Active control experiments for large-optics vibration alleviation

A new method is devised for the active control of flexible structures using output rate weighted linear optimal control. The method has an advantage over the traditional linear optimal control method in that it assigns weightage to the time rate-of-output, which may not be available for direct measurement in several important applications, such as gust and maneuver load alleviation in airplanes and ridequality augmentation in a variety of passenger vehicles. In applications to a single degree-offreedom system and a cantilevered beam, the rate-weighted optimal controller demonstrates a much better performance in terms of the smoothness of transient response, peak rate of transient response and settling time when compared to the traditional linear quadratic regulator. Introduction Generally, there are three different approaches applied to controlling flexible structures: (a) passive addition of structural damping and stiffness (b) generating specificaNy shaped input&* ,and (c) designing an optimal feedback controlle?S4. The first option is usually cumbersome and adds mass to the structure, while the second option, requiring generation of inputs that are insensitive to modeling errors and which do not excite unwanted dynamics, is di&tilt to achieve in practice. This leaves the third option of an active feedback controller as the most practical choice for controlling structural dynamics. The optimal linear *Assistant Professor, Department of Aerospace Engineering. Senior Member, AIAA. Copyright

This paper presents a survey of ground experiments primarily conducted in the United States and U.S. facilities dedicated to the study of active control of flexible structures. The facilities are briefly described in terms of capability, configuration, size, and instruments. Topics on the experiments include vibration suppression, slewing control, and system identification. The experiments are listed in tables containing the experiment's name, the responsible organization, a brief description of the test article configuration, and the actuator/sensor devices used in the experiment. Selected experiments will be further discussed to help illustrate the control problems. Some of the test facilities dedicated to ground testing of large space structures are discussed in more detail, to give the reader a better appreciation of ground-testin g work. Several research issues are mentioned, including real-time computer systems, test article suspension, and new actuator/sensor technology development.

Active vibration control of large flexible space structure is a challenging topic in the system dynamics and control of spacecraft. This paper proposes a novel approach for vibration control on a large hoop truss structure, typically used as mesh satellite antenna. First, to suppress the first-order bending modal response of the hoop truss structure with an initial disturbance, a piezoelectric bending actuator with excellent bending actuation performance was carefully designed as a key component of an active vibration control system. Then, the actuating characteristics of the actuator and the dynamic equations of the active structure were analyzed and formulated based on a finite element method. In order to improve the vibration-attenuating effect of the control system, a Mamdani-type fuzzy logic algorithm was employed in a closed-loop control system. Finally, simulations and experiments were implemented to validate the effectiveness of the proposed active control approach and structure. The experimental results showed that the decay time of first-order bending modal response (around 0.34 Hz) of control system reduces by 75% compared with that of the uncontrolled system. The results demonstrate that the proposed active vibration control system has good application potential in controlling the bending modes of a large flexible spacecraft.

Active robust vibration control of flexible structures

The purpose of this paper is to present a method of active control for suppressing the vibration of a mechanically flexible cantilever beam which is subject to a distributed random disturbance and also a seismic input at the clamped end. First, the mathematical model of the flexible structure is established by a stochastic partial differential equation which describes the Euler-Bernoulli type distributed parameter system with internal viscous damping and subject to the seismic and distributed random inputs. Second, the distributed parameter model, which is considered as an infinite-dimensional system, is reduced to a finite-dimensional one by using the modal expansion, and split into the controlled part and the uncontrolled (residual) one. The principal approach is to regard the observation spillover due to uncontrolled part as a colored observation noise and construct an estimator, and then we construct the optimal control system. Finally, simulation studies are presented by using a real earthquake accelerogram data.

