Design of a Control System using Linear Matrix Inequalities for the Active Vibration Control of a Plate (original) (raw)
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Robust control to parametric uncertainties in smart structures using linear matrix inequalities
Journal of The Brazilian Society of Mechanical Sciences and Engineering, 2004
The study of algorithms for active vibrations control in flexible structures became an area of enormous interest, mainly due to the countless demands of an optimal performance of mechanical systems as aircraft and aerospace structures. Smart structures, formed by a structure base, coupled with piezoelectric actuators and sensor are capable to guarantee the conditions demanded through the application of several types of controllers. This article shows some steps that should be followed in the design of a smart structure. It is discussed: the optimal placement of actuators, the model reduction and the controller design through techniques involving linear matrix inequalities (LMI). It is considered as constraints in LMI: the decay rate, voltage input limitation in the actuators and bounded output peak (output energy). Two controllers robust to parametric variation are designed: the first one considers the actuator in non-optimal location and the second one the actuator is put in an optimal placement. The performance are compared and discussed. The simulations to illustrate the methodology are made with a cantilever beam with bonded piezoelectric actuators.
Active vibration control of aerospace structures using a modified Positive Position Feedback method
2009 American Control Conference, 2009
A Positive Position Feedback controller is modified and a new active vibration control technique is developed. Unlike the conventional Positive Position Feedback, the new controller separates the damping and stiffness control using two parallel first order and second order compensators. The second order compensator has a damping ratio as low as the damping of flexible structure to provide periodic vibration control. Simultaneously, the high damping is made available through a first order compensator. The new controller is applicable to a strain-based sensing/actuating approach and can be extensively applied to piezoelectrically controlled systems. Control gains are obtained by performing the stability analysis. The controller is verified experimentally using a plate vibration suppression setup. The plate is controlled through two piezoelectric patches and its vibrations are monitored by ten sensors mounted on the surface of the plate. The results confirm that the new controller is able to provide good vibration reduction, with the ability to be used to simultaneously control more than one natural frequency.
Journal of …, 2008
This work presents the theoretical and experimental studies conducted in Aerospace Engineering Department of Middle East Technical University on smart structures with particular attention given to the structural modelling characteristics and active suppression of in-vacuo vibrations. The smart structures considered in these analyses are finite and flat aluminium cantilever beam-like (called as smart beam) and plate-like (called as smart fin) structures with surface bonded PZT (Lead-Zirconate-Titanate) patches. Finite element models of smart beam and smart fin are obtained. Then the experimental studies regarding open loop behaviour of the structures are performed by using strain gauges and/or laser displacement sensor to determine the system models. Further studies are carried out to obtain the models of ∞ H and µ vibration controllers which are intended to be used in the suppression of free and forced vibrations of the smart structures. It is observed that satisfactory attenuation levels are achieved and robust performance of the systems in the presence of uncertainties is ensured. The laboratory also allows joint studies to be conducted.
Active Vibration Control of Plate Structure
International Journal of Engineering Research and, 2017
Vibration control and/or reduction can significantly improve the performance and operation of systems and machines in various industries. As technology advances, the methods of vibration control also become more involved and therefore allow for control of more complex structures. This paper focuses on vibration control of a flexible plate system. An experimental setup is designed to demonstrate reduction of flexible modes of the plate system. Actuators, accelerometers, and force sensors are specified to apply appropriate disturbance forces of varying complexity and to measure and record data necessary to update the theoretical model and design an effective controller. The experimental setup is initially made up of Aluminum plate of 3mm thickness. The control scheme involves non-collocation control of a location to which the piezo-patch is mounted. Software and experimental results of the modeling of a smart plate are presented for active vibration control. The smart plate consists of a rectangular aluminum plate modeled in cantilever configuration with surface bonded piezoelectric patches. The patches are symmetrically bonded on top and bottom surfaces. The study uses ANSYS 16.0 software to derive the finite element model of the smart plate. By using this model, the study first gives the influences of the actuator placement and size on the response of the smart plate and determines the maximum admissible piezoelectric actuation voltage.
Simulation Study of Active Vibration Control
Stringent behaviour requirements imposed on flexible structures have necessitated the sensing and control of vibrations in these structures in a suitable manner. This issue is particularly important for space and aircraft structures for which the mission requirements are crucial and the divergence from these requirements may be considerably expensive. One of the most likely alternatives to deal with this aspect of vibrations is the use of active vibration control, which makes the structure a Smart structure. Commercially available FEM softwares such as ANSYS © provide the facility to simulate active vibration control by incorporating control action in the transient analysis of the desired structure. In this paper, the use of ANSYS © software for simulating active vibration control is validated by comparing its response obtained for a two degrees of freedom system, with that obtained by analytical analysis, for unit impulse input. Then, active vibration control of a cantilever beam type of structure is demonstrated with the aid of firstly piezoelectric actuator and strain gauge sensor and then piezoelectric actuator and piezoelectric sensor; for different controller gains which are appropriately assumed. The controller receives strain in first case whereas voltage in second case from sensor and feeds corresponding voltage to the actuator to apply controlling force on the host structure. Responses are obtained for both the cases for unit impulse input. This study demonstrates the use of ANSYS © for simulating active vibration control of a structure with the aid of smart materials.
