Three categories will be described and discussed in this section: (1) Training outstanding talents 培育人才, (2) Internationality 國際性, (3) Research results 研究成果.
(1) Training outstanding talents 培育人才:
Two post-doctors were involved during the period of 2013. Their performances are included in the research results.
Name Degree Starting date
黃郁茹 Yu-Ru Huang
BS, Mathematics, National Taiwan University, 06/2003 MS, Mathematics, National Taiwan University, 06/2005 Ph.D., Mathematics, University of Maryland, 05/2012
June 1, 2012
蘇建元 Chien-Yuan Su
BS, Info. Management, Providence University, 06/2001 MS, Info. & Learning Tech., National Tainan Univ., 06/2006 Ph. D. Engineering Science, NCKU, 01/2012
August 1, 2012
Three papers were presented at Third International Symposium on Solar Sailing, University of Strathclyde, Glasgow, Scotland, June 11-13, 2013.
1. Huang, Y-R., Juang, J.-N., Hung, C.-H., and Wilkie, W. K., “Dynamics of a Coupled
Pendulum Model of a Heliogyro Membrane Blade”; Presenter: Jer-Nan Juang2. Juang, J.-N., Lu, H.-H., Horta, L. G., and Wilkie, W. K., “Challenge Associated with
System Identification and Control of a Heliogyro Membrane Blade”; Presenter: Hen-Hsin Lu3. W. Keats Wilkie, Jerry E. Warren, Jer-Nan Juang, Lucas G. Horta, Karen H. Lyle, Justin
D. Littell, and Robert G. Bryan, Mark W. Thomson, Phillip E. Walkemeyer, Daniel V.Guerrant, Dale A. Lawrence, S. Chad Gibbs, and Earl H. Dowell, “Heliogyro Solar Sail Research at NASA”; Presenter: Keats Wilkie
This activity on cutting-edge technology developments would considerably enhance NCKU global visibility.
Visiting National Institute of Aerospace (NIA) and NASA Langley Research Center
While Prof. Juang in resident at NIA and NASA from July 1 to August 31, several items were completed as follows:
The main task during the first week of the visit was to guide Mr. Jack Lu (工料系陸翰勳同 學) to perform system identification and control of a spinning membrane for application to solar sailing systems. Mr. Lu had visited NASA Langley Research Center and National Institute of Aerospace from August 6, 2012 to July 5, 2013. The purpose of Mr. Lu’s visit at NASA was to work with NASA researchers to analyze the dynamic behavior of a Heliogyro membrane blade and to design feedback controllers. Mr. Lu had completed using simulation data generated from linear and nonlinear models of a spinning membrane to identify linear models using time and frequency domain techniques. A controller design was introduced and its stability robustness was described. We expect to complete a technical paper and submit it to a top 5% journal such as the Journal of Nonlinear Dynamics.
The key task for the rest of the visit was to work with Drs. Lucas Horta, Keats Wilkie, and Jay Warren of NASA Langley, Mr. Chad Gibbs and Prof. Earl Dowell of Duke University, and Mr. Daniel V. Guerrant and Prof. Dale A. Lawrence of University of Colorado for studying the stability problem of a Heliogyro membrane blade subject to solar radiation pressure. Mr. Gibbs and Prof. Earl predicted flutter instability from a non-linear model at a lower radiation pressure and had improved modal convergence characteristics. The most critical instability, which occurs at a non-dimensional radiation pressure of 0.00351, is a coalescence flutter between the first in-plane bending and first torsion degrees of freedom. On the other hand, Dr. Warren used ABAQUES with an attempt to validating the flutter instability behavior of the coupled in-plane and torsion degrees of freedom. Unfortunately, Dr. Jay’s and Mr. Gibbs’ results are not consistent in instability occurrence at a non-dimensional radiation pressure and a specific spinning rate of the Heliogyro membrane blade. Dr. Wilkie, manager of the solar sailing project, suggested to use our NCKU approach to find out what the correct answer should be. Over the past two years under the support of the 邁向頂尖大學計畫經費, we have developed a unique approach by using the discrete-mass method to analyze the nonlinear dynamic behavior of a spinning Heliogyro membrane blade. The flutter instability problem of a solar sailing system is a very serious matter. During the flight of solar sailing in space, the rotational speed that may induce flutter instability must be avoided; otherwise the solar sailing itself is in a precarious situation. So far, no individual or organization has a method to effectively control this precarious situation.
