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Vibration control of flexible beams using self-sensing actuators
Abstract
This paper considers the design and implementation of a smart piezoelectric self-sensing actuator for active vibration control of flexible structures. A disturbance estimation technique is used for estimating the induced strain on a piezoelectric actuator, which results in a self-sensing piezo-actuator. The proposed self-sensing piezo-actuator is then applied for the elimination of vibration in a flexible beam structure, using a simple rate-feedback control. Simulation and experimental results for a cantilever beam are shown to demonstrate the accuracy of the proposed self-sensing actuator for vibration control.
Experimental vibration analysis is a main concern of this study. In designing any structural component the important parameter that has to be considered is vibration. The present work involves the experimental investigation of free vibration analysis of a smart beam. Smart beam consists of glass/epoxy composite as a main substrate and two PZT patches. The PZT patches are glued above and below the main beam. By experimentation the natural frequencies and mode shapes are obtained for both with and without PZT patches of a beam. Finally through experimentation the response of the smart beam is recorded.
The operational efficiency and life of mechanical systems/structures depends to a large extent on their vibration control. Continuously occurring vibrations on the systems can cause fatigue and the effects of these vibrations are particularly severe if they occur at a frequency matching with that of the concerned system’s natural frequency – a stage called resonance. This paper focuses on achieving active vibration control of a smart cantilever beam at its first resonant frequency as it is at this stage that maximum damage to the system performance is expected. The smart system is modelled in the parametric domain using finite element modeling techniques and the obtained model is validated through experimental means. The active vibration control is achieved by employing two control algorithms namely – output feedback and error based control through general purpose operating system (LabVIEW on Windows 7) as well as in real time operating system (LabVIEW FPGA coupled with compact reconfigurable input output modules) and the performances are compared thereby justifying the importance of the deterministic and reliable real time control over the usual PC based control in experimental studies.
A dither motor in self-sensing actuation configuration allows each of the piezoelectric (lead zirconate titanate) elements to be used concurrently for dither rate sensing and dither motion actuation, so that system of improved efficiency and reliability can be achieved. For a self-sensing actuator, bridge circuit either fixed or adaptive is usually required to resolve the mechanical response from the control signal. In this study, a new technique for accurately extracting the mechanical response from the control signal of dither motor is developed. The measured open-loop response of the dither motor in self-sensing actuation configuration compared well with the results from a separate lead zirconate titanate sensor. Closed-loop dither rate control and frequency tracing of the dither motor are implemented and verified upon temperature variations. Method for estimating the equivalent lead zirconate titanate capacitance of the dither motor more accurately online is also provided and confirmed experimentally. The maximum error between the equivalent capacitance measured online and that measured under static conditions is about 1.2%.
All mechanical systems suffer from undesirable vibrations during their operations. These vibrations are unavoidable as they depend on various factors. However, for efficient operation of the system, they have to be controlled within the specified limits. Light weight, rapid and multi-mode control of the vibrating structure is possible by the use of piezoelectric sensors and actuators coupled with feedback algorithms. In this paper, direct output feedback based active vibration control has been implemented on a smart cantilever beam at its resonant frequency using PZT (Lead Zirconate Titanate) sensors and actuators. The work aims to showcase the performance abilities of the conventional PC based control and a dedicated REAL TIME CONTROL at resonance. The platform used is LABVIEW RT with FPGA hardware and the system performance is compared with the conventional time multiplexed Operating System (Windows 7) where LABVIEW is again used with the appropriate DAQ devices.
All mechanical systems suffer from undesirable vibrations during their operations. Their occurrence is uncontrollable as it depends on various factors. However, for efficient operation of the system, these vibrations have to be controlled within the specified limits. Light weight, rapid and multi-mode control of the vibrating structure is possible by the use of piezoelectric sensors and actuators and feedback control algorithms. In this paper, direct output feedback based active vibration control has been implemented on a cantilever beam using Lead Zirconate-Titanate (PZT) sensors and actuators. Three PZT patches were used, one as the sensor, one as the exciter providing the forced vibrations and the third acting as the actuator that provides an equal but opposite phase vibration/force signal to that of sensed so as to damp out the vibrations. The designed algorithm is implemented on Lab VIEW 2010 on Windows 7 Platform.
