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Composite multi-modal vibration control for a stiffened plate using non-collocated acceleration sensor and piezoelectric actuator
Abstract and Figures
A novel active method for multi-mode vibration control of an all-clamped
stiffened plate (ACSP) is proposed in this paper, using the
extended-state-observer (ESO) approach based on non-collocated
acceleration sensors and piezoelectric actuators. Considering the
estimated capacity of ESO for system state variables, output
superposition and control coupling of other modes, external excitation,
and model uncertainties simultaneously, a composite control method,
i.e., the ESO based vibration control scheme, is employed to ensure the
lumped disturbances and uncertainty rejection of the closed-loop system.
The phenomenon of phase hysteresis and time delay, caused by
non-collocated sensor/actuator pairs, degrades the performance of the
control system, even inducing instability. To solve this problem, a
simple proportional differential (PD) controller and acceleration
feed-forward with an output predictor design produce the control law for
each vibration mode. The modal frequencies, phase hysteresis loops and
phase lag values due to non-collocated placement of the acceleration
sensor and piezoelectric patch actuator are experimentally obtained, and
the phase lag is compensated by using the Smith Predictor technology. In
order to improve the vibration control performance, the chaos
optimization method based on logistic mapping is employed to auto-tune
the parameters of the feedback channel. The experimental control system
for the ACSP is tested using the dSPACE real-time simulation platform.
Experimental results demonstrate that the proposed composite active
control algorithm is an effective approach for suppressing multi-modal
vibrations.
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... 35 Due to independent of the accurate mathematical model and the strong ability of anti-disturbance, the ESO-based control frame has been widely used in various industrial systems. [36][37][38] Considering the convergence of NTSMC controller and the disturbances estimation ability of ESO, one potential control strategy is the NTSMC based on ESO (NTSMC-ESO), since the global¯nite-time stability of the closed-loop control system can be ensured due to the NTSMC scheme. Similar as Ref. 38, the vibration energy of the¯rst two modes dominates the multi-mode vibration, since the other high-order modes can be ignored. ...
... [36][37][38] Considering the convergence of NTSMC controller and the disturbances estimation ability of ESO, one potential control strategy is the NTSMC based on ESO (NTSMC-ESO), since the global¯nite-time stability of the closed-loop control system can be ensured due to the NTSMC scheme. Similar as Ref. 38, the vibration energy of the¯rst two modes dominates the multi-mode vibration, since the other high-order modes can be ignored. So, a composite two-loop NTSMC control strategy based on ESO is proposed to suppress the¯rst two-mode vibration of the all-clamped piezoelectric plate structure with two-mode excitations. ...
... In addition, the anti-disturbance burden of NTSMC is reduced to solve the chattering problem because each mode vibration control loop is relatively independent control system in the multi-mode vibration control loop. 38 Meanwhile, the¯nite-time convergence of the system state variables is assured by NTSMC based on the nonlinear sliding-mode surface. The main embodiments of the contributions of the paper are as follows: (1) the condition for state variables of the vibration system to reach equilibrium points in¯nite time can obtained by the proposed NTSMC-based vibration controller; (2) the total disturbance and the phenomenon of the traditional NTSMC are attenuated by the proposed ESO via feedforward channel; (3) NTSMC-ESO decouples the coupling e®ects between each mode, which is vital for multi-mode vibration suppression. ...
Considering the internal and external disturbances, i.e. coupling effect, model uncertainties, and external excitation of an all-clamped piezoelectric plate, a two-loop nonsingular terminal sliding-mode controller (NTSMC) based on extended state observer (ESO) is developed to suppress the two-mode structural vibration. First, a state space model of the structure is established based on system identification with an auxiliary variable method. Second, a three-order ESO of each individual mode is drawn to estimate and compensate the lumped disturbances via feedforward channel in real-time. Third, the NTSMC based on ESO for each single mode is designed to obtain vibration suppressing performance. In addition, the two-mode vibration control is decoupled into single-mode independent control through the proposed ESO. The stability of whole closed-loop system is analyzed by using a Lyapunov stability criterion. Finally, the experimental platform based on NI-PCIe device for a piezoelectric structural vibration control is set up to verify the effectiveness and superiority of the proposed two-mode vibration control method. Compared with the conventional ESO-based sliding-mode control (SMC) method, the experimental results of two-mode structural vibration demonstrate that the vibration suppression performance of first two modes is improved from 8.94dB to 11.7dB and 9.2dB to 14.75dB, respectively.
