This correspondence focuses on the analysis and implementation of multi-input multi-output (MIMO) filtered-u least mean square (FULMS) algorithm for active vibration suppression of a cantilever smart beam with surface bonded lead zirconate titanate patches. By analysing a single-input single-output FULMS algorithm, the MIMO FULMS controller structure is given. Then an active vibration control experimental platform is established, with optimal placement of the actuators and sensors based on the maximal modal force rule. Simulation contrast analysis of FULMS algorithm and the most famous filtered-x least mean square (FXLMS) algorithm is performed while the reference signal is extracted from the exciter as well as directly from the controlled structure. Simulation results show that if the feedback information reflects the reference signal collected by the reference transducers, the FXLMS controller could hardly suppress the vibration while the FULMS controller is still effective. Then the actual control experiment is performed, and the result confirms the simulation results. The designed MIMO FULMS vibration controller has a good control performance, suppressing the vibration significantly with rapid convergence.

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An improved multi‐input multi‐output filtered‐X least mean square‐based vibration control algorithm is proposed to solve the reference signal extraction problem for active vibration control system. The reference signal is constructed by the controller parameters and the vibration residual signal extracted directly from the vibrating structure, which is related to the external disturbance signal. Meanwhile, an FIR filter is adopted for online identification by adding white noise signal to the controller output as identification input signal; the identified model is substituted into the control algorithm, and the online secondary path identification is realized. Thus, the practical application problem of filtered‐X least mean square algorithm is solved. The simulations and experiments show that the proposed algorithm is reliable and effective with good control performance. Copyright © 2013 John Wiley & Sons, Ltd.

Background Neck pain is a common clinical disease, which seriously affects people’s mental health and quality of life and results in loss of social productivity. Improving neck pain’s curative effect and reducing its recurrence rate are major medical problems. Shi’s manipulation therapy has unique advantages and technical features that aid in the diagnosis and treatment of neck pain. Compared with first-line non-steroidal anti-inflammatory drug (NSAID) treatment of neck pain, Shi’s cervical manipulation lacks the relevant research basis of therapeutic advantage, safety, and satisfaction for treating acute and subacute neck pain. Herein, we aim to confirm our hypothesis in a clinical trial that the safety and efficacy of Shi’s cervical manipulation will be more effective, safer, and more satisfactory than NSAIDs to treat acute and subacute neck pain. Methods In this multicenter, positive-controlled, randomized clinical trial, traditional analgesic drug (NSAID) is used to evaluate and show that Shi’s manipulation is more effective, safe, and satisfactory for treating acute and subacute neck pain. Overall, 240 subjects are randomly divided into the trial and control groups, with both groups treated by the corresponding main intervention method for up to 12 weeks. Clinical data will be collected before the intervention and immediately after the first treatment; at 3 days and 1, 2, 4, 8, and 12 weeks after the intervention; and at 26 and 52 weeks after treatment follow-up of clinical observation index data collection. The clinical observation indices are as follows: (1) cervical pain is the primary observation index, measured by Numerical Rating Scale. The secondary indices include the following: (2) cervical dysfunction index, measured by patient self-evaluation using cervical Neck Disability Index; (3) cervical activity measurement, measured by the cervical vertebra mobility measurement program of Android mobile phone system; (4) overall improvement, measured by patient self-evaluation with SF-36; and (5) satisfactory treatment, determined by patient self-evaluation. Discussion We will discuss whether Shi’s cervical manipulation has greater advantages in efficacy, safety, and satisfaction of acute and subacute neck pain than traditional NSAIDs, to provide a scientific basis for the dissemination and application of Shi’s cervical manipulation. Trial registration China Registered Clinical Trial Registration Center ChiCTR1900021371. Registered on 17 February 2019

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