Adaptive feedforward modal space control

Principal component active control is of great interest in recent times because of its extensive use in vibration and noise reduction applications. Existing analysis for such control systems mainly focuses on simplified representations of the closedloop system in order to obtain robust stability conditions, but they exclude key practical considerations, such as open-loop dynamics, the periodic time-varying effects generated by the transformations between the time-domain harmonic signals and the estimation of their Fourier coefficients, multi-rate issues caused by the plant and the controller operating at different sampling rates, modelling errors and particular ways of scaling the control actions. The contribution of this work is to include all the afore-mentioned effects to provide more accurate robustness conditions, which complement existing controller tuning procedures. The robustness analysis is conducted by first exploiting the time-lifting method to reformulate the Linear-Periodic-Time-Variant part of the discrete-time system into an equivalent Linear-Time-Invariant representation. Then by using the theoretical tool of Integral Quadratic Constraints, standard forms of plant uncertainty and scaling of the control actions are incorporated. A vibration control example based on the Airbus EC-145 helicopter main rotor with on-blade actuators is included to demonstrate the benefits of the contributions. The proposed design results are benchmarked against the mixed-sensitivity H∞ method, highlighting for this particular application strengths and weaknesses by each approach.

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“…The error and input signals are captured into the modal space by the following transformations [28], [29]…”

Section: Pc Controllermentioning

confidence: 99%

Robust Analysis for Principal Component Active Control Systems

Yang

Morales

Turner

2021

IEEE Trans. Contr. Syst. Technol.

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“…Modal sensors and modal actuators based on spatially continuous transducers were discussed by Lee and Moon. 14 The present methods are based on discrete sensors and actuators, such as described by Clark, 15 Gawronski, 16 and Morgan, 17 in order to provide more flexibility by using programmable weighting coefficients. The emphasis in the present paper is on acoustic radiation and the connection with previous radiation mode theory.…”

Section: Introductionmentioning

confidence: 99%

Broadband radiation modes: Estimation and active control

Berkhoff

2002

The Journal of the Acoustical Society of America

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In this paper we give a formulation of the most efficiently radiating vibration patterns of a vibrating body, the radiation modes, in the time domain. The radiation modes can be used to arrive at efficient weighting schemes for an array of sensors in order to reduce the controller dimensionality. Because these particular radiation modes are optimum in a broadband sense, they are termed broadband radiation modes. Methods are given to obtain these modes from measured data. The broadband radiation modes are used for the design of an actuator array in a feedback control system to reduce the sound power radiated from a plate. Three methods for the design of the actuator are compared, taking into account the reduction of radiated sound power in the controlled frequency range, but also the possible increase of radiated sound power in the uncontrolled frequency range.

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A Principal Component Algorithm for Feedforward Active Noise and Vibration Control

Cabell

Fuller

1999

Journal of Sound and Vibration

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A principal component least mean square (PC-LMS) adaptive algorithm is described that has considerable benefits for large control systems used to implement feedforward control of single frequency disturbances. The algorithm is a transform domain version of the multichannel filtered-x LMS algorithm. The transformation corresponds to the principal components (PCs) of the transfer function matrix between the sensors and actuators in a control system at a single frequency. The method is similar to other transform domain LMS algorithms because the transformation can be used to accelerate convergence when the control system is ill-conditioned. This ill-conditioning is due to actuator and sensor placement on a continuous structure. The principal component transformation rotates the control filter coefficient axes to a more convenient coordinate system where (1) independent convergence factors can be used on each coordinate to accelerate convergence, (2) insignificant control coordinates can be eliminated from the controller, and (3) coordinates that require excessive control effort can be eliminated from the controller. The resulting transform domain algorithm has lower computational requirements than the filtered-x LMS algorithm. The formulation of the algorithm given here applies only to single frequency control problems, and computation of the decoupling transforms requires an estimate of the transfer function matrix between control actuators and error sensors at the frequency of interest. The robustness of the PC-LMS algorithm to modeling errors is shown to be identical to the filtered-x LMS algorithm, and the statistical properties of the principal components are used to select a subset of the PCs to control, depending on the control application. The variation of the PCs with frequency is investigated, and an online identification procedure is described to compute the transfer function matrix while the controller is operating. The feasibility of the PC-LMS method was demonstrated in real-time noise control experiments involving 48 microphones and 12 control actuators mounted on a closed cylindrical shell. Convergence of the PC-LMS algorithm was more stable than the filtered-x LMS algorithm. In addition, the PC-LMS controller produced more noise reduction with less control effort than the filtered-x LMS controller in several tests.

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Adaptive feedforward modal space control

Cited by 23 publications

References 27 publications

Robust Analysis for Principal Component Active Control Systems

Robust Analysis for Principal Component Active Control Systems

Broadband radiation modes: Estimation and active control

A Principal Component Algorithm for Feedforward Active Noise and Vibration Control

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