Convex combination filtered-X algorithms for active noise control systems

Adaptive filtering schemes exhibit a compromise between convergence speed and steady-state mean square error. Trying to overcome this trade-off, convex combination of adaptive filters have been recently developed for system identification achieving better performance than traditional approaches. The purpose of this work is to apply the convex combination strategy to single-channel and multichannel active noise control systems. In these systems it is necessary to take into account the secondary path between the adaptive filter output and the error sensor and the possible unavailability of the disturbance signal, which depends on the filtering scheme considered. Even though this strategy involves a higher computational burden than the classic adaptive filters, it exhibits a good performance in terms of convergence speed and steady-state mean square error.This work was supported in part by the Spanish Ministerio de Ciencia e Innovacion TEC2009-13741, Generalitat Valenciana PROMETEO 2009/0013, Generalitat Valenciana GV/2010/027, and Universitat Politecnica de Valencia PAID-06-09. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Boaz Rafaely.Ferrer Contreras, M.; Gonzalez, A.; Diego Antón, MD.; Piñero Sipán, MG. (2013). Convex combination filtered-X algorithms for active noise control systems. IEEE Transactions on Audio, Speech and Language Processing. 21(1):154-165. https://doi.org/10.1109/TASL.2012.2215595S15416521

Addressing Stability Robustness, Period Uncertainties, and Startup of Multiple-Period Repetitive Control for Spacecraft Jitter Mitigation

Repetitive Control (RC) is a relatively new form of control that seeks to converge to zero tracking error when executing a periodic command, or when executing a constant command in the presence of a periodic disturbance. The design makes use of knowledge of the period of the disturbance or command, and makes use of the error observed in the previous period to update the command in the present period. The usual RC approaches address one period, and this means that potentially they can simultaneously address DC or constant error, the fundamental frequency for that period, and all harmonics up to Nyquist frequency. Spacecraft often have multiple sources of periodic excitation. Slight imbalance in reaction wheels used for attitude control creates three disturbance periods. A special RC structure was developed to allow one to address multiple unrelated periods which is referred to as Multiple-Period Repetitive Control (MPRC). MPRC in practice faces three main challenges for hardware implementation. One is instability due to model errors or parasitic high frequency modes, the second is degradation of the final error level due to period uncertainties or fluctuations, and the third is bad transients due to issues in startup. Regarding these three challenges, the thesis develops a series of methods to enhance the performance of MPRC or to assist in analyzing its performance for mitigating optical jitter induced by mechanical vibration within the structure of a spacecraft testbed. Experimental analysis of MPRC shows contrasting advantages over existing adaptive control algorithms, such as Filtered-X LMS, Adaptive Model Predictive Control, and Adaptive Basis Method, for mitigating jitter within the transmitting beam of Laser Communication (LaserCom) satellites

Nonlinear Time-Frequency Control Theory with Applications

Nonlinear control is an important subject drawing much attention. When a nonlinear system undergoes route-to-chaos, its response is naturally bounded in the time-domain while in the meantime becoming unstably broadband in the frequency-domain. Control scheme facilitated either in the time- or frequency-domain alone is insufficient in controlling route-to-chaos, where the corresponding response deteriorates in the time and frequency domains simultaneously. It is necessary to facilitate nonlinear control in both the time and frequency domains without obscuring or misinterpreting the true dynamics. The objective of the dissertation is to formulate a novel nonlinear control theory that addresses the fundamental characteristics inherent of all nonlinear systems undergoing route-to-chaos, one that requires no linearization or closed-form solution so that the genuine underlying features of the system being considered are preserved. The theory developed herein is able to identify the dynamic state of the system in real-time and restrain time-varying spectrum from becoming broadband. Applications of the theory are demonstrated using several engineering examples including the control of a non-stationary Duffing oscillator, a 1-DOF time-delayed milling model, a 2-DOF micro-milling system, unsynchronized chaotic circuits, and a friction-excited vibrating disk. Not subject to all the mathematical constraint conditions and assumptions upon which common nonlinear control theories are based and derived, the novel theory has its philosophical basis established in the simultaneous time-frequency control, on-line system identification, and feedforward adaptive control. It adopts multi-rate control, hence enabling control over nonstationary, nonlinear response with increasing bandwidth ? a physical condition oftentimes fails the contemporary control theories. The applicability of the theory to complex multi-input-multi-output (MIMO) systems without resorting to mathematical manipulation and extensive computation is demonstrated through the multi-variable control of a micro-milling system. The research is of a broad impact on the control of a wide range of nonlinear and chaotic systems. The implications of the nonlinear time-frequency control theory in cutting, micro-machining, communication security, and the mitigation of friction-induced vibrations are both significant and immediate

On The Dynamics and Control Strategy of Time-Delayed Vibro-Impact Oscillators

Being able to control nonlinear oscillators, which are ubiquitous, has significant engineering implications in process development and product sustainability design. The fundamental characteristics of a vibro-impact oscillator, a non-autonomous time-delayed feedback oscillator, and a time-delayed vibro-impact oscillator are studied. Their being stochastic, nonstationary, non-smooth, and dynamically complex render the mitigation of their behaviors in response to linear and stationary inputs very difficult if not entirely impossible. A novel nonlinear control concept featuring simultaneous control of vibration amplitude in the time-domain and spectral response in the frequency-domain is developed and subsequently incorporated to maintain dynamic stability in these nonlinear oscillators by denying bifurcation and route-to-chaos from coming to pass. Convergence of the controller is formulated to be inherently unconditional with the optimization step size being self-adaptive to system identification and control force input. Optimal initial filter weights are also derived to warrant fast convergence rate and short response time. These novel features impart adaptivity, intelligence, and universal applicability to the wavelet based nonlinear time-frequency control methodology. The validity of the controller design is demonstrated by evaluating its performance against PID and fuzzy logic controllers in controlling the aperiodic, broad bandwidth, discontinuous responses characteristic of the time-delayed, vibro-impact oscillator

Application of Active Noise Control to Reduce Cabin Noise in Single Engine General Aviation Aircraft

The application of active noise control to reduce cabin noise in single engine, general aviation aircraft is investigated through the use of the \u27filtered x\u27 least mean square algorithm and a simple acoustic feedforward method to generate a reference signal is tested. The system is designed to utilize one reference signal and up to two feedback signals and two audio speakers. The feedforward system consists of a microphone placed in close proximity to the front windshield and isolated from the cabin noise. Cabin noise and reference signals are recorded during flight in a Cessna 172 Skyhawk, a Piper Cherokee 140 and a Piper Malibu Mirage. The recorded data is used in laboratory tests to evaluate the capability of the control system to reduce the cabin noise signal with the recorded reference signal. The reference signal was found to lack coherence with the cabin noise in most aircraft which limited the noise reductions. Alternative feedforward methods are investigated and an alternative reference signal is tested in a laboratory simulation. The results with the recorded data and the modified reference signal are detailed in each case