A technique has been developed which allows a single piece of piezoelec tric material to concurrently sense and actuate in a closed loop system. The motivation behind the technique is that such a self-sensing actuator will be truly collocated and has applications in active and intelligent structures, such as vibration suppression. A theoreti cal basis for the self-sensing actuator is given in terms of the electromechanical consti tutive equations for a piezoelectric material. In a practical implementation of the self- sensing actuator an electrical bridge circuit is used to measure strain. The bridge circuit is capable of measuring either strain or time rate of strain in the actuator.
The usefulness of the proposed device was experimentally verified by actively damping the vibration in a cantilever beam. A single piezoceramic element bonded to the base of the beam functioned both as a distributed moment actuator and strain sensor. Using a rate feedback control law, the first mode of vibration was suppressed, reducing the settling from 35 seconds to 2.5 seconds. Using a positive position feedback law the first two modes of vibration were suppressed; the first mode settling time was reduced from 35 to 0.3 sec onds and the second mode settling time was reduced from 7 seconds to 0.9 seconds.
The self-sensing actuator is a new concept for intelligent materials, where a single piezoelectric element simultaneously functions as both a sensor and an actuator. This concept should be advantageous in many aspects of control, especially for vibration control of flexible structures. The key component of this device is an electric bridge circuit that includes a piezoelement. This circuit could provide significant information about strain in the element if it were wellbalanced. Our aim is to use μ-synthesis to design a controller which guarantees that the performance of a self-sensing actuator is robust against perturbations in the bridge balance and to confirm the advantages of this technique from the viewpoint of control. Experimental results show that the self-sensing actuator driven by the designed controller exhibits excellent performance in suppressing the vibration of a cantilever and is robust compared to the conventional control scheme.
The problem of controlling the bending vibration of cantilevers modeled as thin-walled beams of closed cross-section incorporating a number of nonclassical effects, such as transverse shear, secondary warping and heterogeneity, is investigated. The control is carried out by means of piezoelectric materials bonded or embedded into the host structure. The control law represents a combination of displacement, velocity and acceleration feedback. The capabilities and efficiency of this control methodology are illustrated and a number of relevant conclusions are outlined.
An active vibration control of a smart flexible structure featuring a piezofilm actuator is presented in this study. A governing equation of motion for the smart beam structure is derived and a state space model is obtained in order to formulate a controller. A new discrete- time sliding mode controller is proposed for a single-input linear system with mismatched uncertainties. The main difference between the discrete-time sliding mode control and the continuous-time sliding mode control is the determination of the existence condition of the sliding mode. In the discrete-time case, both the sliding condition and the convergence condition must be satisfied. In the design of the discontinuous controller, a time-varying gain that is a function of the relation between predetermined sliding surface and representative points in the state space is adopted to minimize a sliding region. In addition, for faster reaching to the sliding surface, an equivalent controller separation method is employed. The proposed controller is applied to the smart structure, and control responses of transient and forced vibrations are evaluated by undertaking both simulation and experiment.
An adaptive algorithm implemented on a digital signal processor is used in conjunction with an analog multiplier circuit to compensate for the feedthrough capacitance of a piezoelectric sensoriactuator. The mechanical response of the piezoelectric sensoriactuator is resolved from the electrical response by adaptively altering the gain imposed on the electrical circuit used for compensation, For broadband, stochastic input disturbances, the feedthrough dynamic capacitance of the sensoriactuator can be identified on-line, providing a means of implementing direct-rate-feedback control in analog hardware. Rate feedback control is demonstrated on a cantilevered beam using the hybrid/adaptive circuit, The ability of the circuit to readapt to a change in capacitance is demonstrated by a simple experiment.