A new class of materials known as ‘functionally graded materials’ (FGMs) has emerged recently, in which the material properties are graded but continuous particularly along the thickness direction. In an effort to develop the super heat resistant materials, Koizumi [1] first proposed the concept of FGM. These materials are microscopically heterogeneous and are typically made from isotropic components, such as metals and ceramics. In the quest for developing lightweight high performing flexible structures, a concept emerged to develop structures with self-controlling and self-monitoring capabilities. Expediently, these capabilities of a structure were achieved by exploiting the converse and direct piezoelectric effects of the piezoelectric materials as distributed actuators or sensors, which are mounted or embedded in the structure [2, 3]. Such structures having built-in mechanisms are customarily known as ‘smart structures’. The concept of developing smart structures has been extensively used for active control of flexible structures during the past decade [4]. Recently considerable interest has also been focused on investigating the performance of FG plates integrated with piezoelectric actuators. For example, Ootao and Tanigawa [5] theoretically investigated the simply supported FG plate integrated with a piezoelectric plate subjected to transient thermal loading. A 3-D solution for FG plates coupled with a piezoelectric actuator layer was proposed by Reddy and Cheng [6] using transfer matrix and asymptotic expansion techniques. Wang and Noda [7] analyzed a smart FG compositestructure composed of a layer of metal, a layer of piezoelectric and a FG layer in between, while in [8] a finite element model was developed for studying the shape and vibration control of FG plates integrated with piezoelectric sensors and actuators. Yang et al. [9] investigated the nonlinear thermo-electro-mechanical bending response of FG rectangular plates covered with monolithic piezoelectric actuator layers; most recently, Huang and Shen [10] investigated the dynamics of a FG plate coupled with two monolithic piezoelectric layers undergoing nonlinear vibrations in thermal environments. All the aforementioned studies focused on the rectangular-shaped plate structures. However, to the authors’ best knowledge, no researches dealing with the free vibration characteristics of the circular FGM plate integrated with the piezoelectric layers has been reported. Therefore, the present work attempts to solve the problem of providing analytical solution for free vibration of thin circular FG plates with two full size surface-bonded piezoelectric layers on the top and the bottom of the FG plate. The formulations are based

Sliding mode control of a large flexible space structure

: Volume 2 presents theoretical advances and demonstrations in vibration control against broadband disturbances and in large-angle linear tracking control for flexible optical support structures. Stability results for discrete-time vibration control are also given. The importance of active transducer selection for broadband disturbance accommodation is emphasized. An algorithm for systematically selecting actuators with high influence on the regulated variables is described, together with its theoretical foundation. The algorithm is demonstrated on the ACOSS Model No. 2 structure, obtaining minimal selections with substantially fewer actuators than controlled modes. Disturbance-rejection control designs based on these selections exhibit stability in the presence of residual modes over a frequency range well beyond that of the design model. Sampled-data control for flexible structures is examined using second-order difference equations. A sufficient condition for geometric stability with velocity output feedback requiring non-colocation of actuators and sensors is obtained. Non-colocation reduces to colocation as the sampling period converges to zero. Optimal large-angle slew for linear tracking and terminal convergence is considered. Explicit solutions as a function of matrices satisfying linear algebraic equations are obtained. Demonstrations on a rotating rigid hub with four flexible appendages exhibit the computational efficiency of the solution techniques.

The main trend in structural technology is to change from conventional earthquake resistant structures, which are designed 'not to collapse even under the strongest earthquake' to structural controlled buildings, which are designed 'to suppress the vibrations itself'. Indications are that control methods will be able to make a genuine contribution to this problem area, which is of great economic and social importance. Current researches in the field of active structural control focus on: system identification, model order reduction, limited control authority, available measurements etc. The article reviews some of the developments in the area of controlled civil structures and highlights a robust control perspective in active vibration suppression control of flexible structures, considering a grey box approach in the system identification process.

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.

