Control Of Flexible Structures Research Articles

Development and Comparison of Laplace Domain Models for Nonslender Beams and Application to a Half-Car Model With Flexible Body

Math models of flexible dynamic systems have been the subject of research and development for many years. One area of interest is exact Laplace domain solutions to the differential equations that describe the linear elastic deformation of idealized structures. These solutions can be compared to and complement finite order models such as state-space and finite element models. Halevi (2005, “Control of Flexible Structures Governed by the Wave Equation Using Infinite Dimensional Transfer Functions,” ASME J. Dyn. Syst., Meas., Control, 127(4), pp. 579–588) presented a Laplace domain solution for a finite length rod in torsion governed by a second-order wave equation. Van Auken (2012, “Development and Comparison of Laplace Domain and State-Space Models of a Half-Car With Flexible Body (ESDA2010–24518),” ASME J. Dyn. Syst., Meas., Control, 134(6), p. 061013) then used a similar approach to derive a Laplace domain solution for the transverse bending of an undamped uniform slender beam based on the fourth-order Euler–Bernoulli equation, where it was assumed that rotary inertia and shear effects were negligible. This paper presents a new exact Laplace domain solution to the Timoshenko model for an undamped uniform nonslender beam that accounts for rotary inertia and shear effects. Example models based on the exact Laplace domain solution are compared to finite element models and to slender beam models in order to illustrate the agreement and differences between the methods and models. The method is then applied to an example model of a half-car with a flexible body.

Wave-based control of under-actuated flexible structures with strong external disturbing forces

Wave-based control of under-actuated, flexible systems has many advantages over other methods. It considers actuator motion as launching a mechanical wave into the flexible system which it absorbs on its return to the actuator. The launching and absorbing proceed simultaneously. This simple, intuitive idea leads to robust, generic, highly efficient, precise, adaptable controllers, allowing rapid and almost vibrationless re-positioning of the system, using only sensors collocated at the actuator–system interface. It has been very successfully applied to simple systems such as mass–spring strings, systems of Euler–Bernoulli beams, planar mass–spring arrays, and flexible three-dimensional space structures undergoing slewing motion. In common with most other approaches, this work also assumed that, during a change of position, the forces from the environment were negligible in comparison with internal forces and torques. This assumption is not always valid. Strong external forces considerably complicate the flexible control problem, especially when unknown, unexpected or unmodelled. The current work extends the wave-based strategy to systems experiencing significant external disturbing forces, whether enduring or transient. The work also provides further robustness to sensor errors. The strategy has the controller learn about the disturbances and compensate for them, yet without needing new sensors, measurements or models beyond those of standard wave-based control.

Model based vibration control of smart flexible structure using piezoelectric transducers

This paper focuses on development and implementation of optimal control algorithms for vibration control of flexible beam structures with embedded piezoelectric actuators. Piezoelectric transducers have become the leading active elements in smart structures based on their characteristics and reliability. Piezo laminated beam with collocated pairs of piezoelectric sensors and actuators is modelled using the methodology of system identification. The obtained model has been implemented in the model based optimal control algorithms. Linear quadratic regulator and model predictive control are developed and tested using LabVIEW and NI cRIO platform. The MPC algorithm shows better performance due to the constraint handling and requires more powerfull real-time and FPGA controller target.

変位出力を用いたプロパーな局所コントローラによる大型柔軟宇宙構造物の分散ロバスト最適制御

This paper considers position and attitude control of large flexible space structures composed of a number of subsystems(substructures) which are interconnected by flexible links modeled by springs and dampers. It is assumed that sensors and actuators are collocated in each subsystem. The purpose of the paper is to propose a decentralized control method by local proper controllers using only displacement / angular displacement output, which makes both each closed-loop subsystem and an overall closed-loop system not only robustly stable against uncertainty of characteristic parameters such as mass, damping, and stiffness, but also optimal for a quadratic cost function.

