Adaptive Control and Synchronization of Coupled Generator Systems

Coupled generator systems represent a class of typical nonlinear dynamical systems whose dynamic behaviors often exhibit complex chaotic characteristics. In practical engineering applications, achieving stable control and synchronization has been a persistent research focus. Adaptive control methods have emerged as an effective solution to this challenge due to their capability to adjust control parameters online to accommodate system uncertainties. In coupled generator systems, adaptive control is typically implemented through dynamic adjustment of feedback gains, enabling system state variables to rapidly converge to target trajectories. This can be algorithmically achieved using recursive parameter estimation methods such as recursive least squares (RLS) or gradient descent algorithms. The control law implementation often involves real-time computation of Lyapunov-based adaptation laws to ensure system stability. Simultaneously, synchronization control aims to make multiple coupled generator systems achieve identical dynamic behaviors, such as phase synchronization or complete synchronization. Common synchronization strategies include Master-Slave synchronization, mutual synchronization, and state feedback-based synchronization methods, which can be implemented using coupling matrices and error feedback mechanisms in the control algorithm. Chaos Control Strategies Chaotic phenomena in coupled generator systems may lead to operational instability, necessitating control measures to suppress chaotic behaviors. Common chaos control methods include: Parameter Perturbation Method: Achieving chaos suppression through minor adjustments to system parameters to drive the system away from chaotic states. Implementation involves monitoring Lyapunov exponents and applying parameter modifications when chaos is detected. External Excitation Control: Applying periodic signal disturbances to interfere with chaotic trajectories. This can be coded using sinusoidal or pulse generators with adjustable amplitude and frequency parameters. Feedback Linearization: Utilizing nonlinear feedback to transform the system into a linearly controllable form. This requires computing Lie derivatives and implementing coordinate transformations through Jacobian matrix calculations. Chaos Control for Deformed Coupled Generator Systems When system parameters or structures undergo changes, traditional control methods may fail. In such scenarios, adaptive chaos control techniques become particularly crucial. For instance, adaptive law design based on Lyapunov stability theory can effectively suppress chaotic behaviors in deformed systems, ensuring stable operation. The implementation typically involves developing adaptation rules for time-varying parameters and incorporating robustness measures against modeling uncertainties through sigma-modification or e-modification techniques in the control algorithm. In summary, research on adaptive control, synchronization, and chaos control for coupled generator systems not only contributes to enhancing power system stability but also provides theoretical references for controlling other complex nonlinear systems. The algorithmic implementations discussed demonstrate practical approaches for realizing these control strategies in computational frameworks, emphasizing parameter adaptation mechanisms and stability-guaranteed control law formulations.