A discussion on the collocated active control of beams with piezoelectric patches (original) (raw)
Related papers
Active control of beam structures with piezoelectric actuators and sensors: modeling and simulation
Smart Materials and Structures, 2001
The active damping of structures is an important emerging field. In this context, it is necessary to be able to develop new control methods for flexible structures and simulate their effects. In order to be able to deal with the optimization of active device locations, spillover and any other general problems linked to control and model reduction, a simple but sufficiently rich model is very useful. This is the reason why this technical note deals with the modeling and simulation of the active vibration control of beam structures using piezoelectric actuators and sensors. In order to model beam structures equipped with piezoelectric devices, we develop a simple finite composite beam element, taking into account the properties of piezoelectric elements. This model uses six mechanical degrees of freedom and four electric degrees of freedom. Then, a linear quadratic regulator method is used to compute the control, including the implementation of a state observer. Several simulations are presented.
Computers & Structures, 2006
This paper presents a numerical study concerning the active vibration control of smart piezoelectric beams. A comparison between the classical control strategies, constant gain and amplitude velocity feedback, and optimal control strategies, linear quadratic regulator (LQR) and linear quadratic Gaussian (LQG) controller, is performed in order to investigate their effectiveness to suppress vibrations in beams with piezoelectric patches acting as sensors or actuators. A one-dimensional finite element of a three-layered smart beam with two piezoelectric surface layers and metallic core is utilized. A partial layerwise theory, with three discrete layers, and a fully coupled electro-mechanical theory is considered. The finite element model equations of motion and electric charge equilibrium are presented and recast into a state variable representation in terms of the physical modes of the beam. The analyzed case studies concern the vibration reduction of a cantilever aluminum beam with a collocated asymmetric piezoelectric sensor/actuator pair bonded on the surface. The transverse displacement time history, for an initial displacement field and white noise force disturbance, and point receptance at the free end are evaluated with the open-and closed-loop classical and optimal control systems. The case studies allow the comparison of their performances demonstrating some of their advantages and disadvantages.
Stability and vibrations control of a stepped beam using piezoelectric actuation
MATEC web of conferences, 2018
The objects of this studies are the stability and transversal vibrations of the system composed of three segments, where in the centre part of the system two piezoelectric patches are perfectly bonded to the top and bottom surface of the host beam. The system is kinematically loaded as a result of prescribed displacement of one or both end supports. For the analysis purposes three different beam end supports have been taken into consideration, which prevent longitudinal displacements i.e. clamped-clamped, clamped-pinned and pinned-pinned. This type of beam loading not only affect its natural vibration frequencies but also the system's stability. By introducing the electric field to the piezo patches, depending on its vector direction, in-plane stretching or compressive residual force may be induced. Presented results show that piezo actuation can significantly modify both the critical buckling force and the vibration frequency.
Equivalent stiffness and damping of sandwich piezoelectric beams submitted to active control
Smart Materials and Structures, 2006
In this paper, a modal approach is realized to define the damping properties of piezoelectric/elastic/piezoelectric beams. This method is based on the classical laminated beam theory and some simple assumptions about the electric fields. This leads to an electromechanical beam constitutive law. The piezoelectric layers play the role of sensor and actuator and two feedback control laws are considered. The equivalent stiffness, eigenfrequencies and loss factors of the whole system beam/control device are obtained.
2003
Active control of a vibrating beam using smart materials such as piezoelectric materials is examined in this paper. A model based on Euler-Bernoulli beam equation has been developed and. then extended with bonded three piezoelectric patches which act as sensor, actuator and exciter. The sensor and actuator are collocated to achieve a minimum phase. The aim of this research work is to control the first three resonant modes. To achieve this, a compensated inverse PID controller is developed and-tuned to damp these modes using MATLAB. The designed controller for damping each mode is then combined in parallel to damp any of the three modes. Finally, the simulation results are verified experimentally and the real-time implementation is carried out with XPC target toolbox in MATLAB.
Robust H/sub 2/ vibration control of beams with piezoelectric sensors and actuators
2003 IEEE International Workshop on Workload Characterization (IEEE Cat. No.03EX775), 2003
This paper studies vibratior; control of a beam with bonded piezoelectric sens(irs and actuators. Basic equations for piezoelectric sensors and actuators are presentcd. The equation of motion for the beam structure is derived by using the Harnilton's principle. A robust H2 controller is designed. The numerical simulation shows that the vibration can bc significantly suppressed by the proposed controller. 0-7803-7939-X/03/$17.00 0 2003 IEEE 157 PhysCon 2003, St. Petersburg. Russia
Adaptive-robust Control of a Smart Beam with Support Excitation Using Piezoelectric Layers
In this paper, vibrations of a beam with support excitation and a tip mass are suppressed using piezoelectric layers. The beam is fixed to a motion support from one end and the other end is free with an attached mass. The beam is considered as an Euler-Bernoulli beam. The governing equations of motion are derived based on the generalized function theory and Lagrange-Rayleigh-Ritz technique. An adaptive-robust control scheme is applied to control the vibrations of the beam. The mathematical modelling of the beam with control algorithm is derived and in purpose to study the effect of the amount of tip mass, size and location of the piezoelectric layers and the type of the support excitation on the beam vibrations, the system is simulated. Finally, the results of simulation are presented.
Adaptive Non Model-Based Piezoelectric Control of Flexible Beams with Translational Base
An adaptive, non model-based controller is proposed for the tracking control of a flexible cantilever beam with a translational base support. A piezoelectric (PZT) patch actuator is bonded on the top surface of the beam to apply a controlled moment for vibration suppression requirement. By selecting a Lyapunov function candidate based on a very simple energy relationship, an adaptive nonlinear feedback gain for the PZT input voltage and a simple PD controller for the moving base input force are designed to make the closed-loop system energy dissipative and hence stable. Due to the non model-based nature of the controller, some favorable features appear such as elimination of control spillovers, suppression of residual oscillations of the beam and simplicity of the control implementation. The feasibility of the controller is demonstrated using numerical simulations. Although the controller derivation is based on the original distributed partial differential model, a twonode finite element model is used for the numerical solution of the coupled PDE of the system.
IET Control Theory & Applications, 2011
Displacement feedback control of a cantilever beam is studied using non-collocated piezoelectric patch sensors and actuators. The solution to the problem is obtained using two different methods, one analytical and another numerical. The analytical method involves an integral equation formulation of the problem where the eigensolutions of the integral equation are shown to be the eigensolutions of the governing differential equation of motion of the smart beam. This approach eliminates the difficulties associated with discontinuities caused by patch sensors and actuators which introduce Heaviside functions and derivatives of the Heaviside functions into the differential equation formulation. The numerical method of solution uses a finite-element model of the controlled beam with modified beam element mass and stiffness matrices to account for the piezo patches and the control effect. The control circuit consists of a piezoceramic and polyvinylidene fluoride sensor patch and a lead zirconium titanate actuator patch. The mass and stiffness of the piezoceramic actuator patch are taken into account in the mass and stiffness calculations. Numerical examples with non-collocated sensor and actuator patches are presented and the first three natural frequencies are given using the integral equation and the finite-element methods. The results of these methods match very closely which provides a verification of the results.