A study of time-domain FXLMS algorithms with control output constraint

Area of Science:

• Acoustics and Signal Processing
• Control Systems Engineering

Background:

• Active noise control (ANC) systems aim to reduce unwanted sound.
• The Filtered-X Least Mean Squares (LMS) algorithm is a common adaptive filter used in ANC.
• Implementing output constraints is crucial for practical ANC system stability and performance.

Purpose of the Study:

• To investigate and compare three distinct methods for applying output constraints to the control filter in a single-input, single-output (SISO) ANC system.
• To evaluate the effectiveness and limitations of each constraint method under the Filtered-X LMS algorithm.

Main Methods:

• The study focuses on the time-domain Filtered-X LMS algorithm for ANC.
• Three output constraint algorithms are examined: leakage algorithm (transformation method with penalty function), re-scaling algorithm (active set method), and clipping algorithm.
• Performance is compared based on constraint satisfaction, stability, and convergence speed.

Main Results:

• The re-scaling algorithm demonstrates successful operation under output constraints.
• The leakage algorithm typically requires a high leakage coefficient to meet constraints, leading to performance degradation.
• The clipping algorithm presents potential issues with system stability and convergence rate.

Conclusions:

• The re-scaling algorithm is a robust method for managing control filter output constraints in ANC systems.
• The leakage and clipping algorithms exhibit significant drawbacks in terms of performance, stability, and convergence.
• Choosing the appropriate output constraint method is critical for optimizing ANC system performance.