H-infinity LMI Robust Control for DFIG Systems

Application of H-infinity LMI Robust Control in DFIG Systems

Doubly-Fed Induction Generator (DFIG) serves as the core component of wind power generation systems, whose dynamic performance is susceptible to uncertainties such as wind speed fluctuations and grid disturbances. The robust design methodology combining H-infinity control with Linear Matrix Inequalities (LMI) effectively enhances DFIG stability under complex operating conditions.

Core Principles H-infinity control minimizes the H-infinity norm of the system transfer function (representing energy gain under worst-case disturbances), thereby reducing the impact of external disturbances on system outputs. LMI serves as a convex optimization tool for solving controller parameter matrices while ensuring satisfaction of Lyapunov stability conditions. For DFIG modeling, the dynamic equations of both Rotor-Side Converter (RSC) and Grid-Side Converter (GSC) are typically transformed into state-space form. Robustness requirements (such as disturbance rejection and parameter variation suppression) are encoded into matrix inequalities through LMI constraints. Implementation Insight: The design process involves formulating the control problem using MATLAB's Robust Control Toolbox functions like `hinfsyn` or `hinfstruct`, which solve the LMI optimization problem numerically.

Design Advantages Disturbance Rejection: Suppresses low-frequency disturbances caused by mechanical torque variations from wind speed fluctuations and grid voltage dips. Parameter Robustness: Tolerates practical deviations in generator parameters (inductance, resistance), avoiding performance degradation common in traditional PI control due to model mismatch. Dynamic Response: Enables flexible adjustment of transient characteristics for key indicators like speed tracking and power output through weighting functions. Algorithm Note: Weighting functions are strategically designed using frequency-domain specifications to shape the controller's response characteristics.

Implementation Key Points The nonlinear DFIG model must be linearized around operating points, constructing a generalized plant that incorporates uncertainty terms. LMI solvers (such as MATLAB's `hinfstruct`) can automatically generate controllers satisfying H-infinity performance criteria. Practical applications require balancing robustness against control complexity to avoid real-time computational burdens from high-order controllers. Code Consideration: The `hinfstruct` function allows structured controller synthesis with predefined order constraints, facilitating real-time implementation.

Future Directions Further research could integrate LMI with fuzzy control or adaptive strategies to handle wider wind speed variations, while exploring reduced-order controller designs to enhance engineering applicability. Development Perspective: Potential implementations may involve MATLAB's Control System Toolbox for model reduction techniques like balanced truncation or Hankel norm approximation.