This visit has considerable value in working with NASA researchers to conduct scientific research to develop cutting-edge technologies for space exploration. Our NCKU graduate students had an opportunity to exchange ideas with graduate students from top-ranked American Universities. I believe that NCKU and NASA/NIA will have more success on the exchange of academic research. NIA Langley Professor Chris Fuller was particularly impressed by Mr. Jack Lu for outstanding performance in his class. Prof. Fuller will provide research assistantship if Jack Lu is interested in performing his doctoral research on acoustic noise reduction problems at NASA.
(3) Research results 研究成果:
Experiment Results for a 3-dof Hanging Model
The laboratory test structure (Fig. 5) for validation of our analytical studies consists of a vertical 3-dof hanging model and a digital camcorder for deflection measurements. The overall dimensions are 54 cm in height and 15 cm in width, and the total mass is approximately 312 g.
The structure is hinged at its top to a board.
Fig. 5 Hanging mass experiment setup
A flow diagram of building the three-mass-set hang model is shown in Fig. 6. Each horizontal pair required two straws to prevent masses from additional swaying. Each discrete mass was made by stacking 13 coins (New Taiwan Dollar), which were wrapped with a tape, and then tied up with a string. Putting a double-string through a straw to link one coin-mass to another completed the model. Colors of the masses and links were adjusted for an easy capture by a digital camcorder to make mass tracking more accurate. A typical image of three masses captured by the digital camcorder of 1075 by 1111 pixels is shown in Fig. 7.
In Fig. 8, we demonstrate a total of 4810 data points of the experimental free-decay responses for the top mass m11, the center mass m21, and the bottom mass m31with the initial displacements given by a hand and the sample interval 1/30 sec. The bottom-mass displacement is approximately twice larger than the top-mass displacement. Note that the initial conditions are different from the theoretical simulation for analyzing linear and nonlinear behavior.
Fig. 6 A flow diagram for making the coupled pendulum model.
Fig. 7 Image capture by a digital camcorder
Fig. 8 Experimental data rescaled to actual size (cm), center adjusted to zero
In Fig. 9, we give the flow diagram of using the Eigensystem Realization Algorithm (ERA) on the experimental data shown in Fig. 8. The ERA method developed at NASA Langley Research Center is commonly used for producing a state-space model from experimental data for structural analysis and controller design. Each ERA was performed using a single matrix (4810 x 3) of data from the three response measurements and one initial condition at a time. The first step is to convert the positions of three masses in pixels to actual displacement response y(k) where k is the time index. The second step is to form two Hankel matrices H(0) and H(1) consisting of the response y(k), and perform singular value decomposition on Hankel matrix H(0) to determine the system order by truncating relatively small singular values. The third step is to determine the discrete-time state-space matrices A (state matrix), B (input matrix), C (output matrix), and D (direct transmission matrix). For the free-decay response, the state matrices A, C, and x(0) (initial condition) are identified instead of A, B, C, and D. The last step is to transform A, C, and x(0) into modal coordinates for identification of system damping ratio, frequencies, and mode shape, and for model reduction if necessary for controller designs. The identified matrices/vectors A, C, and x(0) describe a linear model that produces an “optimal-linear” map from the initial condition to the measured free-decay response.
Fig. 9 Flow diagram of using ERA on experimental data
We performed system identification with two different sets of data in length (2811 and 4810 points) for the purpose of comparison. The theoretical and ERA-identified system frequencies and damping ratios are compared in Table 1. The identified results agree with the theoretical results in frequencies. The final aspect of the ERA method available for assessing identification accuracy is the process of data reconstruction. This procedure consists of comparing the original free-decay time histories with those calculated using the ERA-reduced model, which contains 3 modes. If the ERA modal decomposition process is performed accurately, the reconstruction results should closely match the original data. A typical top-mass actual time history is compared with a 3-mode reconstruction in Figs. 10 and 11, and the reconstruction result is seen closely following the original data in both amplitude and phase.
