Jen-Kuang Huang

Sensation of rotation about a vertical axis with a fixed visual field in different illuminations and in the dark

SummaryThis paper compares the motion sensations of a subject rotated about a vertical axis for two fixed visual fields (a large peripheral field and a single central spot) and in darkness.Motion sensation is described in terms of threshold, frequency response, and subjective displacement and velocity.The perception of angular acceleration showed significantly lower threshold and reduced latency time for the illuminated presentation. The level of illumination, however, produced no significant difference in threshold. The subjective frequency response, measured by a nulling method, showed a higher gain in the illuminated presentation, particularly at low frequencies and accelerations. With the subject rotating a pointer to maintain a fixed heading during triangular velocity stimuli, subjective displacements showed no difference for all different visual cues. Magnitude estimates of the after-rotation associated with deceleration from a constant velocity showed a quicker rising speed, larger subjective velocity and longer duration in the illuminated presentation. All the results suggest that the oculogyral illusion is principally responsible for producing a lower threshold in the illuminated presentation, although the fixed peripheral visual field tends to reduce reliance upon vestibular signals. At lower intensity rotation stimuli, this effect is especially apparent.

Suppression of Thermal Postbuckling and Nonlinear Panel Flutter Motions Using Piezoelectric Actuators

Active output feedback control of large amplitude nonlinear panel flutter at supersonic speeds with and without temperature effect is presented. A coupled structural-electrical modal formulation using finite elements is applied. Suppression of three types of panel response is studied: limit cycle oscillations, static thermal postbuckling, and chaotic motion. The controller, composed of a linear quadratic regulator and an extended Kalman filter, is developed and investigated. The extended Kalman filter considers the nonlinear state-space matrix and has a gain sequence evaluated online. The norms of the feedback control gain are employed for the optimal placement of piezoelectric actuators, and the norms of the Kalman filter estimation gain are used to validate the best locations for the sensors. A symmetric laminated composite plate at supersonic speeds with or without the influence of elevated temperatures is investigated. Two types of piezoelectric materials, PZT5A and macrofiber composite actuators, embedded in the composite panel are considered to suppress the nonlinear panel flutter. Simulation results show that the linear quadratic regulator/Kalman filter controller can suppress all three types of panel response with or without thermal effects.

Panel Flutter Limit-Cycle Suppression with Piezoelectric Actuation

An optimal control design is presented to suppress panel flutter limit-cycle motions using piezoelectric actuators. First, the nonlinear dynamic equations of motion based on the classical continuum method are derived for a simply supported isotropic panel with a pair of patched piezoelectric layers. After linearizing the dynamic modal equations, an optimal controller is developed to provide an optimal combination of inplane force and bending moments through piezoelectric actuators for flutter suppression. For the panel configuration studied, numerical simulations based on the nonlinear model show that the maximum suppressible dynamic pressure X,.,. can be increased about three times of the critical dynamic pressure Xc, by the piezoelectric actuation, and the bending moment is much more effective in flutter suppression than the inplane force. Within the maximum suppressible dynamic pressure, limit-cycle motions can be completely suppressed. For the actuator design, the two-set actuators perform better than the one-patched actuator, and the one-patched actuator, may have better performance than the completely covered actuator. The results demonstrate that piezoelectric materials are effective in panel flutter suppression.

Active Control of Nonlinear Panel Flutter Using Aeroelastic Modes and Piezoelectric Actuators

