Nonlinear Dynamics and Control of Flexible Structures

Many future space missions involving flexible structures for large optics may require active vibration control to satisfy mission objectives. Thus, it is important for active control of flexible structures to be practically demonstrated in ground based experiments. These experiments can validate (or invalidate) existing theories and technology and provide directions for future research. This paper discusses three experiments conducted by Harris which successfully demonstrate control of flexible structures. The paper concludes with some remarks on the lessons learned from conducting these experiments.

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.

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.

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

An area of current interest in the decentralized control of large flexible structures is the development of adaptive strategies that will allow for acceptable vibration suppression and tracking in the presence of uncertainties. One such strategy is the Gavel-Siljak approach, which is based upon direct control using adaptive gains. The approach treats the interconnections effects between subsystems as uncertain quantities. The current study is aimed at examining the appropriateness of such an algorithm for the control of multibody flexible structures. A two body simulation model is developed. The application of the adaptive control algorithm to this structure is discussed in the context of the simulation model. Results using this model are presented and discussed.

Sliding mode control of a large flexible space structure

This work presents an optimization framework for tailoring the nonlinear dynamic response of lightly damped mechanical systems using spectral submanifold (SSM) reduction. We derive the SSM-based backbone curve and its sensitivity with respect to parameters up to arbitrary polynomial orders, enabling efficient and accurate optimization of the nonlinear frequency–amplitude relation. Sensitivity expressions are obtained via the adjoint method, which significantly reduces computational cost compared to direct differentiation as the number of parameters increases. A key feature of the framework is the automatic adjustment of the expansion order of SSM-based reduced-order models using user-defined error tolerances during optimization. We demonstrate the effectiveness of the approach through several numerical examples, including the first application of topology optimization in nonlinear structural dynamics via arbitrary-order SSMs. Hence, the proposed framework extends the applicability of SSM-based optimization to practical engineering problems, providing a robust tool for designing and optimizing nonlinear mechanical structures.

Model predictive control (MPC) has become a practical approach for implementing active safety control strategies in autonomous vehicles (AVs). This paper introduces a Fast Iterative MPC (FI-MPC) framework with rule-based iteration convergence criteria to tackle the significant challenges of control precision and solving time discrepancies between linear and nonlinear MPC algorithms within tracking control strategies for AVs. Differing from linear and nonlinear MPC structures, the core concept of FI-MPC involves incorporating the unmodeled nonlinear dynamics of the vehicle or tires into a linear framework to achieve optimal iterative control solutions. The goal is to mitigate the mismatch between linear and high-fidelity nonlinear dynamics models, thus achieving real-time high-precision tracking control of nonlinear vehicle dynamics under challenging conditions. In addition, rule-based convergence criteria are designed to enhance the iteration mechanism of FI-MPC, further conserving the computational resources of the onboard controller by reducing unnecessary iteration steps. To validate the effectiveness of the FI-MPC algorithm, this study investigates the trajectory tracking problem for a four-wheel-drive AV for a weave test scenario. Co-simulation and hardware-in-the-loop testing results at various speeds confirm that FI-MPC enables high-precision control of nonlinear dynamics while ensuring excellent real-time performance.

There is a recognised need to address issues of vibration control by making use of recent developments in data-driven modelling. The present study considers the difficulties imposed by the limitations of the actuator in the range of active vibration control. The paper proposes and examines a data-based Gaussian process (GP) model of a proof mass actuator in a flexible structural framework, aiming to improve control performance. This requires incorporating an inverse GP of static nonlinearity within the Wiener-Hammerstein model. The model starts with designing model predictive control (MPC) for a cantilever beam, in which the aim is to identify the optimal control force. Utilising the GP is the second step towards quantifying the uncertainty and limitation of the proof mass actuator by designing an inverse GP for the static nonlinearity. This quantification forwards to an MPC controller using a steady-state target optimisation tracking approach, in which this controller provides the optimal voltage required to eliminate vibration within the controller’s limitations. The numerical outcome shows that the proposed scheme was capable of supplying the necessary voltage, which eliminated the structure’s vibration within an actuator’s limits. The results of this work encourage additional research into the developed strategy, particularly in the context of experimental real-time implementation.

This paper presents design, implementation and experimental results of active vibration control of adaptive truss structure using fuzzy neural method. An adaptive truss structure with self-learning active vibration control system is developed. A fuzzy neural network (FNN) controller with adaptive membership functions is presented. The experimental setup of a two-bay truss structure with active members is constructed, and the FNN controller is applied to vibration suppression of the truss. The controller first senses the output of the accelerometer as an error to activate the adaptation of the weights of the controller, and then a control command signal is calculated based on the FNN inference mechanism to drive the active members. Experimental results demonstrate that the active FNN controller can effective reduce the truss vibration.

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.

We establish strong stability for a class of nonlinear boundary feedback controllers using an abstract wave-equation formulation of a beam stabilization problem arising in the control of flexible structures in space.

The multi-coupled nonlinear factors existing in the giant magnetostrictive actuator (GMA) have a serious impact on its output characteristics. If the structural parameters are not properly designed, it is easy to fall into the nonlinear instability, which has seriously hindered its application in many important fields. The electric–magnetic-machine coupled dynamic mathematical model for GMA is established according to J-A dynamic hysteresis model, ampere circuit law, nonlinear quadratic domain model and structure dynamics equation. Nonlinear dynamic analysis method is applied to study the nonlinear dynamic behaviour of the key structure parameters to reveal their influence on the system stability. The design principle of structural parameters is obtained by studying stability of GMA, which provides theoretical basis and technical support for the structural stability design.

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.

: 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.