... As a special case, linear ESO (LESO) based control method is usually preferred to solve the practical engineering problems, since it has a simple structure and also fewer tuning parameters. In addition, LESO-based control method is increasingly implemented for the vibration suppression of piezoelectric structures due to its high robustness, strong anti-disturbance ability and less requirement on system model knowledge in past decade (Language et al., 2020;Li et al., 2014aLi et al., , 2014bLiu et al., 2020;Zhang et al., 2014;Zheng et al., 2014). Although some practical applications in different fields show that nearly the same performance can be achieved by using NESO-based and LESO-based control methods, some theoretical results prove that the control performance of peaking values and noise tolerance of NESO is better than LESO under similar bandwidth tuning parameters (Wu et al., 2020;Guo, 2017, 2018 card is also a serious challenge in structural vibration system. ...
... The actual collocated placement of accelerometers and piezoelectric actuators is hard to be realized in practical vibration engineering, which is also an important factor for system time delay. A LESO-based vibration control method is proposed to compensate the time delay caused by the non-collocated placement of the sensor/actuator pair in ref. (Li et al., 2014b), where the vibration suppression experimental results of a piezoelectric stiffness plate show that the predictor-based LESO method can effectively suppress the structural vibration within a certain frequency range. Unfortunately, the control performance of the LESO-based controller with smith predictor may degrade significantly because of the high frequency noise amplification effect of the traditional differentiator. ...
... The reduced order ESO, whose stability is rigorously analyzed for the linear time invariant case, is proposed to compensate the matched time delay (Pawar et al., 2017). Smith predictor based ESO, utilizing the output predictive value, is another effective time delay compensation control method (Li et al., 2014b(Li et al., , 2021Liu et al., 2019;Zhang et al., 2020;Zheng and Gao, 2014). It is noted that although many enhanced ESO-based control methods have been proposed for controlling dynamical systems with total disturbances and time delay, synchronously, their performance analysis have not been fully studied and compared. ...
Considering the problems of model uncertainties, higher harmonics, uncertain boundary conditions, external excitations and system time delay in practical vibration control system, a novel active vibration control method is proposed to suppress the vibration of a thin plate structure with acceleration sensor and piezoelectric bimorph actuator in this paper. First, a nonlinear extended state observer (NESO)-based controller is designed to ensure the anti-disturbance performance of the structural vibration control system. Then, an enhanced differentiator-based time delay compensation method is introduced to improve the vibration suppression performance of the NESO-based controller. A real time hardware-in-the-loop benchmark for an all-clamped piezoelectric thin plate is designed to verify and compare the performance of the developed controller against conventional ESO-based methods (linear ESO with/without time delay compensation, NESO without time compensation). The best vibration suppression and disturbance rejection performance of the proposed NESO-based controller with an enhanced time delay compensator is verified in the comparative experimental results. This work is able to provide practitioners with vital guidance in designing active vibration control system in the presence of disturbances and time delay.
... In [16], the state matrix A of the state-space realization is filled with the experimentally identified modal parameters while the actuation and observation matrices B and C respectively still contain the theoretical electromechanical coupling factors with the possible dispersion mentioned earlier for complex, curved shaped composite structures. A common solution to deal with non-collocated control is to correct the modal phase with suitable time delays within the closed-loop such as in [17,19]. Qiu Z proposed also in [18] to introduce an identified time delay to correct the phase from the theoretical modal model obtained by FE method, controlling the first 3 bending modes and 2 torsional modes of a composite plate. ...
... The designed LQG frequency-shaped controller is compared in the next subsection to classical LQG approach applied directly to the system G with the state spacerealization (11) and an observer of the form (19) applied to (11). In this case, the weight matrices Q 0 and R 0 of the LQR associated LQR problem (A , B , Q 0 , R 0 ) are: ...
This paper proposes an experimental modal identification method for vibration control of multi-actuators and multi-sensors complex smart structures. The general formulation avoids the difficulty of the coupling coefficients identification in electromechanical systems through a modal reduced-order model and uses first-order polynomials as phase correctors for the numerators of the identified transfer functions. Then, a frequency-shaped linear quadratic controller is designed to control multiple modes on a smart composite structure with integrated transducers. The experimental results obtained in terms of multi-modal vibration control were promising with attenuations up to 20dB on the target modes, confirming the efficiency of the proposed identification and control method for future applications with more extended and complex composite smart structures.
... Based on free vibration analysis of stiffened laminated plates [8], a mathematical model for stiffened square plate is developed. Different numerical and analytical methodologies have been used for studying the behaviour of plates (bare and stiffened) under various loading conditions [9][10][11][12][13][14][15][16][17][18]. Recent studies suggest that curvilinear stiffeners are more effective in stiffening the overall plate as compared to the straight stiffeners [19][20][21][22][23]. ...