Active Structural Vibration Control: A Review
The Shock and Vibration Digest, 2003
In this paper we review essential aspects involved in the design of an active vibration control system. We present a generic procedure to the design process and give selective examples from the literature on relevant material. Together with examples of their applications, various topics are briefly introduced, such as structure modeling, model reduction, feedback control, feedforward control, controllability and observability, spillover, eigenstructure assignment (pole placement), coordinate coupling control, robust control, optimal control, state observers (estimators), intelligent structure and controller, adaptive control, active control effects on the system, time delay, actuator-structure interaction, and optimal placement of actuators.
Mathematical Problems in Engineering, 2008
This paper deals with the study of algorithms for robust active vibration control in flexible structures considering uncertainties in system parameters. It became an area of enormous interest, mainly due to the countless demands of optimal performance in mechanical systems as aircraft, aerospace, and automotive structures. An important and difficult problem for designing active vibration control is to get a representative dynamic model. Generally, this model can be obtained using finite element method FEM or an identification method using experimental data. Actuators and sensors may affect the dynamics properties of the structure, for instance, electromechanical coupling of piezoelectric material must be considered in FEM formulation for flexible and lightly damping structure. The nonlinearities and uncertainties involved in these structures make it a difficult task, mainly for complex structures as spatial truss structures. On the other hand, by using an identification method, it is possible to obtain the dynamic model represented through a state space realization considering this coupling. This paper proposes an experimental methodology for vibration control in a 3D truss structure using PZT wafer stacks and a robust control algorithm solved by linear matrix inequalities.
Active vibration damping of a smart flexible structure using piezoelectric transducers: H˞ design a
Proceedings of the 16th IFAC World Congress, 2005, 2005
This paper deals with active vibration control of a plate like smart flexible structure. This plate is equipped with several thin piezoelectric patches. Some of them are used as sensors and the others as actuators. They are optimally positioned and not collocated. The main goal of control is to reduce the most energetic vibrating modes. By using a state-space representation of a MIMO model of the equipped structure, derived from Finite Elements Modeling and modal analysis, a synthesis setup is derived to design an H ∞ controller. The resulting controller is reduced and tested experimentally.
2012
This work is aimed at the active vibration control of a flexible structures using piezoelectric material. A simple supported plate structure, which is supported at two opposite ends, is taken as the flexible structure with piezoelectric materials as sensors and actuators. Sensors and actuators, which are square in shapes, are embedded to the parent structure. The active controller was designed to control first three modes of vibration of plate. First, the analysis for the transient vibrations in a simple supported plate structure was performed which was followed by the analysis of the same simple supported plate structure when embedded upon with a pair of sensor and actuator. The plate was discretised into several small rectangular elements (6X6, 7X7… 11X11) of identical size in order to assign the different locations to sensors and actuators, which were assumed to be of the exact shape of the discretized plate elements. Further a LQR controller is applied for attenuating the global structural vibration. Settling time for each different location of piezoelectric patch location was observed which was then followed by an interpretation for the optimal location for piezoelectric patch for maximizing the vibration control. The model designed for study was duly verified with the results from past literature and an agreement between the both was observed.
Smart Materials and Structures, 1999
This numerical study presents a detailed optimal control design based on the general finite element approach for the integrated design of a structure and its control system. Linear quadratic (LQ) theory with output feedback is considered on the basis of the state space model of the system. Three-dimensional finite elements are used to model the smart structure containing discrete piezoelectric sensors and actuators by the use of combination of solid, transition and shell elements. Since several discrete piezoelectric patches are spatially distributed in the structure to effectively observe and control the vibration of a structure, the system model is thus utilized to design a multi-input-multi-output (MIMO) controller. A modal analysis is performed to transform the coupled finite element equations of motion into the state space model of the system in the modal coordinates. The output feedback controller is then employed to emulate the optimal controller by solving the Riccati equations from the modal space model. An optimal controller design for the vibration suppression of a clamped plate is presented for both the steady state and the transient case. Numerical simulation is also used to predict the reduction in the sound pressure level inside an enclosure radiated from this optimally controlled plate.