Decentralized robust optimal control of large flexible space structures by local proper controllers using displacement output

Decentralized robust optimal control of large flexible space structures by local proper controllers using displacement output

Adaptive positive position feedback for multi-modal vibration control of a flexible beam

The multi-modal vibration control of flexible structures is recognised as a significant challenge owing to the well-known phenomenon of spillover and frequency varying. Spillover phenomenon and variation in the modal dynamics may cause instability and degradation in performance. To overcome these defects, an adaptive positive position feedback (PPF) method is proposed for controlling the vibration of a flexible beam with bonded piezoelectric sensors and actuators. Finite element method is used for dynamic modelling of an experimental flexible beam. An online adaptive parameter estimator based on the gradient algorithm with parameter projection and a dead zone is presented to identify the modal frequencies in the presence of disturbances. Multi-modal PPF controller is adjusted with estimated frequencies and is able to damp the target modes quickly. Simulation results show that modal frequencies are estimated quite accurately and the vibration of the structure is significantly suppressed.

Feedback Linearization Control of Flexible Structures with Hysteresis

In this paper the feedback linearization control of flexible structures with hysteresis is addressed. The system of type where a passive flexible structure is mounted on a moving rigid base, e.g. traveling cranes, cantilevers, non-rigid robotic manipulators, is considered. The controlled displacement of the base excites the flexible structure. The feedback nonlinearity, as a function of state, includes the hysteresis restoring force and structural damping. The applied feedback linearization is combined with a proportional-integral-derivative (PID) action so as to track zero reference deflection and compensate for model uncertainties, at the same time. Since the control access point is the base actuation force, the feedback linearization and proportional-integral-derivative control signals are shifted prior to the base control loop using the corresponding inverse transform. An experimental example of elastic robotic arm justifies the consideration of nonlinearities with hysteresis. The proposed control method is evaluated within numerical simulation.

Discrete-time dynamic output feedback input shaping control of vibration in uncertain time-delay flexible structures

This paper proposes an observer-based discrete-time neuro-sliding mode control (NSMC) scheme combined with input shaping control for uncertain time-delay flexible structures. Only partial information of system states is known. It is shown that the proposed scheme not only guarantees closed-loop system stability, but also it effectively suppresses residual vibration and yields good robustness in the presence of state delays, input delays, parameter uncertainties, external disturbances and inaccurate impulse application instants simultaneously. The knowledge of upper bound of uncertainties is not required. Furthermore, it is shown that increasing the robustness to parameter uncertainties does not lengthen the duration of the impulse sequence. Simulation results demonstrate the efficacy of the proposed control scheme.

Linear time‐varying control of the vibrations of flexible structures

Recent results on pole placement for linear time-varying (LTV) systems are exploited here for the control of flexible structures. The infinite-dimensional system is approached as usual by a restricted number of modes of interest, according to the frequency range in which the system is exploited. The difference with the previous approaches (e.g. gain scheduling) is that only one finite dimension linear model is used and its parameters (frequency and damping of the modes) are varying according to the operating conditions. The control model is thus LTV and a regulator is analytically synthesised to ensure closed-loop stability and performances. This regulator is also LTV and thus automatically (without any special switching action) tracks the operating conditions of the system. The case of a flexible beam is studied in simulation as well as in the laboratory experimentation. Hence, a suitable application of the proposed LTV synthesis is done to find a compromise between the complexity of interpolation and its efficiency. Furthermore, the bad dissipation factor of flexible systems leads them to be good candidates to proof the efficiency of the proposed gain scheduling strategy. This work validates on a real system the LTV pole placement approach and opens the way to a new gain scheduling strategy for the control of LTV, non-linear or infinite-dimensional systems.

Compliant liquid column damper modified by shape memory alloy device for seismic vibration control

Liquid column dampers (LCDs) have long been used for the seismic vibration control of flexible structures. In contrast, tuning LCDs to short-period structures poses difficulty. Various modifications have been proposed on the original LCD configuration for improving its performance in relatively stiff structures. One such system, referred to as a compliant-LCD has been proposed recently by connecting the LCD to the structure with a spring. In this study, an improvement is attempted in compliant LCDs by replacing the linear spring with a spring made of shape memory alloy (SMA). Considering the dissipative, super-elastic, force-deformation hysteresis of SMA triggered by stress-induced micro-structural phase transition, the performance is expected to improve further. The optimum parameters for the SMA-compliant LCD are obtained through design optimization, which is based on a nonlinear random vibration response analysis via stochastic linearization of the force-deformation hysteresis of SMA and dissipation by liquid motion through an orifice. Substantially enhanced performance of the SMA–LCD over a conventional compliant LCD is demonstrated, the consistency of which is further verified under recorded ground motions. The robustness of the improved performance is also validated by parametric study concerning the anticipated variations in system parameters as well as variability in seismic loading.

Effects of photostrictive actuator and active control of flexible membrane structure

The purpose of this paper is to investigate the flexible structure of parabolic shell using photostrictive actuators. The analysis is made to know its dynamic behavior and light-induced control forces for coupled parabolic shell. The effects of an actuator location as well as membrane and bending components under the control action have been analyzed considering the approximate spherical model. The parabolic membrane shell accuracy is being mathematically approximated and validated comparing the light induced control forces using approximate equivalent spherical shell model. The parabolic shell with kapton smart material and photostrictive actuators has been used to formulate the governing equation in the transverse direction. The Kirchhoff-Love assumptions are used to obtain the governing equation of shell with actuator. The mechanical membrane forces and bending moments for parabolic thin shell with actuator is used to analyze the dynamic effect. The results show that membrane control action is much more significant than bending control action. Photostrictive actuators oriented along circumferential direction (actuator-2) can give better control effect than actuators placed along longitudinal direction (actuator-1). The slight difference is observed between spherical and parabolic shell for a surface with focal length to the diameter ratio of 1.00 or more than unity. Space applications often have the shape of parabolical shells or shell of revolution, due to their required focusing, aiming, or reflecting performance. The present approach is focused that photostrictive actuators can effectively control the vibration of parabolical membrane shell. Also, the actuator's location plays an important role in defining the control force.

Shape Tracking of Planar Hyper-Flexible Beams via Embedded PVDF Deflection Sensors

In this paper, we present an embedded shape-sensing method for soft robotics. Soft actuators and structures are paramount for safe human-robot interaction and are of interest in biomimetics, biotechnology and defense. Control of compliant manipulators is challenging because of their large deformations, hence a form of shape feedback is required. We propose a tracking system for continuum structures using deflection sensors made of polyvinylidene fluoride (PVDF), a thin piezoelectric polymer. We demonstrate that hyper-flexible beam shapes may be parameterized with a small set of basis functions and that the deflection sensors can be used to determine the weights of the basis functions. In other words, shape reconstruction of the beam shape is reduced to solving a linear interpolation problem defined by the sensors. Interpreting the sensors with this method can reduce the cumulative errors associated with piecewise methods. We demonstrate shape tracking of a hyper-flexible beam in two-dimensional (2-D) on two experimental test beds: a pneumatic bellows actuator and a hyper-flexible plastic ruler. In addition, the data were used in simulation, for systematic investigation of several aspects: number of sensors, their relative-size, and the type of basis functions used for parameterization. We demonstrate tracking capabilities and propose guidelines for the ideal sensor layout. Our approach facilitates kinematic monitoring and control of continuum manipulators and flexible structures.

Actuator topology design using the controllability Gramian

This work develops a methodology for the optimal design of actuators for the vibration control of flexible structures. The objective is the maximization of a measure of the controllability Gramian. The test case is the embedding of piezoelectric inserts in elastic structures for vibration control in modal space. A topology optimization was formulated to distribute two material phases in the domain: a passive linear elastic material and an active linear piezoelectric material, with a volume constraint in the latter. The objective function is the trace of the controllability Gramian of a LQR control system. Analytical sensitivities for the finite element model are derived for the objective function and constraints. Results are shown for two dimensional vibration control of a short beam with varying number of electrodes (control inputs) and vibration modes.

Dynamic behavior of time-delayed acceleration feedback controller for active vibration control of flexible structures

This paper addresses the design problem of the controller with time-delayed acceleration feedback. On the basis of the reduction method and output state-derivative feedback, a time-delayed acceleration feedback controller is proposed. Stability boundaries of the closed-loop system are determined by using Hurwitz stability criteria. Due to the introduction of time delay into the controller with acceleration feedback, the proposed controller has the feature of not only changing the mass property but also altering the damping property of the controlled system in the sense of equivalent structural modification. With this feature, the closed-loop system has a greater logarithmic decrement than the uncontrolled one, and in turn, the control behavior can be improved. In this connection, the time delay in the acceleration feedback control is a positive factor when satisfying some given conditions and it could be actively utilized. On the ground of the analysis, the developed controller is implemented on a cantilever beam for different controller gain–delay combinations, and the control performance is evaluated with the comparison to that of pure acceleration feedback controller. Simulation and experimental results verify the ability of the controller to attenuate the vibration resulting from the dominant mode.