Light weight thin alloys and composite materials have revolutionized aerospace, marine, electronics and construction industries. Based on their application and structural behaviour, plates are often designed in arbitrary shapes. This paper deals with free vibration analysis of simply supported plates with different geometries. The plates are modeled with a stiffener which is curvilinear in shape. To enable comparison of plates, three parameters viz., the area of plates, starting point of the stiffener and curvature of the stiffener were kept constant. The Finite Element model was developed for free vibration analysis using FEAST (Finite Element Analysis of Structures). The geometries considered were circular, square, rectangular (with aspect ratio of 1.25, 1.50 and 1.75, respectively) and skew square (with 70o, 76.67o and 83.33o skew angles, respectively). It was observed that the stiffness increased with the increase in aspect ratio of bare plates unlike the case of stiffened plates. In the case of stiffened plates, the stiffness increased with increase in aspect ratio up to 1.50 and thereafter decreased for the aspect ratio of 1.75. The bare and stiffened plates showed an increase in stiffness with increase in skewness of the geometry. Among the geometries considered, the stiffener was found to be most effective for the circular plate (110% increase in stiffness compared to bare plate) and least effective for the rectangular plate (50% increase in stiffness compared to bare plate) with 1.75 aspect ratio. The rectangular plate with aspect ratio 1.75 had the maximum overall stiffness and the circular plate had the minimum overall stiffness in the case of bare plates. In the case of stiffened plates, skew plates with 70o skew angle had the maximum overall stiffness and the circular plate had the minimum overall stiffness.
A comprehensive review of smart materials actuators is presented from control aspects for various applications. The smart materials actuators considered in this work are actively being applied to diverse control systems: magnetorheological elastomer, magnetorheological fluid, piezoelectric material, shape memory alloy, magneto-strictive material, and electro-active polymer. Both classical and modern control approaches, which have been realized for diverse applications over the last 10 years, are surveyed and discussed using the tables and figures. In order to quickly visualize and compare the different control characteristics of each actuator, the table summarizes several aspects of the specific device/system, controller type, control target, control criterion, inherent property, and outcome. The total publications and appearance of these actuators in every year are shown through the figures to understand the research status and trend easily. In addition, the featured structures of control schemes are analyzed and discussed to provide future research direction for the enhancement of control performance. It is no doubt that this review analysis significantly supports full information so that researchers related to smart materials can understand and compare the salient characteristic of each actuator and hence develop a new or advanced one for a certain control application.
This paper presents the development of a new kind of magnetorheological elastomer blend made with natural rubber, acrylonitrile-butadiene rubber (NR-NBR), and electrolytic iron particles through solution mixing. The compressive stress and elastic modulus of the composites in the isotropic and anisotropic states of the filler were studied. A unique study of the filler distribution and filler orientation mechanism was proposed from the compressive properties and scanning electron microscopy (SEM). Strong improvement in the elastic modulus of the NR-NBR blend from isotropic to anisotropic change was achieved compared to NR and NBR in single-rubber composites. The filler content in the anisotropic magnetorheological elastomers was optimized by measuring the field-dependent elastic modulus in the presence of an externally applied magnetic field. The blend rubber composites showed better sensitivity in the presence of a magnetic field than the NR and NBR composites. The improvement might be due to the better filler orientation and strong adhesion of filler particles by the NR phase in the blend matrix. The new elastomer blends may have applications in active dampers, vibrational absorption, and automotive bushings.
All-clamped plate structures are usually subject to strong coupling, model uncertainties and system time-delay. To address these challenges, this work proposes a novel vibration control method based on a linear active disturbance rejection controller (LADRC) with time-delay compensation (TDC-LADRC). The mathematical model of the piezoelectric plate is first established based on system identification with an auxiliary variable method. Then ADRC is designed for the delay-free part by a smith predictor with a novel differentiator. An extended state observer (ESO) is drawn to estimate the internal and external disturbances, such as mode errors, higher harmonics and external environmental excitations. Then, real-time compensation is introduced via feed-forward mechanism to attenuate their adverse effects, so that optimal vibration suppression performance can be achieved by the proposed controller. Finally, based on NI-PCIe6343 acquisition card, an experimental setup is designed to verify and compare the performance of the proposed TDC-LADRC against the traditional LADRC and the traditional predictor based LADRC (PLADRC). Comparative experimental results show that the proposed TDCLADRC possesses the best disturbance rejection and vibration suppression performance.
Considering the internal and external disturbances in actual engineering structure, a composite active vibration control method is proposed for an all-clamped piezoelectric panel. First, the theoretical modal analysis and laser vibrometer are employed to obtain the natural frequency and mode shape of the panel, for reasonable arrangement of actuator and accelerometer. Second, a nonlinear extended state observer is introduced to estimate the total disturbances, i.e., modeling uncertainties, high-order harmonics, coupling and external excitations. Third, the estimated value is used to compensate and attenuate the influence of the total disturbances in real time. In addition, the feedback controller based on the proportional differential and acceleration feedback method is designed to enhance the vibration suppression performance of the whole system. Finally, a semi-physical platform is built in MATLAB/Simulink real-time environment with the NI-PCIe6343 acquisition card to verify the effectiveness and superiority of the proposed method.
In the present study, active control of a smart beam under forced vibration is analyzed. The aluminum smart beam is composed of two piezoelectric patches and strain gauge. One of the piezoelectric patches is used as controlling actuator while the other piezoelectric patch is used as vibration generating shaker. The smart beam is harmonically excited by the piezoelectric shaker at its fundamental frequency. The strain gauge is utilized to sense the vibration level. Active vibration reduction under harmonic excitation is achieved using both strain and displacement feedback control. Control actions, the finite element (FE) modeling and analyses are directly carried out by using ANSYS parametric design language (APDL). Experimental applications are performed with LabVIEW. Dynamic behavior at the tip of the beam is evaluated for the uncontrolled and controlled responses. The simulation and experimental results are compared. Good agreement is observed between simulation and experimental results under harmonic excitation.
Piezoelectric panel is a fundamental element in many structures characterised with multi-variables, coupling and uncertain external excitation. Many advanced active control schemes have been reported for the multi-modal of piezoelectric structure. However, these control schemes, including the multi-loop PID method usually cannot achieve satisfying performance in the presence of strong external disturbances and coupling effects. To this end, an amended disturbance observer (DOB) based on multi-loop PID scheme is developed to control a two-mode piezoelectric panel. The system considered here is with lumped disturbances including external disturbances, such as the variations of the output of the modal and the external excitation, and internal disturbances, such as coupling effects. The proposed control approach consists of two compound controllers, and each controller includes a PID feedback part and a feed-forward compensation part based on DOB for disturbances. In order to obtain a better vibration suppressing performance, a chaos optimisation method based on Logistic map and a new transient performance function is designed to tune the parameters of PID controller. A rigorous analysis is also given to show why the DOB can effectively suppress the variations. At last, in order to verify the proposed algorithm, the dSPACE real-time simulation platform is used and an experimental platform for the all-clamped stiffened panel structure active vibration control is set up. The simulation and experiment results demonstrate that the proposed method has a much better vibration suppressing property with almost the same input voltage than the multi-loop PID method in the piezoelectric panel.
The standard extended state observer based control (ESOBC) method is only applicable for a class of single-input-single-output essential-integral-chain systems with matched uncertainties. It is noticed that systems with nonintegral-chain form and mismatched uncertainties are more general and widely exist in practical engineering systems, where the standard ESOBC method is no longer available. To this end, it is imperative to explore new ESOBC approach for these systems to extend its applicability. By appropriately choosing a disturbance compensation gain, a generalized ESOBC (GESOBC) method is proposed for nonintegral-chain systems subject to mismatched uncertainties without any coordinate transformations. The proposed method is able to extend to multi-input-multi-output systems with almost no modification. Both numerical and application design examples demonstrate the feasibility and efficacy of the proposed method.
The interest of this paper is to develop a general and systematic robust control methodology for active vibration control of flexible structures. For this purpose, first phase and gain control policies are proposed to impose qualitative frequency-dependent requirements on the controller to consider a complete set of control objectives. Then the proposed control methodology is developed by employing phase and gain control policies in the dynamic output feedback H∞ control: according to the set of control objectives, phase and gain control policies incorporate necessary weighting functions and determine them in a rational and systematic way; on the other hand, with the appropriate weighting functions efficient H∞ control algorithms can automatically realize phase and gain control policies and generate a satisfactory H∞ controller. The proposed control methodology can be used for both SISO and MIMO systems with collocated or non-collocated sensors and actuators. In this paper, it is validated on a non-collocated piezoelectric cantilever beam. Both numerical simulations and experimental results demonstrate the effectiveness of the proposed control methodology.