This work presents a survey on the control law development to actively attenuate the vibrations of a flexible structure submitted to fluid flow. Firstly, a robust controller with LQG/LTR approach was developed. Numerical tests were carried out being robustness characteristics to flow induced vibration and to noise rejection verified, for the case of equal nominal and real plants. The same robustness was not verified, when parametric variations were introduced. Therefore, another controller, based on regulator and filter pole placement approach, was developed where the direct loop obeys stability and performance robustness criterions, allowing to obtain good numerical results, even in the presence of significant parametric variations.

A parameter dependent Riccati equation approach is taken to analyze the stability properties of an output feedback adaptive control law design. The adaptive controller is intended to augment a nominal, fixed gain, observer based output feedback control law. Although the formulation is in the setting of model following adaptive control, the realization of the adaptive controll er does not require implementing the reference model. In this regard, the cost of implementing the adaptive controller above that of a fixed gain control law is far less than that of other methods. The error signals are shown to be uniformly ultimately bounded and an expression for the ultimate bound is provided. The control design process and theoretical results are illustrated using a model for wing-rock dynamics. Research in adaptive output feedback control of uncertain nonlinear systems is motivated by the many emerging applications that employ novel actuation devices for active control of flexible structures and fluid flows. These applications include actuators such as piezo-electric films and s ynthetic jets, which are typically nonlinearly coupled to t he plant dynamics they are intended to control. Models for these applications vary from accurate low frequency models to models that crudely approximate the true dynamics even at low frequencies. Examples of applications include active damping of flexible structures, control of aeroservoelasti c aircraft, and active control of flows. Adaptive control can be used to satisfy performance requirements in the presence of large scale parameter uncertainty, and improved safety in the event of actuator failure.

: The goals of these research projects were to examine the nonlinear dynamics and control of flexible structures, some of which might be used for space applications. This project was a collaborative one involving structural, electrical and mechanical engineers. A major part of the research was on trusses/frames structures. Five different truss structures from three to ten meters in size were constructed, two with active controls. However, nonlinear dynamics of continuous beam type structures were also investigated. One of the principal themes was to explore what types of nonlinearities would result in chaotic and unpredictable vibrations. Loose joints in truss structures, friction, buckling and geometric nonlinearities were all found to lead to chaotic motions under certain periodic forcing conditions. Actuators and sensors for space truss active vibration suppression was investigated. New methods were developed for structural control using techniques for simulated annealing for actuator placement, nonlinear random vibrations of pin-jointed trusses, vibration analysis and new models to analyze chaotic dynamics in nonlinear structures with large deformations and friction forces. Finally, a major numerical effort resulted in new codes to predict large motions of structures under active control using parallel processing algorithms.

In this paper we propose an active vibration control method for multiple high-rise buildings arranged in parallel. According to the proposed method, some flexible buildings connected by control devices called "active control bridges", are controlled through active interactions among them. This method has the merit of achieving sufficient control force under low frequency. Using this method, it is possible to control vibrations of super-tall buildings against strong winds and large earthquakes. In this study, three model buildings are connected with two actuators. The objective of this research is to control the first bending and torsional modes of each building using this method. The control effect is evaluated by exciting the base of the structures by time response and measuring the frequency response of the structures. Both simulation and experimental results show that fairly good control performance has been achieved by this method.

Time delay exists inevitably in active control, which may not only degrade the system performance but also render instability to the dynamic system. In this paper, a novel active controller is developed to solve the time delay problem in flexible structures. By using the independent modal space control method, the differential equation of the controlled mode with time delay is obtained from the time-delay system dynamics. Then it is discretized and changed into a first-order difference equation without any explicit time delay by augmenting the state variables. The modal controller is derived based on the augmented system using the discrete variable structure control method. The switching surface is determined by minimizing a discrete quadratic performance index. The modal coordinate is extracted from sensor measurements and the actuator control force is converted from the modal one. Since the time delay is explicitly included throughout the entire controller design without any approximation, the system performance and stability are guaranteed. Numerical simulations show that the proposed controller is feasible and effective in active vibration control of dynamic systems with time delay. If the time delay is not explicitly included in the controller design, instability may occur.