Spectral Conditions for Negative Imaginary Systems With Applications to Nanopositioning

The negative imaginary (NI) property is exhibited by many systems such as flexible structures with force actuators and position sensors and can be used to prove the robust stability of flexible structure control systems. In this paper, we derive methods to check for the NI and strict negative imaginary (SNI) properties in both the single-input single-output as well as multi-input multi-output cases. The proposed methods are based on spectral conditions on a corresponding Hamiltonian matrix obtained for a given system transfer function matrix. Under certain conditions, a given transfer function matrix satisfies the NI property if and only if the corresponding Hamiltonian matrix has no pure imaginary eigenvalues with odd multiplicity. It is also shown that a given transfer function matrix satisfies the SNI property if and only if the corresponding Hamiltonian matrix has no eigenvalues on the imaginary axis, except at the origin. The results of this paper are applied to check the NI property in two nanopositioning applications.

Directional notch filters for motion control of flexible structures

A new method to design notch filters for MIMO motion control systems with flexible mechanical structures is proposed. The method involves so-called directional notch filters that work only in the direction of the targeted resonant mode. As a result, only one SISO notch filter is required per mode to suppress a resonance throughout the MIMO system. Compared to the conventional approach where a notch filter is placed and tuned in each of the separate control loops, the new approach reduces the order of the controller significantly and facilitates the design process. The directional notch filter is computed using either the input or output mode shapes of the system. A new numerical optimization method to obtain these mode shapes from frequency response data is described. Experiments on a flexible beam setup demonstrate the feasibility of the proposed method in practice.

Self-sensing actuation using online capacitance measurement with application to active vibration control

Self-sensing actuation has been extensively used in vibration control of flexible structures over the last three decades. Positive position feedback controller has been commonly used in this field due to the robustness against spillover phenomena. Piezoelectric clamped capacitance is the most important parameter that affects the performance of this technique. In this study, the effect of capacitance change on performance and stability of a self-sensing system with positive position feedback controller is investigated. Based on this analysis, some modifications are suggested to increase the stability of the closed-loop system against capacitance change. An online Fourier transform–based capacitance measurement method is used, which guarantees good performance and stability of closed-loop system in the presence of capacitance change. Experimental results are also presented to show the effectiveness of this method in vibration control of cantilever beam.

Experimental Study of Adaptive Fuzzy Sliding Mode Control for Vibration of a Flexible Rectangular Plate

In this paper, an approach is developed for active vibration control of flexible rectangular plate structures using control theory. The flexible rectangular plate system is first modeled through a new type of modeling method—discretization and reduced-order modeling method (DROMM); and second, the validity of the obtained new model is investigated by comparing the plate natural frequencies, static analysis, and forced vibration response analysis between a finite-element model and the new model. After validating the model, an adaptive fuzzy sliding mode multiple-input multiple-output (MIMO) controller is applied to the plate dynamic equation through the MATLAB/Simulink platform. The simulation and experimental results clearly demonstrate an effective vibration suppression capability that can be achieved using an adaptive fuzzy sliding mode MIMO controller.

2A15 Decentralized Robust Optimal Control of Large Flexible Space Structures by Local Proper Controllers Using Displacement Output(The 12th International Conference on Motion and Vibration Control)

2A15 Decentralized Robust Optimal Control of Large Flexible Space Structures by Local Proper Controllers Using Displacement Output(The 12th International Conference on Motion and Vibration Control)

Improving Delay-Margin of Noncollocated Vibration Control of Piezo-Actuated Flexible Beams via a Fractional-Order Controller

Noncollocated control of flexible structures results in nonminimum-phase systems because the separation between the actuator and the sensor creates an input-output delay. The delay can deteriorate stability of closed-loop systems. This paper presents a simple approach to improve the delay-margin of the noncollocated vibration control of piezo-actuated flexible beams using a fractional-order controller. Results of real life experiments illustrate efficiency of the controller and show that the fractional-order controller has better stability robustness than the integer-order controller.