Many electroactive functional materials have been used in small- and microscale transducers and precision mechatronic control systems for years. It was not until the mid-1980s that scientists started integrating electroactive materials with large-scale structures as in situ sensors and/or actuators, thus introducing the concept of smart materials, smart structures, and structronic systems. This paper provides an overview of present smart materials and their sensor/actuator/structure applications. Fundamental multifield optomagnetopiezoelectric-thermoelastic behaviors and novel transducer technologies applied to complex multifield problems involving elastic, electric, temperature, magnetic, light, and other interactions are emphasized. Material histories, characteristics, material varieties, limitations, sensor/actuator/structure applications, and so forth of piezoelectrics, shape-memory materials, electro- and magnetostrictive materials, electro- and magnetorheological fluids, polyelectrolyte gels, superconductors, pyroelectrics, photostrictive materials, photoferroelectrics, magneto-optical materials, and so forth are thoroughly reviewed.
The flutter of a stiffened laminate composite panel subjected to
nonlinear aerodynamic force is investigated by means of a new analytical
model in the present study. The von-Karman large deflection plate theory
is used to account for the geometrical nonlinearity of the stiffened
composite panel, and the third order piston theory is employed to
estimate the nonlinear aerodynamic pressure induced by the supersonic
airflow. The interaction between the panel and the stiffener is
considered to be a pair of acting force and reacting force. According to
the Hamilton principle and the Euler-Bernoulli beam theory, the
coupled partial differential governing equations of the panel and the
stiffener are established. On the basis of deformation compatibility
between the panel and the stiffener, the assumption mode shapes of the
panel are introduced into the dynamic partial differential governing
equations of the stiffener to calculate the acting/reacting force
between the panel and the stiffener. When the expression of the
acting/reacting force is substituted into the dynamic differential
governing equations of the panel, the fourth-order Runge-Kutta
numerical integration method is employed to simulate the dynamic
response of the stiffened panel. The effects of various parameters, such
as the stiffening scheme and the geometric dimension of the stiffener,
on the critical flutter dynamic pressure and the amplitude of the
transverse vibration of the panel are studied in details. The simulation
indicates that the critical flutter dynamic pressure can be greatly
enhanced by introducing a proper stiffening scheme.
In active vibration control of smart structures, the actuator and sensor placement is a key point of the control system design. Even the most robust control logics could easily make a structure unstable if the actuators and sensors were not correctly positioned. The objective of this paper is to propose an H2 norm approach for the actuator and sensor placement. Unlike most modal H2 norm actuator and sensor placement methodologies, this work aims not only to maximize the norms of the controlled modes but also to reduce spillover problems by taking into account the residual modes and minimizing their H2 norms. It discusses the optimal actuator and sensor configuration in a finite element model of a square plate fixed on three sides with piezoelectric patch actuators and acceleration sensors. Finally, downstream of the actuator and sensor positioning, IMSC, PPF and NDF controls have been tested and discussed.
To compensate for the nonlinearity and to achieve finely-tuned tracking accuracy of a gun control system driven by an AC machine, an improved active disturbance rejection control (IADRC) strategy with neural network embedding (NN-IADRC) is developed in this paper. The proposed IADRC, which has amnestic memory effects, can be regarded as an extension of the conventional ADRC (CADRC), making it a special case of the IADRC. To further attenuate the dependence on system models and enhance the disturbance rejection capacities of the IADRC strategy, an on-line NN-based optimum updating approach is also developed in this paper. Finally, a series of experiments are conducted on the semi-physical simulation platform to estimate the performance of the control system and the effects of the memory factor on the system. The experimental results confirm that the proposed NN-IADRC is highly robust. The results also confirm that it performs more excellently than the CADRC and that its fine tuning has attained tracking accuracy.
A continuous nonsingular terminal sliding mode control approach is proposed for mismatched disturbance attenuation. A novel nonlinear dynamic sliding mode surface is designed based on a finite-time disturbance observer. The time taken to reach the desired setpoint from any initial states under mismatched disturbance is guaranteed to be finite time. In addition, the proposed method exhibits the fine properties of nominal performance recovery as well as chattering alleviation.
Considering the spillover and harmonic effect in real active vibration control, a novel composite controller based on disturbance observer (DOB) for the all-clamped panel is presented. The single-mode of the piezoelectric panel can be regarded as a second-order system. The unmodeled error of the current controlled mode, harmonic effects, uncontrolled mode effects, etc., are regarded as the lumped disturbances which can be estimated by the DOB, and the estimated value is used for the feed-forward compensation design. Then, an optimal linear quadratic regulator (LQR) strategy is employed for the feedback design. In order to solve the difficulty of determining the weight matrices of LQR, a chaos optimization method based on logistic map is proposed. So the weight matrices can be tuned automatically. Combining with a new transient performance function, the optimal weight matrices can be obtained. The composite controller can effectively suppress the lumped disturbances of the all-clamped panel. Experiment comparisons with conventional LQR are given to verify the effectiveness of the proposed method.