MATLAB Code Implementation of Proportional Resonant Control

Proportional Resonant Control (PR Control) is a control strategy commonly used in power electronics and motor drive systems, particularly suitable for tracking periodic reference signals (such as sine waves) or suppressing specific frequency disturbances. Unlike traditional PI control, PR control provides infinite gain at the resonant frequency, enabling zero steady-state error tracking of AC signals. ### PR Control Principle The PR controller consists of a proportional term and a resonant term, typically represented by the transfer function: [ G_{PR}(s) = K_p + \frac{2K_i s}{s^2 + \omega_0^2} ] where ( K_p ) is the proportional gain, ( K_i ) is the resonant gain, and ( \omega_0 ) is the resonant frequency (the target frequency for tracking or suppression). The resonant term generates extremely high gain at frequency ( \omega_0 ), ensuring precise tracking or disturbance rejection at this specific frequency. ### Implementation Approach Discretization Design: Since practical control systems typically use digital implementation, the continuous-domain PR controller must be discretized using methods like bilinear transformation (Tustin method) and converted into difference equation form suitable for digital control. Frequency Adaptive Mechanism: For systems with potential frequency variations (such as grid frequency fluctuations), a frequency adaptive mechanism can be incorporated to dynamically adjust the ( \omega_0 ) parameter of the resonant term. Stability Analysis: Controller parameters (( K_p ), ( K_i )) must be validated for stability using Bode plots or root locus methods to avoid system oscillation caused by excessively high resonant peaks. ### MATLAB Implementation Key Points Transfer Function Modeling: Use MATLAB's `tf` function to construct the continuous model of the PR controller, combined with the `c2d` function for discretization. The code implementation involves defining numerator and denominator coefficients and selecting appropriate discretization methods. Frequency Domain Verification: Utilize the `bode` plot function to observe the gain characteristics of the controller at the resonant frequency, ensuring proper peak response at the target frequency. Real-time Simulation: Build closed-loop systems in Simulink, inject sinusoidal reference signals, and test tracking performance and harmonic suppression effects. Implement discrete PR controllers using MATLAB Function blocks or embedded MATLAB code. PR control demonstrates excellent performance in applications such as photovoltaic inverters and UPS systems, but parameter tuning must balance dynamic response and anti-interference capability. For multi-frequency disturbances, the controller can be extended to multi-resonant controllers (such as repetitive control) to further enhance performance.