduces sensing requirements while regulating the converter and maintaining power factor close to unity. Simulations indicate improved robustness and lower overshoot than conventional PI control.
- The observer-based ST SMC reduces the number of current sensors and decreases system cost and volume.It uses output-voltage measurement to support observer-based control.
- The controller remains robust when load resistance and source-frequency conditions change.The conclusion specifically identifies variations in load resistance RL and source voltage frequency ω.
- The proposed observer-based ST SMC maintains the converter power factor close to unity.
- A strong Lyapunov function is used to prove stability of the observer and controller as a whole system.
- Simulation results show better performance than conventional PI control, with less overshoot and less sensitivity to disturbance and parametric uncertainty.