The issue of precision position control is critical if piezoelectric actuator technology is to be applied in increasingly demanding applications. In one particular application, the NASA NAOMI project, piezoelectric actuators have been proposed as the pointing and focusing elements for thousands of small mirror-lenslets because of their fast response time and load- carrying ability. In this application the positions of these actuators must be precisely controlled both statically and dynamically to the nanometer level. This requirement necessitates a careful study of the concept and design of the driving electronics of the system. This paper is focused on finding an appropriate method for driving piezoelectric stack actuators for ultraprecision position and motion control. In this paper the theoretical basis of the electrical control of piezoelectric stack actuators is derived using the fundamental physical laws governing dielectrics and piezoceramics. It is shown that the relationships used for voltage control of piezoelectric actuators result from an approximation of the constitutive equations. An exact input/output relationship for piezoelectric actuators is derived and shows that displacement relies fundamentally on charge, not voltage. Experimental verification was obtained to illustrate the differences between driving piezoactuators with voltage control and charge control.
Two dimensional thin rectangular elements with pseudointernal degrees of freedom are used to develop the finite element model of piezoelectric materials. The internal DOF are for the better representation of bending moments generated by the feedback piezoelectric voltage and are condensed to the physical nodal DOF using the Guyan reduction technique. The control efficiency effect of the location of the piezoelectric actuator pair on the beam is studied
An electromechanical model is developed to predict the natural frequencies of a structural system with a piezoelectric sensor and actuator. Analysis shows that a generalized stiffness is induced in the closed-circuit condition and it is a function of the structure dimensions, the location of the piezoelectric elements, and the piezoelectric constant. The sensor and actuator equation derived from the electromechanical model shows that a single piezoelectric element can be employed concurrently in sensing and actuation. Experimental verifications of structural vibration suppression are conducted on a beam structure with surface-bonded piezoelectric elements as well as on two composite laminated structures - and - with embedded piezoelectric sensors and actuators. Compared with previous studies of vibration suppression by separate piezoelectric sensor(s) and actuator(s), the concurrent sensing and actuation technique offers the advantages of improved performance and reliability as each piezoelectric element can be employed as sensor and actuator simultaneously.
This paper deals with the application of piezoelectric materials
in active control of unwanted vibrations in flexible structures using
spatial control. Two new controller design methodologies, spatial LQG
control and spatial H<sub>∞</sub> control are presented in the
paper. Some experimental results are also included
A self-sensing actuator is a new concept for intelligent material,
where a single piece of piezoelectric element simultaneously performs as
both a sensor and an actuator. This idea should be advantageous
especially for control of flexible structures. The key of this device is
an electric bridge circuit that includes a piezoelectric element as a
component. This circuit could give significant information about strain
in the element if it were well-balanced. Our aim is to design
controllers which enable practical self-sensing actuation in the
presence of uncertainty that loses the balance of the circuit. In this
paper, we proposed two approaches to realize self-sensing actuation
which deal with this uncertainty differently. Experimental results
proved the effectiveness of self-sensing actuation in both vibration
suppression and tracking control of a cantilever
Application of Self-sensing Actuator to Control of A Cantilever Beam Albuqiierque, NM, pp. I 867-1872 Robust Vibration Control of A Cantilever Beam Using Self-Sensing Actuator
- T Takigami
- K Oshiina
- Y Hayakawa
- K Oshiina
- T Takigaini
- Y Hayakawa
T.Takigami, K. Oshiina and Y. Hayakawa, " Application of Self-sensing Actuator to Control of A Cantilever Beam, " Proc. Ainer. Control Conf. (ACC), Albuqiierque, NM, pp. I 867-1872, June 1997. U K. Oshiina, T. Takigaini and Y. Hayakawa, " Robust Vibration Control of A Cantilever Beam Using Self-Sensing Actuator, " JSME Intl. Journal, Series C, Vol. pp. 166-185, 1992. 40, NO. 4, pp. 68 1-687, 1997.