Abstract:A simple loop shaping technique is applied to design an optimal, robust feedback controller to reduce the interior noise of an acoustic cavity. It is a data-based technique that uses the measured plant response to tune the parameters of a fixed-structure controller in a graphical way. The two cases studied are narrowband noise control in a small cavity and broadband noise control in a long duct. Each control system consists of a microphone, a loudspeaker, and a controller connecting the two transducers that ar… Show more
“…j is the function for negative feedback control, and j is the inverse of the optimal mechanical impedance function in N s m . The biggest difference between the feedback controller for VMI control and the feedback controller for disturbance rejection control [15], such as ANC and AVC, is the presence of an additional feedback loop in the feedback controller. VMI control requires an additional feedback loop in the controller to obtain an error signal between the control mechanical impedance and the optimal mechanical impedance at the target frequency.…”
Section: B Robustness Of the Vmi Control Systemmentioning
confidence: 99%
“…Therefore, the degree of robustness can be expressed as a circle of radius and for j and j , respectively, as shown in Fig. 3(a) [15]. Their inequalities are expressed in ( 10) and (11).…”
Section: B Robustness Of the Vmi Control Systemmentioning
This paper describes an optimal filter design method for a virtual mechanical impedance (VMI) control system. Existing passive methods for reducing machinery noise are limited in use due to weight reduction, cooling, and appearance problems. The VMI control method, which does not require a sensor and can be implemented with a small number of actuators, is an active method that can replace the existing passive methods when mechanical tuning is difficult. However, the existing VMI control method can only reduce the single-tone noise. In this regard, we improved the VMI control system to reduce the radiated sound power of the enclosure panel at multiple frequencies. To achieve this, we propose an optimal filter design method for a multichannel feedback controller. Unlike the existing VMI control, the method capable of multifrequency control considers the radiation efficiency, damping, and estimation errors of the structural-acoustic system. The controller designed using the proposed method satisfies the required robustness and minimum steadystate error in the target frequency band. The results obtained from the finite element-based model and the experimental model show that the radiated sound power of the enclosure panel is reduced at multiple target frequencies after control.
“…j is the function for negative feedback control, and j is the inverse of the optimal mechanical impedance function in N s m . The biggest difference between the feedback controller for VMI control and the feedback controller for disturbance rejection control [15], such as ANC and AVC, is the presence of an additional feedback loop in the feedback controller. VMI control requires an additional feedback loop in the controller to obtain an error signal between the control mechanical impedance and the optimal mechanical impedance at the target frequency.…”
Section: B Robustness Of the Vmi Control Systemmentioning
confidence: 99%
“…Therefore, the degree of robustness can be expressed as a circle of radius and for j and j , respectively, as shown in Fig. 3(a) [15]. Their inequalities are expressed in ( 10) and (11).…”
Section: B Robustness Of the Vmi Control Systemmentioning
This paper describes an optimal filter design method for a virtual mechanical impedance (VMI) control system. Existing passive methods for reducing machinery noise are limited in use due to weight reduction, cooling, and appearance problems. The VMI control method, which does not require a sensor and can be implemented with a small number of actuators, is an active method that can replace the existing passive methods when mechanical tuning is difficult. However, the existing VMI control method can only reduce the single-tone noise. In this regard, we improved the VMI control system to reduce the radiated sound power of the enclosure panel at multiple frequencies. To achieve this, we propose an optimal filter design method for a multichannel feedback controller. Unlike the existing VMI control, the method capable of multifrequency control considers the radiation efficiency, damping, and estimation errors of the structural-acoustic system. The controller designed using the proposed method satisfies the required robustness and minimum steadystate error in the target frequency band. The results obtained from the finite element-based model and the experimental model show that the radiated sound power of the enclosure panel is reduced at multiple target frequencies after control.
“…The loop shaping design procedure and synthesis for several kinds of single-input and single-output (SISO) systems have been implemented during recent years due to the selection of the frequency domain characteristics of the open and the closed-loop systems, this means, designing the control strategy based on the gain and phase margin specifications of the open-loop plant and the specifications of the closed-loop system [1][2][3][4][5][6]. The H ∞ loop shaping robust controller design was studied in recent years to synthesize controllers for SISO plants with unmodeled dynamics and/or uncertainties due to the importance of the controller synthesis in the process control field.…”
In this paper, a loop shaping controller design methodology for single input and a single output (SISO) system is proposed. The theoretical background for this approach is based on complex elliptic functions which allow a flexible design of a SISO controller considering that elliptic functions have a double periodicity. The gain and phase margins of the closed-loop system can be selected appropriately with this new loop shaping design procedure. The loop shaping design methodology consists of implementing suitable filters to obtain a desired frequency response of the closed-loop system by selecting appropriate poles and zeros by the Abel theorem that are fundamental in the theory of the elliptic functions. The elliptic function properties are implemented to facilitate the loop shaping controller design along with their fundamental background and contributions from the complex analysis that are very useful in the automatic control field. Finally, apart from the filter design, a PID controller loop shaping synthesis is proposed implementing a similar design procedure as the first part of this study.
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