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Disturbance-Adaptive Finite-Time Control of Three-Phase Rectifiers

Koto Omiloli, Satish Vedula, Ayobami Olajube, Olugbenga Moses Anubi

Abstract

Three-phase AC-DC rectifiers are fundamental components in modern power electronics systems, yet achieving rapid voltage regulation and precise current tracking under load and grid disturbances remains challenging due to nonlinear dynamics and measurement uncertainties. This paper presents a finite-time control method for three-phase AC-DC rectifiers that achieves millisecond-scale regulation of DC-link voltage and grid currents under varying conditions. The proposed design employs a transformed augmented error-state dynamics model, extending the voltage dynamics to a two-state system to construct an adaptive sliding surface that guarantees fast finite-time convergence. A nonlinear sliding-mode voltage regulator with an online disturbance estimator ensures rapid and robust voltage tracking, while a fast current controller achieves finite-time dq-axis current tracking with minimal chattering. Theoretical results establish finite-time stability and provide explicit gain selection conditions. Simulation results demonstrate up to 99.40 per cent and 87.5 per cent reductions in voltage and current convergence times, respectively, compared to conventional robust controllers. Laboratory experiments further validate the approach, showing 33.33 per cent lower voltage ripple, 33.33 per cent faster rise time, and 32.43 per cent reduced steady-state error relative to a recent method. These results confirm improvements in transient performance, convergence, and overall system stability, highlighting the method's practical applicability for high-performance rectifier control.

Disturbance-Adaptive Finite-Time Control of Three-Phase Rectifiers

Abstract

Three-phase AC-DC rectifiers are fundamental components in modern power electronics systems, yet achieving rapid voltage regulation and precise current tracking under load and grid disturbances remains challenging due to nonlinear dynamics and measurement uncertainties. This paper presents a finite-time control method for three-phase AC-DC rectifiers that achieves millisecond-scale regulation of DC-link voltage and grid currents under varying conditions. The proposed design employs a transformed augmented error-state dynamics model, extending the voltage dynamics to a two-state system to construct an adaptive sliding surface that guarantees fast finite-time convergence. A nonlinear sliding-mode voltage regulator with an online disturbance estimator ensures rapid and robust voltage tracking, while a fast current controller achieves finite-time dq-axis current tracking with minimal chattering. Theoretical results establish finite-time stability and provide explicit gain selection conditions. Simulation results demonstrate up to 99.40 per cent and 87.5 per cent reductions in voltage and current convergence times, respectively, compared to conventional robust controllers. Laboratory experiments further validate the approach, showing 33.33 per cent lower voltage ripple, 33.33 per cent faster rise time, and 32.43 per cent reduced steady-state error relative to a recent method. These results confirm improvements in transient performance, convergence, and overall system stability, highlighting the method's practical applicability for high-performance rectifier control.
Paper Structure (12 sections, 4 theorems, 44 equations, 12 figures, 3 tables)

This paper contains 12 sections, 4 theorems, 44 equations, 12 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Notations and Definitions
  3. Problem Formulation
  4. CONTROL DEVELOPMENT
  5. Voltage Regulation
  6. Current Regulation
  7. Numerical and Experimental Results
  8. Numerical Simulation Results
  9. Experimental Results
  10. Scenario 1 - Step Voltage Reference
  11. Scenario 2 - Current Tracking under Constant Load
  12. Conclusion

Key Result

lemma 1

1: Let $z: \mathbb{R}_+ \rightarrow \mathbb{R}$ be a function satisfying $\underset{t}{\sup}|\dot{z}(t)| \leq \gamma$, $\underset{t}{\sup} |\ddot{z}(t)|\le \epsilon$. Then for the filter dynamics in d1 and d2, there exists, $T < \infty$ such that the

Figures (12)

  • Figure 1: System-level circuit implementation of the proposed adaptive control scheme.
  • Figure 2: DC-link voltage responses under varying load disturbances using (a) the proposed method, (b) the proportional–integral cascaded method, (c) the adaptive STA method, (d) the integral terminal SMC, (e) disturbance estimation using the ESO and (f) disturbance estimation using the proposed method.
  • Figure 3: Comparison of the voltage control signals for the proposed method with existing methods. $E_1$, $E_2$, $E_3$ and $E_4$ are the respective control signal norms computed.
  • Figure 4: $d$-axis current response demonstrating effective tracking of the reference signal derived from the voltage regulation loop.
  • Figure 5: Current regulation comparison across the proposed method, the proportional–integral cascaded method, the adaptive STA method, and the integral terminal SMC.
  • ...and 7 more figures

Theorems & Definitions (13)

  • Definition 1: Signum function
  • Definition 2: Saturation function
  • lemma 1
  • proof
  • Theorem 1
  • Remark 1
  • proof
  • lemma 2
  • proof
  • Theorem 2
  • ...and 3 more