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The problem of robust pole placement in active structural vibration control by the method of receptance is considered in this paper. Expressions are derived for the eigenvalue sensitivities to parametric perturbations, which are subsequently minimised to improve performance robustness of the control of a dynamical system. The described approach has application to a vibrating system where variations are present due to manufacturing and material tolerances, damages and environment variabilities. The closed-loop eigenvalue sensitivities are expressed as a linear function of the velocity and displacement feedback gains, allowing their minimisation with carefully calculated feedback gains. The proposed algorithm involves curve fitting perturbed frequency response functions, FRFs, using the rational fraction polynomial method and implementation of a polynomial fit to the individual estimated rational fraction coefficients. This allows the eigenvalue sensitivity to be obtained entirely from structural FRFs, which is consistent with the receptance method. This avoids the need to evaluate the M,C,K matrices which are typically obtained through finite element modelling, that produces modelling uncertainty. It is also demonstrated that the sensitivity minimisation technique can work in conjunction with the pole placement and partial pole placement technique using the receptance method. To illustrate the working of the proposed algorithm, the controller is first implemented numerically and then experimentally.

The use of virtual sensing allows the frequency range of a local active noise control system located close to a listener's ears to be extended beyond what is possible when only controlling from remote physical sensors, particularly if head tracking is also used to determine the position of the virtual sensors. As the frequency range is extended, however, the uncertainties in the acoustic responses become more significant, and the design of multichannel adaptive controllers that are robustly stable to these uncertainties becomes more important. In order to fully characterise the uncertainties, a very large number of measurements would, in principle, need to be taken, due to the combination of all the possible changes in the acoustic environment. For uncertainties due to the simultaneous change in position of several objects within the acoustic environment, however, it is shown that the uncertainties can be accurately predicted by the superposition of these uncertainties, due to the change in position of the objects individually. This allows the uncertainty that is due to the change in position of a number of objects to be rapidly evaluated from a limited number of experiments and considerably simplifies the controller design process, which is illustrated here for an active headrest system using two different virtual sensing techniques.

Shutting the window is usually the last resort in mitigating environmental noise, at the expense of natural ventilation. We describe an active sound control system fitted onto the opening of the domestic window that attenuates the incident sound, achieving a global reduction in the room interior while maintaining natural ventilation. The incident sound is actively attenuated by an array of control modules (a small loudspeaker) distributed optimally across the aperture. A single reference microphone provides advance information for the controller to compute the anti-noise signal input to the loudspeakers in real-time. A numerical analysis revealed that the maximum active attenuation potential outperforms the perfect acoustic insulation provided by a fully shut single-glazed window in ideal conditions. To determine the real-world performance of such an active control system, an experimental system is realized in the aperture of a full-sized window installed on a mockup room. Up to 10-dB reduction in energy-averaged sound pressure level was achieved by the active control system in the presence of a recorded real-world broadband noise. However, attenuation in the low-frequency range and its maximum power output is limited by the size of the loudspeakers. Ministry of National Development (MND) National Research Foundation (NRF) Published version This research is supported by the Singapore Ministry of National Development and the National Research Foundation, Prime Minister’s Office under the Cities of Tomorrow (CoT) Research Programme (CoT Award No. COT-V4-2019-1). Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not reflect the views of the Singapore Ministry of National Development and National Research Foundation, Prime Minister’s Office, Singapore.

Active control of the sound power scattered by a sphere is theoretically investigated using spherical harmonic expansions of the primary and secondary fields. The sphere has a surface impedance that is uniform, real, and locally reacting while being subjected to an incident monochromatic plane wave. The scattered power is controlled with a number of monopole sources, initially on the surface of the sphere, and is expressed as the sum of squared amplitudes of the spherical harmonics due to both the scattered and control fields. This quadratic function is minimized to identify the optimal strengths for different numbers of control sources. At low frequencies, the scattered field is dominated by the first few spherical harmonic terms, and its power can be significantly reduced with a single controlling monopole for a soft or absorbent sphere and with two monopoles for a hard sphere. The number of secondary sources required to significantly attenuate the scattered field at higher frequencies is found to be proportional to the square of the frequency, and the attenuation also falls off rapidly if the secondary sources are moved away from the surface of the sphere, no matter what its surface impedance.

