Woosuk Chang

Design of Robust Vibration Controller for a Smart Panel Using Finite Element Model

This paper presents a model reduction method and uncertainty modeling for the design of a low-order H∞ robust controller for suppression of smart panel vibration. A smart panel with collocated piezoceramic actuators and sensors is modeled using solid, transition, and shell finite elements, and then the size of the model is reduced in the state space domain. A robust controller is designed not only to minimize the panel vibration excited by applied uniform acoustic pressure, but also to be reliable in real world applications. This paper introduces the idea of Modal Hankel Singular values (MHSV) to reduce the finite element model to a low-order state space model with minimum model reduction error. MHSV measures balanced controllability and observability of each resonance mode to deselect insignificant resonance modes. State space modeling of realistic control conditions are formulated in terms of uncertainty variables. These uncertainty variables include uncertainty in actuators and sensors performances, uncertainty in the knowledge of resonance frequencies of the structure, damping ratio, static stiffness, unmodeled high resonance vibration modes, etc. The simplified model and the uncertainty model are combined as an integrated state space model, and then implemented in the H∞ control theory for controller parameterization. The low-order robust controller is easy to implement in an analog circuit to provide a low cost solution in a variety of applications where cost may be a limiting factor.

Closed-loop finite element modeling of smart structures: an overview

Smart structures incorporate sensors, actuators and control electronics that permit the structures to tailor their response to changes in the environment in an optimal fashion. The sensors and actuators are constructed from functional materials such as piezoelectric, electrostrictive, shape memory alloys and magnetostrictive materials and more recently using MEMS (Micro Electro Mechanical Systems) devices. All functional materials and devices therefrom involve coupled fields involving elastodynamic, viscoelastic, electric, magnetic and thermal fields. The materials are anisotropic and often nonlinear. Finite element modeling has been successfully used to model these complex structures. More recently, closed ioop numerical simulation of the tailored response of a smart structure has become possible by combining the finite element equations of the sensor response to applied dynamical and/or thermal loads to the input voltage or current to the actuators via a control algorithm. This hybrid approach permits us to simulate the response of the structure with feedback control. Simple feedback controllers have now been replaced by robust controllers that provide stability under a range of uncertainties and do not require a very accurate system model. The talk will present an overview of the approaches of various researchers and consider numerical applications and comparison with experiments for active vibration damping, noise control and shape modification.

Robust, compact, and inexpensive analog controllers for cabin noise control

Active Noise Control has been an area of research interest in the recent decades with the goal of providing reduced noise levels in automobile and aircraft enclosures. Although digital controllers are adaptable and efficient, they lack the simplicity of analog controllers due to the requirement of a computer, D/A and A/D boards. Analog controllers on the other hand can be designed to be compact using current IC technology and hence are relatively very cheap. The following paper studies the application of an analog robust controller to abate the noise radiated into a non-reverberant wooden enclosure by a clamped aluminum plate. Since only the odd-odd modes radiate efficiently, a SISO robust analog controller was designed and built inexpensively for a piezoelectric actuator and accelerometer sensor placed at the center of the plate. A reduction of 17 dB is observed when the panel is excited at its fundamental frequency, the dominant radiating mode. When the plate is excited with narrowband noise (40 - 316 Hz), the controller reduces the noise levels in the enclosure by 9 dB. The experimental results agree well with the controller simulation carried out using MATLAB.

Design of model reduction and robust controller for underwater echo cancellation

This paper presents the design and development of a simple and robust control system for structural acoustics based on state space control theory. The controller was developed using model Hankel singular value (MHSV)‐based model reduction, and analog controllers are fabricated. MHSV is developed for a model coordinate system describing vibrating structures, and analog controllers were designed from transfer functions of controllers, which have great advantage over digital controllers in terms of simplicity and cost. This controller design for structural acoustics is applied for controlling sound transmission and reflection. MHSV shows good model reduction of finite‐element‐based structure models. The feasibility of this controller for the underwater active reflection cancellation is also studied. 1‐3 piezocomposite material is used as a transducer that generates the acoustic signal. Its electroacoustic model is developed using the Mason circuit and the control parameters are directly derived. The controll...

Comparison of computational schemes in the design of a large-scale projector array

Modeling and simulation for the design of a projector array involves computations in the transducer and acoustic domains. In the transducer domain, each transducer is often described by the two-port, equivalent-circuit model, in which the radiation impedance containing the influence of the neighboring transducers as well as the medium is not known a priori. To obtain the radiation impedance and the subsequent transducer response a set of coupled transducer equations must be solved simultaneously in conjunction with the (computationally expensive) wave-field calculation in the acoustic domain. In this talk, we compare two computational schemes for speed, which differ in the way the mutual interaction of transducers is treated: the first scheme explicitly accounts for the mutual interaction in terms of the mutual impedance, whereas in the second scheme the interaction is reflected implicitly in the iterative solution of the transducer equations. Here, the speed is largely determined by the number of wave-fi...