Suppression of nonlinear panel flutter at supersonic speeds has been investigated traditionally with system equations of motion in terms of in vacuo modal coordinates. For isotropic and symmetrically laminated orthotropic composite plates, the limit-cycle oscillations converged with six in vacuo natural modes at a zero yaw angle. However, as laminated composite plates undergo the effect of an arbitrary yawed flow angle, complicated characteristics emerge by increasing the required in vacuo natural modes for an analysis of limit-cycle oscillations. To design an effective controller, the large number of modes should be reduced. As a result, the small number of modes produces a capability to alleviate the costly computational effort in designing controllers for the suppression of nonlinear panel flutter. In the present study, aeroelastic modes that provide the reduced order basis are used for panel limit-cycle motion. Two or six to seven aeroelastic modes are implemented for developing an active controller of panel flutter with isotropic and anisotropic laminated composite plates at a zero or nonzero yaw angle. Along with the aeroelastic modal equations of lesser number, a linear quadratic regulator, which is one of the output feedback controllers, is constructed to suppress nonlinear panel flutter. An added extended Kalman filter compensates for the nonlinearity of structural motion resulting from updating the system information online. The norms of feedback control gain and the norms of Kalman filter estimation gain are employed for the optimal placement of PZT5A or macro-fiber composite piezoelectric actuators and sensors. Numerical results show that the designed controller based on aeroelastic modal coordinates can suppress the large-amplitude panel nonlinear flutter response. The maximum flutter-free dynamic pressure for isotropic and composite plates is evaluated to measure how much the performance is improved.

INDIRECT IDENTIFICATION OF LINEAR STOCHASTIC SYSTEMS WITH KNOWN FEEDBACK DYNAMICS

An algorithm is presented for identifying a state-space model of linear stochastic systems operating under known feedback controller. In this algorithm, only the reference input and output of closed-loop data are required. No feedback signal needs to be recorded. The overall dosed-loop system dynamics is first identified. Then a recursive formulation is derived to compute the open.loop plant dynamics from the identified rinsed-loop system dynamics and known feedback controller dynamics. The controller can be a dynamic or constant-gain full-state feedback controller. Numerical simulations and test data of a highly unstable large-gap magnetic suspension system are presented to demonstrate the feasibility of this indirect identification method.

Adaptive Control of Nonlinear Free Vibrations of Composite Plates Using Piezoelectric Actuators

A coupled structural-electrical finite element modal formulation is employed for the control of nonlinear free vibrations of beams and composite plates. Multiple modes of the nonlinear free vibration are considered in closed-loop simulations. Two different controllers are designed and investigated for the suppression of nonlinear free vibrations. The first is the position output feedback controller comprising a linear quadratic regulator (LQR) and an extended Kalman filter (EKF). The EKF is used to consider the nonlinear state-space matrix and has a gain sequence evaluated online. The second controller is the output feedback adaptive LQR/EKF controller. This adaptive controller includes an adaptive modal frequency identification and state estimation algorithm. Numerical simulations show that the adaptive LQR/EKF controller with system identification is effective in suppressing nonlinear free vibrations of a beam and a composite plate with unpredictable sudden frequency changes. The placement of piezoelectric self-sensing actuators is based on three approaches: one is the norm of optimal feedback control gain matrix method, the second is the H 2 norm, and the last one is the norm of Kalman filter estimation gain method.