Personal sound zones (PSZ) systems use an array of loudspeakers to render independent audio signals to multiple listeners within a room. The performance of a PSZ system, designed using weighted pressure matching, depends on the selected target responses for the bright zone. In reverberant environments, the target responses are generally chosen to be the room impulse responses from one of the loudspeakers to the control points in the selected bright zone. This approach synthesizes the direct propagation component and all the reverberant components in the bright zone, while minimizing the energy in the dark zone. We present a theoretical analysis to show that high energy differences cannot be achieved for the diffuse reverberant components in the bright and dark zones, and so trying to synthesize these components in the bright zone does not lead to the best performance. It is then shown that the performance can be improved by using windowed versions of these measured impulse responses as target signals, in order to control which reverberant components are synthesized in the bright zone and which are not. This observation is supported by experimental measurements in two scenarios with different levels of reverberation.

Feedforward adaptive controllers are widely used for active noise control. For good broadband performance, the secondary path delay must be shorter than that of the primary path. In this work, a hybrid analog-sampled adaptive feedforward controller is developed to eliminate the additional delay associated with the sampling. An adaptive finite-impulse-response system is used for the sampled controller, and a state filtered adaptive linear combiner is used for the analog controller. Two approximations are used for the linear combiner. The first minimizes the added electrical noise by having individual state filters, all driven by the reference signal, while the second gives a superior bandwidth by driving each component filter with the output of the previous one. A sampled version of the normalized projection algorithm is developed for the analog controller. The different error paths used to filter the reference signal for the controllers’ adaptation are emphasized. Finally, the performance of the proposed controller is assessed. The results highlight the capabilities of the suggested controller and the different state filters, especially their ability to achieve significant attenuation levels close to the causality limit and when long delays of the reference signal are required.

The convergence speed of multichannel adaptive active noise control algorithms can be improved if the reference signals are preconditioned, so it is advantageous to whiten them and reduce their cross-correlations. However, this preconditioning depends on the properties of the reference signals, which will generally change over time. It may still be possible to approximate the properties of the measured reference signals using a limited number of exemplar cases. By classifying the measured reference signals into the closest of these cases, the most appropriate preconditioning can be selected for the adaptive algorithm at any one particular time. Also, one method of implementing virtual sensors is to use the additional filter method, which provides targets for the measured error signals to follow, generated from the reference signals. The performance of this virtual sensing is known to be degraded if the properties of the reference signals change, so this classification method could also be used to select the most appropriate additional filter.

The use of a digital twin to update a feedback controller is considered, and this is illustrated using simulations of a position-controlled dynamical system with a time-varying nonlinear element. The feedback control system consists of a dc motor driving the displacement of a three degree of freedom structure through a lead screw that is subject to backlash, whose gap angle changes over time due to wear for example. The backlash is shown to destabilise the feedback loop when using a PID controller designed for the linear system. However, stability can then be re-established by including a dead zone within the controller. The design of the dead zone depends on the extent of the gap angle in the backlash and is a trade-off between stabilising the system and avoiding excessive steady-state errors and undesired transient behaviour. When the backlash gap angle changes significantly from the one used to design the dead zone, both performance and stability are affected. Therefore, a digital twin of the system is used to estimate the backlash gap angle as it changes with time and this estimate is used to re-design the dead zone, which is then communicated back to update the controller. The digital twin and controller-design process can be implemented offline and remotely from the physical twin and the real-time controller via an asynchronous link with variable time delays. As a result of combining the feedback loop and digital twin, good performance and stability are maintained at all times.