Conceptual Design of Cylindrical Hydrophone Arrays for Stabilization of Receiving Characteristics under Ocean Ambient Noise

An underwater sound surveillance system detects and tracks enemy ships in real-time using hydrophone arrays, in which seabed-mounted sensor arrays play a pivotal role. In this paper the conceptual design of seabed-mounted, cylindrical hydrophone arrays for use in shallow coastal waters is performed via finite element calculations. To stabilize the receiving characteristics under the ocean ambient noise, a technique for whitening the ambient noise spectrum using a metal baffle is proposed. Optimization of the array configuration is performed to achieve the directivity in the vertical and azimuthal directions. And the effects of the sonar dome shape and material on the structural vibration and sound scattering properties are studied. It is demonstrated that a robust hydrophone array, having a sensitivity deviation less than 4 dB over the frequency range of interest, can be obtained through the whitening of the ambient noise, the optimization of the array configuration, and the design of acoustically transparent sonar domes.

Model Reduction for Complex Adaptive Structures

A complex adaptive structure for the purposes of this paper is treated as a structure with embedded piezoelectric sensors and actuators that are connected through a control loop so that the structure can adaptively or optimally respond to an external disturbance [1–4]. Such structures, also called smart structures, present special challenges in analytical and numerical modeling. The piezoelectric devices involve coupled electric and elastodynamic fields, the devices are multiple in number, the size of the structure is typically much larger in size relative to the sensors and actuators, and in real applications the geometry of the structure is complex. The response of such a structure to an external excitation and the response of the embedded sensors can only be simulated numerically. The finite element method has been successfully used to solve such problems, but the size of the resulting matrices becomes very large even for simple geometries [5–9]. To give an example, to obtain the transient response of a simple clamped plate with five pairs of sensors and actuators it is necessary to retain the first 50 structural modes and this results in an 800 × 800 matrix. In order to then interface such a numerical model with a control algorithm such as an H∞ robust controller including modeling and device uncertainties, may challenge even the fastest computers to provide the required actuator excitations for real time controlled response of the adaptive structure. The objective of this paper is to address this issue and present a technique to condense or reduce the system model while still retaining the essential dynamical features of the smart structure [7].

Model reduction and frequency-weighted optimal vibration control of smart panels

The optimal control algorithm is one of the feasible feedback algorithms for vibration suppression of flexible structures. One of the commonly encountered problems of the optimal control implementation is the spillover problem. The spillover generally occurs when modeling a continuous structure that has infinite number of resonance modes as a nominal model with finite modes for controller design. This paper presents a design of an optimal controller that is low order and can prevent the spillover problem when the unmodeled resonance modes perturb the feedback control loop. For low order controller design, this paper proposes modal Hankel singular values (MHSV) for efficient nominal model reduction. Low order controller can be derived from the reduced nominal model. For design of more stable controller, this paper applies frequency dependent weight functions to the cost function. The weight functions prevent the spillover by making optimal controller not to excite the resonance modes that are not included in nominal model. The optimal controller is derived from the nominal model. This weight function approach optimizes the control performance and control stability by smoothening the discrepancy between the weights of on the modeled modes to be controlled and unmodeled modes to be stabilized. A finite element model is exploited to develop the controller and to test its control performance and stability against high resonance mode spillover.

Active and passive noise control using electroactive polymer actuators (EAPAs)

Electro-active polymer actuators (EAPA) have been a topic of research interest in the recent decades due to their ability to produce large strains under the influence of relatively low electric fields as compared to commercially available actuators. This paper investigates the feasibility of EAPA for active and passive cabin noise control. The passive damping characteristics of EAPA were determined, by measuring the transmission loss of four samples of various thickness and composition in an anechoic chamber in the 200 - 2000 Hz frequency range. This was then compared to that of Plexiglas and silicone rubber sheets of comparable thickness. The transmission loss of EAPA and Plexiglas were observed to be about the same. The transmission loss of EAPA was greater than that of silicone rubber, of the same thickness. The experimental and theoretical results computed using the mass law agree well. EAPA produces a strain of 0.006 for an applied field of 1 V/m. The ability of EAPA to potentially provide active as well as passive damping in the low to intermediate frequency range, along with being light- weight, pliable and transparent, makes it attractive for noise control applications as active/passive windows or wall papers.

Compact, inexpensive, analog robust controller modules for cabin noise control

Control of noise in an enclosure when the noise source is exterior to the enclosure has applications to rooms, automobiles, helicopters, airplanes, and other vehicles. Reducing the interior noise to acceptable levels is necessary for safety and comfort. One approach to control of interior noise is through vibration suppression of the trim panels that often line the interior of such enclosures. It is ultimately these trim panels that reradiate the noise to the interior. In order to actively control the vibrations of the trim panels, using discrete piezoelectric sensors and actuators, control electronics are needed. Adaptive digital control, while being efficient and powerful, also requires the presence of a computer and DSP boards. There may also be frequency limitations posed by the speed of available DSP boards. An alternative approach is to design compact and inexpensive analog controller units, which also offers the possibility of having such controllers designed as ASIC chips. To demonstrate the efficacy of this approach, results will be presented for the control of noise in a cabin with multiple trim panels when excited by broadband noise from the exterior using MEMS vibration sensors and PZT actuators.