Table 1 Analytical and identified system damping ratios and frequencies
Theoretical
frequencies Identified frequency using 2811 points Identified frequency using 4810 points
Freq. (Hz) Freq. (Hz) Damping (%) Freq. (Hz) Damping (%)
0.7576 0.763 0.117 0.763 0.111
1.7797 1.798 0.342 1.798 0.340
2.9467 3.088 0.342 3.088 0.342
0 100 200 300 400 500
−5
−4
−3
−2
−1 0 1 2 3 4 5
First 500 data points of top mass
Sample points
Reconstructed data Experiment data
Fig. 10 Comparison of the top-mass first 500 measurements with a 3-mode reconstruction.
3000 3100 3200 3300 3400 3500
−1.5
−1
−0.5 0 0.5 1 1.5
3001 to 3500 data points of top mass
Sample points
Reconstructed data Experiment data
Fig. 11 Comparison of the top-mass 3001-3500 measurements with a 3-mode reconstruction
Experimental Setup for In-plane Motion
Performing experiments of the slender spinning membrane on the ground is limited because of gravitational force and friction of either the air in the ambient space or other contact surface.
An air table (see Figs. 12, 13) was recently built providing a low friction flat surface for masses to move freely on it. It allows us to perform experiments of in-plane motion that will closely resemble experiments in space without gravity.
The center of the air table has a motor for use to control the rotation of a spinning object consisting of a discrete set of finite number of masses. There are two cameras on the top of the air table for measuring the displacement of the spinning object. We will use image processing and system identification to analyze the spinning system. The experiment is divided into two steps. The first step is to perform experiments off-line with a digital camera and analyze the system to verify and validate the experimental process and image data quality. The second step is to conduct the experiment on-line/real-time with a high-speed digital camera in a synchronous way. It means that the high-speed camera obtains the image data and simultaneously transmits the data to computer for data processing and controller designs.
Fig. 12 Schematic diagram of the air table setup
Fig. 13 Air table consisting of 8+2 air bars with 0.3 µm hole
Fig. 14 Specification of the air table
To this end, the design of an object for spinning experiments is completed and its CAD diagram was sent to a company for manufacturing. We are almost ready to conduct experiments on the air table. Nevertheless, there are two issues that need to be addressed. First, the air table is located in an environment with considerable dust in air and high humidity that affects its performance. We are looking for an inexpensive design of making a clean space for the air table.
Another issue is how to set up a camera at a location higher than the ceiling above the table. To record the object motion on the whole table of one square meter, the camera must be located about 2 meters above the table. In summary, we have completed all steps for performing experiments except for manufacturing the objects and finding a way of setting up the camera in a very limited space.
Self-healing embedded system
Figure 15 shows the basic architecture of the self-healing embedded system for real-time control.
Figure 16 describes the steps for real-time control of the considered object on the air table.
Whether the embedded system is running, the main system and the secondary system in standby mode continue to collect Data. In other words, Memory Module A and Memory Module B will continue to have the latest Data. Memory Module A will back up data to States Buffer A in a
fixed time interval, while Memory Module B will back up data to States Buffer B. If one wants to update the Memory Module Information System A or System B after restarting the system, States Buffer will return all backup information to the Memory Module. So there will be no data convergence problems. The notations A and B may be arbitrarily assigned or switched later.
Fig. 15 Self-healing embedded system
Fig. 16 Proposed real-time control process
Technical Publications
SCI Publications (Published)
1. Lee, C.-H., and Juang, J.-N., System identification for A General class of Observable and Reachable Bilinear Systems” Journal of Vibration and Control, published online 12 April 2013 DOI: 10.1177/1077546312473768 (SCI, IF=1.966, top 15/125 in Engineering.
SCI Publications (Accepted)
2. Juang, J.-N., Hung, C.-H., and Wilkie, W. K., “Dynamics of a Spinning Membrane”, To appear in The Journal of the Astronautical Sciences, 2013, Special Issue: the Jer-Nan Juang Astrodynamcs Symposium.
3. