Adaptive-Gain Second Order Sliding Mode Observer Design for Switching Power Converters (1303.5841v2)

Abstract: In this paper, a novel adaptive-gain Second Order Sliding Mode (SOSM) observer is proposed for multicell converters by considering it as a class of hybrid systems. The aim is to reduce the number of voltage sensors by estimating the capacitor voltages only from the measurement of load current. The proposed observer is proven to be robust in the presence of perturbations with \emph{unknown} boundary. However, the states of the system are only partially observable in the sense of observability rank condition. Due to its switching behavior, a recent concept of $Z(T_N)$ observability is used to analysis its hybrid observability, since its observability depends upon the switching control signals. Under certain condition of the switching sequences, the voltage across each capacitor becomes observable. Simulation results and comparisons with Luenberger switched observer highlight the effectiveness and robustness of the proposed observer with respect to output measurement noise and system uncertainties (load variations).

• The paper proposes an adaptive-gain Second Order Sliding Mode (SOSM) observer to estimate capacitor voltages using only load current, reducing sensor requirements in multi-cell power converters.
• It introduces Z(TN)-observability, a novel concept for hybrid systems like power converters, enabling state estimation based on switching sequences where traditional methods fail.
• The observer is proven to achieve finite-time convergence of the observation error, demonstrating its robustness and reliability under uncertainties like noise and load variations in simulations.

Adaptive-Gain Second-Order Sliding Mode Observer Design for Switching Power Converters

The paper presents a sophisticated approach to designing an adaptive-gain Second Order Sliding Mode (SOSM) observer tailored for multi-cell power converters, classified as a type of hybrid system. The core objective is the reduction of voltage sensors, achieved by estimating capacitor voltages based solely on load current measurements, thereby enhancing system simplicity and reducing cost and complexity.

The authors introduce an adaptive-gain SOSM observer that remains robust against perturbations with unknown boundaries. A particular emphasis is placed on $Z(T_N)$-observability—a recent concept applicable exclusively to hybrid systems. This novel observability criterion is vital due to the unique observability challenges associated with the switching behavior of multi-cell converters. It asserts that under specific switching sequence conditions, capacitor voltages become observable, which traditional observability matrix rank conditions have failed to guarantee.

Key Contributions and Results

1. Observability in Hybrid Systems: The observability of the system is inherently limited by the inability to fully satisfy the observability matrix rank condition for hybrid systems. The use of $Z(T_N)$-observability addresses this limitation, making it possible to estimate states based on switching control signals, which makes the application particularly innovative in the field of power conversion.
2. Adaptive-Gain SOSM Algorithm: The observer utilizes an SOSM algorithm, integrating both nonlinear and linear elements. The nonlinear component substantially enhances the observer's behavior near the origin, while the linear term boosts performance when states deviate from the origin. This dual-sided approach allows the algorithm to inherit favorable attributes from both linear and nonlinear regimes.
3. Finite Time Stability: The paper proves that the output observation error and its time derivative converge to zero in finite time using the SOSML observer. This is a significant finding, as it implies that the observer error for the capacitor voltages exponentially converges to zero, making the system both robust and reliable.
4. Simulation Results: The proposed observer's robustness is demonstrated through a detailed set of simulations, including a comparison with a conventional Luenberger switched observer. Under conditions of output measurement noise and system uncertainties such as load variations, the adaptive-gain SOSM observer showed more resilience, maintaining effective performance where traditional approaches struggled.

Practical and Theoretical Implications

From a theoretical standpoint, the paper advances the observability analysis in hybrid systems, particularly with the effective application of $Z(T_N)$-observability in power converters. Practically, the development of a sensor-independent observation method signifies a notable reduction in system design complexity and cost. This methodology also potentially enhances reliability by mitigating issues stemming from sensor noise and mismatch.

Future Directions

While the paper provides strong foundational concepts and results, several extensions could be explored for future research. These include applying the proposed methods to other types of converters and extending the observer design with alternative hybrid time trajectories. Investigating adaptive-gain methodologies in broader classes of dynamical systems might also yield significant advancements in robust observer design.

In conclusion, this research moves forward the field of power converters by introducing an efficient, cost-effective observability framework. Through strategic algorithm integration and advanced analysis, it lays the groundwork for future innovations in adaptive control and state estimation in hybrid systems.