reduction effect [9; 10; 11]. When primary noise cannot be acquired, but the expected signal and error signal can be obtained simultaneously through the error sensor, the feedback system is used in active noise control [12; 13]. In addition, this method has been successfully applied in some engineering projects, such as active noise reduction earplugs [14; 15] and active noise reduction headtests [16; 17]. A single-channel feedback active control algorithm was proposed by Ericsson and widely used [18]; then, it was improved by [PERSON] et al. and applied to the multichannel control system [19]. [PERSON] et al. proposed the delay-less algorithm in the frequency-domain feedback system [20; 21]. In the existing algorithms, feedback control is often transformed into feedforward control through an internal synthesis reference signal to achieve feedback active noise control [22]. The internal model structure is usually employed due to its simple mechanism, easy implementation, and wide application. Firstly, adaptive filter output is first prefiltered by the true secondary path; then, it is offset by an error signal to obtain the internal synthesis reference signal. In this algorithm, assuming perfect modeling, the modeling secondary path information is completely consistent with the actual secondary path [23; 24]. However, the difference always existed between model secondary path information and the actual secondary path. Moreover, the adaptive filter is the inverse of the model secondary path impulse, and the secondary path is a nonminimum phase system, so perfect noise reduction is difficult to realize in a feedback ANC system. [PERSON] et al. adopted the internal model structure and proposed a simplified feedback control algorithm (abbreviated to SAIMC algorithm). The internal reference signal was directly derived from the error signal detected by error microphone, and then the feasibility and stability of the simplification were analyzed, the feedback control system structure was simplified, and the number of calculations was reduced [25]. However, the secondary path information still needs to be obtained for these algorithms first. To model the information of secondary path impulse response, the online modeling method [26; 27] or offline modeling method [28] can be used. However, errors always existed between the actual and modeled secondary path information. If these errors are large, the system is unstable [29]. [PERSON] et al. proposed to choose the different phases to estimate the phase response that can select the best update direction for the frequency in the 0\({}^{\circ}\) and 180\({}^{\circ}\) directions to approach the phase information corresponding to the secondary path impulse response [30]. [PERSON] et al. improved this method and applied it to the frequency domain, adding the two directions of \(\pm\)90\({}^{\circ}\) so that the frequency near \(\pm\)90\({}^{\circ}\) could also have fast convergence [31]. [PERSON] et al. realized the four update directions of 0\({}^{\circ}\), 180\({}^{\circ}\), and \(\pm\)90\({}^{\circ}\) in the time domain using the Hilbert transform and estimated the total acoustic delay to compensate part of the secondary path information, which could reduce the number of subbands when realizing broadband noise active control, but the convergence speed was slow [32]. [PERSON] et al. improved the algorithm, adopted the phase estimation method in each subband, and applied it to the frequency domain to reduce the calculation amount [33; 34]. To avoid modeling the secondary path information, [PERSON] et al. proposed the feedback active control algorithm without secondary path modeling (referred to as the WSMANC algorithm) [35]. The algorithm analyzes the secondary path impulse response, which is composed of direct sound delay and a series of reflected sound delays and electrical delays. The direct sound and electrical delay are estimated and added together as the total delay, which can then be used as the estimated secondary path impulse response.