Adaptive 2-DOF Control for Tracking Sinusoidal Signals With Unknown Frequency

Tracking sinusoidal signals with unknown and time-varying frequencies is essential in many adaptive control applications. This paper presents a real-time method for tracking sinusoidal reference signals with unknown frequencies within a narrow bandwidth. The reference signals may include multiple harmonics and a DC bias. The proposed approach integrates a sinusoidal internal model with a Two-Degree-of-Freedom control structure. Unlike traditional methods that rely on offline tuning, this technique updates the controller coefficients online. A high-pass filter with notch characteristics (<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>f</i></sub>) is used to derive update equations for the Two-Degree-of-Freedom controller and the internal model parameters. These equations are obtained by matching the closed-loop transfer function of the algorithm to that of the desired filter (1 − <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>f</i></sub>). The method is evaluated in MATLAB/Simulink using a second-order plant as an example. Two test cases are presented: the first involves a reference signal with a frequency change and a DC bias, while the second includes two additional harmonics. The algorithm is also tested without coefficient updating for comparison. Results show that the proposed method can accurately track signals with unknown and changing frequencies. It keeps the tracking error very small and quickly adjusts to frequency changes, making it suitable for real-time control in dynamic systems.