Abstract
FxLMS (Filtered-x Least Mean Square) algorithm is widely used in the field of AVC (active vibration control) for its good convergence and strong adaptability. However, the convergence rate and steady-state error are mutually restricted for the fixed step FxLMS algorithm. Increasing step size μ to accelerate the convergence rate will result in larger steady-state error and even cause control divergence. In this paper, a new DVSFxLMS (error signal Differential term feedback Variable Step size FxLMS) algorithm is proposed by establishing nonlinear function between μ and error signal, while using differential term of the error signal as the feedback control function. Subsequently, a DVSFxLMS controller is designed to carry out the AVC simulation and experiments on cantilever beam with PSA (piezoelectric stack actuator). Simulation and experimental results show that the proposed DVSFxLMS algorithm has faster convergence rate and smaller steady-state error than the traditional FxLMS algorithm, which also has strong antinoise ability and adaptive control ability to quickly track the variable external disturbance.
Highlights
Adaptive filter technology has wide range applications in the field of digital signal processing
E weight coefficients of the adaptive controller are adjusted according to the adaptive algorithm that usually is LMS algorithm, so that the mean square value of the vibration response measured by sensor converges to the minimum direction. e developed FxLMS vibration control algorithm has advantages of good convergence and strong adaptability, and does not depend on the accurate model of controlled structure, which has become one of the hotspots of AVC algorithm research [2,3,4,5]
The calculation amount of the algorithm should be as small as possible, and the parameters that need to be adjusted should be as few as possible to enhance the practicality of the algorithm. erefore, based on the algorithm in [13], and combining the advantages of the algorithm in [16], while a feedback control function inversely proportional to the differential term of error signal Δe(n) |e(n) − e(n − 1)| is introduced, a new variable step size LMS algorithm is proposed in this paper:
Summary
Adaptive filter technology has wide range applications in the field of digital signal processing. E digital filter adjusts weight coefficients through the adaptive algorithm to improve its signal processing performance. When applying adaptive filtering technology to the field of AVC, a FIR (finite impulse response) filter is usually used as a feedforward controller, called the adaptive controller. E weight coefficients of the adaptive controller are adjusted according to the adaptive algorithm that usually is LMS algorithm, so that the mean square value of the vibration response measured by sensor converges to the minimum direction. In order to solve this contradiction, it is necessary to adjust the step size μ of LMS algorithm in real time during control process, which is called the variable step size LMS algorithm [7,8,9]. Qin and Ouyang [11] proposed a variable step size SVSLMS (Sigmoid function Variable Step size LMS)
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