Compatible L 2 Norm Convergence of Variable-Step L1 Scheme for the Time-Fractional MBE Mobel with Slope Selection

2021 ◽  
Author(s):  
Yin Yang ◽  
Jindi Wang ◽  
Yanping Chen ◽  
Honglin Liao
Keyword(s):  
Norm Convergence ◽  
Slope Selection ◽  
Variable Step

A Variable Step-Size for Sparse Nonlinear Adaptive Filters

2021 ◽  
Author(s):  
Alberto Carini ◽  
Markus V. S. Lima ◽  
Hamed Yazdanpanah ◽  
Simone Orcioni ◽  
Stefania Cecchi
Keyword(s):  
Adaptive Filters ◽  
Variable Step Size ◽  
Step Size ◽  
Variable Step

Active control for vehicle interior noise using the improved iterative variable step-size and variable tap-length LMS algorithms

2019 ◽  
Vol 67 (6) ◽  
pp. 405-414 ◽  
Author(s):  
Ningning Liu ◽  
Yuedong Sun ◽  
Yansong Wang ◽  
Hui Guo ◽  
Bin Gao ◽  
...  
Keyword(s):  
Steady State ◽  
Noise Control ◽  
Convergence Speed ◽  
Interior Noise ◽  
Lms Algorithm ◽  
Variable Step Size ◽  
Step Size ◽  
Vehicle Interior ◽  
Vehicle Interior Noise ◽  
Variable Step

Active noise control (ANC) is used to reduce undesirable noise, particularly at low frequencies. There are many algorithms based on the least mean square (LMS) algorithm, such as the filtered-x LMS (FxLMS) algorithm, which have been widely used for ANC systems. However, the LMS algorithm cannot balance convergence speed and steady-state error due to the fixed step size and tap length. Accordingly, in this article, two improved LMS algorithms, namely, the iterative variable step-size LMS (IVS-LMS) and the variable tap-length LMS (VT-LMS), are proposed for active vehicle interior noise control. The interior noises of a sample vehicle are measured and thereby their frequency characteristics. Results show that the sound energy of noise is concentrated within a low-frequency range below 1000 Hz. The classical LMS, IVS-LMS and VT-LMS algorithms are applied to the measured noise signals. Results further suggest that the IVS-LMS and VT-LMS algorithms can better improve algorithmic performance for convergence speed and steady-state error compared with the classical LMS. The proposed algorithms could potentially be incorporated into other LMS-based algorithms (like the FxLMS) used in ANC systems for improving the ride comfort of a vehicle.

scholarly journals Variable step control to improve scanning speed of gene sequencing stage

2021 ◽  
pp. 002029402110022
Author(s):  
Xiaohua Zhou ◽  
Jianbin Zheng ◽  
Xiaoming Wang ◽  
Wenda Niu ◽  
Tongjian Guo
Keyword(s):  
Motion Control ◽  
High Precision ◽  
High Speed ◽  
Stable State ◽  
Gene Sequencing ◽  
Scanning Speed ◽  
Settling Time ◽  
Step Motion ◽  
Variable Step ◽  
Step Control

High-speed scanning is a huge challenge to the motion control of step-scanning gene sequencing stage. The stage should achieve high-precision position stability with minimal settling time for each step. The existing step-scanning scheme usually bases on fixed-step motion control, which has limited means to reduce the time cost of approaching the desired position and keeping high-precision position stability. In this work, we focus on shortening the settling time of stepping motion and propose a novel variable step control method to increase the scanning speed of gene sequencing stage. Specifically, the variable step control stabilizes the stage at any position in a steady-state interval rather than the desired position on each step, so that reduces the settling time. The resulting step-length error is compensated in the next acceleration and deceleration process of stepping to avoid the accumulation of errors. We explicitly described the working process of the step-scanning gene sequencer and designed the PID control structure used in the variable step control for the gene sequencing stage. The simulation was performed to check the performance and stability of the variable step control. Under the conditions of the variable step control where the IMA6000 gene sequencer prototype was evaluated extensively. The experimental results show that the real gene sequencer can step 1.54 mm in 50 ms period, and maintain a high-precision stable state less than 30 nm standard deviation in the following 10 ms period. The proposed method performs well on the gene sequencing stage.

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