###### Abstract  
Traditional adaptive filtering algorithms are non-recursive systems that cannot use a time-variant reference input in real time and are not appropriate for control signals with uncertainties and unanticipated conditions. The main purpose of this research is to design novel adaptive digital filtering algorithms based on internal model control (IMC). The new methods consist of a process model for the target plant so as to estimate its dynamic behavior for active vibration and noise attenuation schemes in order to improve the stability, robustness, and tracking performance. On the basis of on the existing least mean squares, the methods are combined with an internal model controller, or the whole adaptive filtering system could become a feedback control system structure based on IMC. The performances were validated in numerical simulations with various conditions that could have happened in realistic applications, and the results were compared with the original algorithms. This study shows that the active noise and vibration systems that are applied to vehicles, mechanical systems, and other targets are enhanced through improving the performance of conventional adaptive filtering algorithms and by using internal model control effectively. active vibration and noise mitigation; adaptive filtering system; filtered-X LMS; internal model control; least mean squares; smart structures +
Footnote †: journal: Applied Soft  
There are large volumes of research on enhanced LMS strategies. For example, hybrid structures have been proposed, which combine a feedback control with the filtered-X least mean square (FX-LMS) algorithm [1,2]. A different feedback control scheme is introduced with internal model control (IMC) [3]. A modified FX-LMS method with adaptive step-size is developed for improving the rate of convergence [4,5]. An LMS algorithm with variable steps is applied so as to determine the hysteresis parameters and a creep model for stability and faster convergence [6]. It has shown that a changeable coefficient for convergence could also improve the performance [7]. Because the LMS can be unstable under unpredictable noise, a novel LMS strategy is investigated, where reference signals are calculated in advance in order to guarantee convergence and stability, particularly in case where the signal magnitude exceeds a defined threshold [8]. An LMS algorithm against saturation is introduced so as to enhance the performance, by restraining the controller output with a large disturbance [9]. An additional filter is used to decrease disturbances in the primary path, which were induced from an uncorrelated noise of the secondary path [10]. A new LMS algorithm with phase compensation is suggested so as to deal with signals with DC (direct current) components [11]. There have also been efforts devoted to using lin order MC to improve the traditional LMS method. [PERSON] and [PERSON] investigated an internal model feedback control system based on the FX-LMS algorithm and applied it to stochastic analyses of band-limited white noise [12]. [PERSON] and [PERSON] developed an adaptive IMC scheme based on adaptive finite impulse response (FIR) filters [13]. [PERSON] et al. proposed an internal-model-P (proportional) cascade control system, with all of the models in the control system constructed by LMS filters for online identification [14]. The main purpose of this study is to suggest a LMS algorithm based on state-of-the-art internal model control (IMC) for smart structures. The fundamental element is the IMC, which integrates the model as part of the controller. This algorithm enables effective mitigation of unwanted disturbances with adaptive filtering systems, and can handle noise and unexpected signals with systems containing uncertainties, using a feedback loop in the active control system.