A Modern Control Approach to Active Noise Control

Shoureshi, R.; Brackney, Larry; Kubota, Naoki; Batta, George R.

doi:10.1115/1.2899195

Cited by 15 publications

(17 citation statements)

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“…By construction, therefore, is a stable matrix polynomial, establishing that the regulator is stabilizing. Moreover, in view of (27), is strictly proper and is proper, i.e., and is finite. It then follows from (23) that and are strictly proper, and hence the regulator is realizable.…”

Section: Linear Stabilizing and Realizable Regulatorsmentioning

confidence: 98%

“…(We note that if is not stable, also the latter parameterization requires an observer-based prestabilization, increasing the dimension of the regulator; see, e.g., [32, p. 226]. ) Theorem 2.1: Let be a stable matrix with being its characteristic polynomial, and let and be the matrix polynomials (26) Moreover, let be an arbitrary stable scalar polynomial and let and be arbitrary matrix polynomials of dimensions and , respectively, such that (27) Then the regulator (28) with (29) is stabilizing and realizable, and for this regulator (30) and (31) where is given by (17). Conversely, any stabilizing and realizable regulator (28) is equivalent to one constructed in this way.…”

Section: Linear Stabilizing and Realizable Regulatorsmentioning

confidence: 99%

“…Some examples are connected to industrial machines and helicopters [2], [9]- [12], [27], [28], control of aircraft in 0018-9286/99$10.00 © 1999 IEEE the presence of wind shear [19], [23], [31], and control of the roll motion of a ship [14].…”

Section: Introductionmentioning

confidence: 99%

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Universal regulators for optimal tracking in discrete-time systems affected by harmonic disturbances

Lindquist

Yakubovich

1999

IEEE Trans. Automat. Contr.

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The authors consider the problem of controlling a discrete-time linear system by output feedback so as to have a second output z z z t t t track an observed reference signal r r r t t t . First, as a preliminary, we consider the problem of asymptotic tracking, i.e., to design a regulator such that jz jz jz t t t 0 0 0r rThis problem has been studied intensely in the literature, mainly in the continuoustime case. It is known that only under very special conditions does there exist a linear regulator which achieves this design goal and which is universal in the sense that it works for all reference signals and does not depend on them. On the other hand, if r r r t t t is a harmonic signal with known frequencies but with unknown amplitudes and phases, there exist such regulators under mild conditions, provided the dimension of r r rt t t is no larger than the number of controls. This is true even if the plant itself is corrupted by an unobserved additive harmonic disturbance w w wt t t of the same type as r r rt t t, if the dimension of w w wt t t is no larger than the number of outputs available for feedback control.However, if the first dimensionality condition is not satisfied, asymptotic tracking is not possible, but a steady-state tracking error remains. Therefore, the authors turn to another approach to the tracking problem, which also allows for damping of other system and control variables, and this is our main result. The measure of performance is given by a natural quadratic cost function. The object is to design an optimal regulator which is universal in the sense that it does not depend on the unknown amplitudes and phases of r r r t t t and w w w t t t and is optimal for all choices of r r r t t t and w w w t t t . The authors prove that an optimal universal regulator exists in a wide class of stabilizing and possibly nonlinear regulators under natural technical conditions and that this regulator is in fact linear, provided that the second dimensionality condition above is satisfied. On the other hand, if it is not satisfied, the existence of an optimal universal regulator is not a generic property, so as a rule no optimal universal regulator exists.The authors provide complete solutions of all the problems described above.

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Section: Linear Stabilizing and Realizable Regulatorsmentioning

confidence: 98%

Section: Linear Stabilizing and Realizable Regulatorsmentioning

confidence: 99%

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Universal regulators for optimal tracking in discrete-time systems affected by harmonic disturbances

Lindquist

Yakubovich

1999

IEEE Trans. Automat. Contr.

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“…Feedback-based controllers, such as linear quadratic Gaussian (LQG) and H ∞ optimal controllers, achieve good results for suppressing transient disturbances. 7 Recent research into adaptive feedforward controllers, including filtered-x and filtered-u leastmean-square (LMS) algorithms, has demonstrated that robust performance in persistent disturbance rejection, such as driving the residual error to zero, can be achieved with little prior knowledge of plant dynamics. [8][9][10] Snyder et al noted that the convergence of these algorithms depends on the plant dynamics and the model error.…”

Section: Introductionmentioning

confidence: 99%

Active vibration control of trim panel using a hybrid controller to regulate sound transmission

Kim

2009

Int. J. Precis. Eng. Manuf.

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NOMENCLATURE C l = closed-loop transfer function e(k) = residual vibration at error accelerometer p(R,θ,φ) = farfield sound pressure Tr (R f ) = trace of auto-covariance matrix of filtered-x signal W k = adaptive feedforward controller w = panel acceleration η = convergence factor This paper presents a method for actively controlling the sound transmission through an aircraft trim panel using a hybrid feedforward/feedback control technique. The method involves measuring the frequency transfer function of the trim panel system and then creating an autoregressive moving average model using frequency domain curve fitting. The control technique is designed to minimize the vibration of a panel that has a limited piston-like motion. The hybrid controller consists of an adaptive feedforward controller that operates in conjunction with a linear quadratic Gaussian feedback controller. The feedback controller increases the damping capacity of the secondary plant to augment the convergence rate of the adaptive feedforward controller. Experimental results indicate that the hybrid controller effectively reduces the vibration of active trim panels and therefore also reduces the sound transmission of the panel.

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“…This work can be applied in a variety of settings, for example in active noise control which was studied in [9] for scalar-input scalar-output systems using a minimum variance performance measure. The suppression of harmonic disturbances also arises in the active control of vibrations in helicopters [6], where a continuous-time model is used in the context of LQ control and Kaiman filtering.…”

Section: Robust Adaptive Nonlinear Output Regulation -An Application mentioning

confidence: 99%

Robust Adaptive Control of UCAVs

Ikeda¹,

Ramsey²,

Lavretsky³

et al. 2004

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A Modern Control Approach to Active Noise Control

Cited by 15 publications

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Universal regulators for optimal tracking in discrete-time systems affected by harmonic disturbances

Universal regulators for optimal tracking in discrete-time systems affected by harmonic disturbances

Active vibration control of trim panel using a hybrid controller to regulate sound transmission

Robust Adaptive Control of UCAVs

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