Active vibration control of a smart plate using a piezoelectric sensor–actuator pair at elevated temperatures

Abstract

A new scheme for active structural vibration control using piezoelectric patches at elevated temperatures is analytically derived and experimentally verified. A control law is derived using augmented piezoelectric constitutive equations which include the temperature dependence of piezoelectric stress coefficient (e 31 ) and permittivity (∈ 33 ). Since the temperature dependence of 'e 31 ' and '∈ 33 ' is not analytically known, their experimental values measured at elevated temperatures are used. Using augmented constitutive equations, a finite element model of a smart two-dimensional isotropic plate instrumented with a collocated piezoelectric sensor-actuator pair is derived. A control law for active vibration control of the first mode of the smart cantilevered plate is derived using negative velocity feedback. Active vibration control of the first mode of a smart cantilevered plate is experimentally achieved at elevated temperatures ranging from 25 to 75 • C under two cases: (i) using a control law which ignores the temperature dependence of 'e 31 ' and '∈ 33 ' and (ii) using a control law which includes the temperature dependence of 'e 31 ' and '∈ 33 '. A comparison between these two control laws shows that: (i) active vibration control (AVC) performance is not maintained at elevated temperatures using a control law which ignores the temperature dependence of 'e 31 ' and '∈ 33 ' and (ii) AVC performance is maintained at elevated temperatures when we use a control law which includes the temperature dependence of 'e 31 ' and '∈ 33 '.

Temperature compensation in a smart structure by application of DC bias on piezoelectric patches

“…Variation of piezoelectric coefficient e 31 and permittivity 2 33 with change in AC electric field can be included in constitutive equations using curve fit method and AVC of smart piezo structure can be done by including these equations in Kalman estimator. AVC of a cantilevered plate using piezoelectric patches can be done at elevated temperatures without loss in performance by considering augmented constitutive equations of piezoelectricity (Gupta et al, 2011(Gupta et al, , 2012. Where augmented constitutive equations in e-form are given as (2009) and Wang et al (2003) and 2 33 is calculated from value of 2 33 /2 0 given by Wang et al (1998Wang et al ( , 2003.…”

“…Augmented constitutive equations can be incorporated in finite element model and Kalman estimator and subsequently vibrations can be controlled using negative velocity feedback (Gupta et al, 2011(Gupta et al, , 2012. This technique of doing temperature compensation in a piezo smart structure requires online updation with temperature to be done of values of piezoelectric coefficient and permittivity in the Kalman observer.…”

Optimal piezoelectric control of a plate subject to time-dependent boundary moments and forcing function for vibration damping

“…In the above studies isotropic piezoelectric materials were employed as actuators and sensors while the orthotropic piezo-actuators can also be used for this purpose [26]. Special cases of vibration control due to thermal loads [27][28][29][30] and moving loads [31] using piezoelectric actuation were also studied. In the present study, the optimal vibration control problem for a simply supported rectangular plate subject to an external excitation and transient moment boundary conditions is formulated and solved with the control exercised by a piezo-patch actuator.…”

Implementation of modified positive velocity feedback controller for active vibration control in smart structures

“…7 Active vibration control using smart materials has become more popular, in part due to the fast response, easy fabrication process, lack of moving parts, light weight material, low cost, high force output, low power consumption, and lack of a generated magnetic field while converting electrical energy into mechanical energy. 8 Since flexible smart structures are distributed parameter systems, they often have a large number of participating modes to control. It is often necessary, therefore, to obtain a suitable reduced-order model by neglecting the high-frequency modes.…”