Rate weighted optimal control of flexible structures

Approximation of an ideal infinite dimensional compensator for an infinite dimensional system is discussed. Two approaches are considered; one is to design a compensator for a finite dimensional model of the system, and the other approach, which is stressed here, is to truncate an infinite dimensional ARMA representation of the ideal compensator. Performance of the closed-loop system is discussed, and an example from control of flexible structures is presented.

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.

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.

An improved data-driven predictive optimal control approach for designing hybrid electric vehicle energy management strategies

1 A Survey on Computational Optimal Control.- Issues in the Direct Transcription of Optimal Control Problems to Sparse Nonlinear Programs.- Optimization in Control of Robots.- Large-scale SQP Methods and their Application in Trajectory Optimization.- Solving Optimal Control and Pursuit-Evasion Game Problems of High Complexity.- 2 Theoretical Aspects of Optimal Control and Nonlinear Programming.- Continuation Methods In Boundary Value Problems.- Second Order Optimality Conditions for Singular Extremals.- Synthesis of Adaptive Optimal Controls for Linear Dynamic Systems.- Control Applications of Reduced SQP Methods.- Time Optimal Control of Mechanical Systems.- 3 Algorithms for Optimal Control Calculations.- Second Order Algorithm for Time Optimal Control of a Linear System.- An SQP-type Solution Method for Constrained Discrete-Time Optimal Control Problems.- Numerical Methods for Solving Differential Games, Prospective Applications to Technical Problems.- Construction of the Optimal Feedback Controller for Constrained Optimal Control Problems with Unknown Disturbances.- Repetitive Optimization for Predictive Control of Dynamic Systems under Uncertainty.- Optimal Control of Multistage Systems Described by High-Index Differential-Algebraic Equations.- A New Class of a High Order Interior Point Method for the Solution of Convex Semiinfinite Optimization Problems.- A Structured Interior Point SQP Method for Nonlinear Optimal Control Problems.- 4 Software for Optimal Control Calculations.- Automated Approach for Optimizing Dynamic Systems.- ANDECS: A Computation Environment for Control Applications of Optimization.- Application of Automatic Differentiation to Optimal Control Problems.- OCCAL: A mixed symbolic-numeric Optimal Control CALculator.- 5 Applications of Optimal Control.- A Robotic Satellite with Simplified Design.- Nonlinear Control under Constraints of a Biological System.- An Object-Oriented Approach to Optimally Describe and Specify a SCADA System Applied to a Power Network.- Near-Optimal Flight Trajectories Generated by Neural Networks.- Performance of a Feedback Method with Respect to Changes in the Air-Density during the Ascent of a Two-Stage-To-Orbit Vehicle.- Linear Optimal Control for Reentry Flight.- Steady-State Modelling of Turbine Engine with Controllers.- Shortest Paths for Satellite Mounted Robot Manipulators.- Optimal Control of the Industrial Robot Manutec r3.

Different kinds of membrane structures have been proposed for future space exploration and earth observation. However, due to the low stiffness, high flexibility, and low damping properties, membrane structures are likely to generate large-amplitude (compared to the thickness) vibrations, which may lead to the degradation of their working performance. In this work, the governing equations are established at first, taking into account the modal control force induced by the polyvinylidene fluoride (PVDF) actuator. The optimal vibration control of the membrane structure is explored subsequently. A square PVDF actuator is attached on the membrane to achieve the vibration suppression. The influence of actuator position and control gains on the vibration control performance are studied. The optimal criteria for actuator placement and energy allocation are developed. Several case studies are numerically simulated to demonstrate the validity of the proposed optimization criteria. The analytical results in this study can serve as guidelines for optimal vibration control of membrane structures. Additionally, the proposed optimization criteria can be applied to active control of different flexible structures.

A neural network based time optimal control of flexible structures is presented. The implementation is done on a flexible inverted L structure with surface-bonded piezoceramic sensors/actuators. The state-space presentation, from control input voltages to sensor output voltages is established in multivariable form. A variable gain multi-input multi-output linear quadratic regulator controller is designed and implemented. The controller gains are varied as the modal energy of the system decreases. The gains are varied in such a manner that the system utilizes maximum control energy from fixed amplitude of control voltage. The gains are calculated by solving the Riccatti equation with weightage in performance index that varies according to the states of the system. Thus at periodic intervals, the gains are updated to fully utilize the available control voltage. Comparison of the present technique is done with the classical bang-bang controller.

In this paper, we present an optimal control approach using Linear Matrix Inequalities (LMIs) for trajectory tracking control of a three-wheeled omnidirectional mobile robot in the presence of external disturbances on the robot's actuators and noise in the robot's sensor measurements. First, a state-space representation of the omnidirectional robot dynamics is derived using a point-mass dynamic model. Then, we propose an LMI-based full-state feedback H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> -optimal controller for the tracking problem. The robot's tracking performance with the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> -optimal controller is compared to its performance with a classical full-state feedback tracking controller in simulations with circular and bowtie-shaped reference trajectories. In order to evaluate our proposed controller in practice, we also implement the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> -optimal and classical controllers for these reference trajectories on a three-wheeled omnidirectional robot. The H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> -optimal controller guarantees stabilization of the robot motion and attenuates the effects of frictional disturbances and measurement noise on the robot's tracking performance. Using the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> -optimal controller, the robot is able to track the reference trajectories with up to a 47.8% and 45.8% decrease in the maximum pose and twist errors, respectively, over a full cycle of the trajectory compared to the classical controller. The simulation and experimental results show that our LMI-based H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> -optimal controller is robust to undesired effects of disturbances and noise on the dynamic behavior of the robot during trajectory tracking and can outperform the classical controller in attenuating their effects.

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.

In this paper, we present a global optimal and stable fuzzy controller design method for both continuous- and discrete-time fuzzy systems under both finite and infinite horizons. First, a sufficient condition is proposed which indicates that the global optimal effect can be achieved by the fuzzily combined local optimal controllers. Based on this sufficient condition, we derive a local concept approach to designing the optimal fuzzy controller by applying traditional linear optimal control theory. The stability of the entire closed-loop continuous fuzzy system can be ensured by the designed optimal fuzzy controller. The optimal feedback continuous fuzzy system can not only be guaranteed to be exponentially stable, but also be stabilized to any desired degree. Also, the total energy of system output is absolutely finite. Moreover, the resultant feedback continuous fuzzy system possesses an infinite gain margin; that is, its stability is guaranteed no matter how large the feedback gain becomes. Two examples are given to illustrate the proposed optimal fuzzy controller design approach and to demonstrate the proved stability properties.

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

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.

Optimal structural modifications to enhance the optimal active vibration control of large flexible structures

Maneuver load alleviation, gust load alleviation, and natural laminar flow are integrated into aircraft conceptual design. The concurrent design of the aircraft and its active load alleviation systems can yield significant gains. The simultaneous application of maneuver load alleviation and gust load alleviation to a short-haul aircraft leads to an 11% reduction in fuel burn and 7% reduction in direct operating cost. These savings are diminished if maneuver load alleviation and gust load alleviation are applied independently. The synergy between active load control and natural laminar flow is also explored. It is possible to invest some of the weight savings from load alleviation to achieve extensive laminar flow. The combination of load alleviation and natural laminar flow increases the fuel and cost savings to upwards of 18 and 11%, respectively. It is concluded that load alleviation can shift the transonic transport optimum toward low-sweep, natural laminar flow wings. Sensitivity studies finally demonstrate that contemporary commercial aircraft should be able to meet the control requirements for effective gust load alleviation.