Identification of Linear Stochastic Systems Through Projection Filters

A novel method is presented for identifying a state-space model and a state estimator for linear stochastic systems from input and output data. The method is primarily based on the relationship between the state-space model and the finite difference model of linear stochastic systems derived through projection filters. It is proved that least-squares identification of a finite difference model converges to the model derived from the projection filters. System pulse response samples are computed from the coefficients of the finite difference model. In estimating the corresponding state estimator gain, a z-domain method is used. First the deterministic component of the output is subtracted out, and then the state estimator gain is obtained by whitening the remaining signal. An experimental example is used to illustrate the feasibility of the method. YSTEM identification, sometimes also called system modeling, deals with the problem of building a mathematical model for a dynamic system based on its input/output data. This technique is important in many disciplines such as economics, communication, and system dynamics and control.1 The mathematical model allows researchers to understand more about the properties of the system, so that they can explain, predict, or control the behaviors of the system. Recently, a method has been introduced in Refs. 2 and 3 to iden- tify a state-space model from a finite difference model. The differ- ence model, called autoregressive with exogeneous input (ARX), is derived through Kalman filter theories. However, the method re- quires to use an ARX model of large order, which causes intensive computation in the embedded least-squares operation. In Ref. 4 a method is derived to obtain a state-space model from input/output data using the notion of state observers. This approach can use an ARX model with an order much smaller than that derived through the Kalman filter, but the derivation is based on a deterministic ap- proach. In Ref. 5, it has been proved that, as the order of the ARX model increase to infinity, the observer identification converges to the Kalman filter identification. However, for a stochastic system and an ARX model of a small order, to what the least-squares iden- tification of the ARX model will converge in a stochastic sense is not clear. This paper addresses the above-mentioned problems using a stochastic approach. The approach is primarily based on the re- lationship between the state-space model and the finite difference model via the projection filter.3 First, an ARX model is chosen, and then the ordinary least squares is used to estimate the coefficient matrices. Based on the relationship between the projection filter and the state-space model matrices, the system pulse response samples (i.e., the system Markov parameters) can be calculated from the co- efficients of the identified ARX model. The eigensystem realization algorithm (ERA)6 is used to decompose the Markov parameters into a state-space model. In contrast to the time-domain approaches used in Refs. 2 and 5, a different method is developed in this paper using a z-domain approach to compute the state estimator gain. After identifying a state-space model, the deterministic part of the output is subtracted out. The remaining signal represents the stochastic part. A moving- average (MA) model is then introduced to describe the remaining signal. The MA model is computed by identifying the correspond- ing autoregressive (AR) model first and then inverting it. From the identified MA model, the state estimator gain is then calculated. Finally, identification of a 10-bay structure is used to illustrate the feasibility of the approach.

Rapid Rotational/Translational Maneuvering Experiments of a Flexible Steel Beam

Future space manipulators may need translational base motion to expand the access region of a manipulator. The objective of this experiment is to demonstrate slewing of flexible structures with coupled rotational and translational axes while simultaneously suppressing vibrational motion during the maneuver. A flexible steel beam carried by a translational cart is maneuvered by an active controller to perform position control tasks. Several experimental results are presented to show how the flexibility of the steel beam influences the multi-input and multi-output feedback controller.

Timoshenko Beam Modeling for Parameter Estimation of NASA Mini-Mast Truss

In this paper a distributed parameter model for the estimation of modal characteristics of NASA Mini-Mast truss is proposed. A closed-form solution of the Timoshenko beam equation, for a uniform cantilevered beam with two concentrated masses, is derived so that the procedure and the computational effort for the estimation of modal characteristics are improved. A maximum likelihood estimator for the Timoshenko beam model is also developed. The resulting estimates from test data by using Timoshenko beam model are found to be comparable to those derived from other approaches.

Adaptive Control of Nonlinear Free Vibration of Shallow Shell Using Piezoelectric Actuators

A coupled structural-electrical nonlinear modal finite-element multiple-mode formulation for laminated composite shallow shells with embedded piezoelectric sensors and actuators is presented for the suppression of large-amplitude undamped free vibrations. Composite shells exhibiting both softening and hardening behavior are investigated. The linear quadratic regulator combined with an extended Kalman filter is employed as an active controller for the suppression of nonlinear free vibrations. However, when the frequency of limit-cycle oscillations is suddenly changed from the softening to the hardening response characteristics or vice versa, active controller has difficulties to adjust the control parameters to cope with the changed structural response. To mitigate this issue, the currently developed controller is adaptively designed using the system identification which has the ability to identify the frequency of limit-cycle oscillations. It is shown that the adaptive controller constructed of the linear quadratic regulator and extended Kalman filter with system identification is suitable for suppression of the sudden change of shallow-shell response characteristics. The norm of optimal feedback control gain method for actuators and the norm of Kalman filter estimator gain method for sensors are employed to determine their optimal locations, respectively. Two different self-sensing actuator types, PZT5A and macrofiber composite, are used and their control performance for the suppression of the oscillations is compared. The numerical results illustrate that the adaptive controller can successfully suppress the nonlinear free vibrations, even with unknown sudden changes in the multimode response characteristic.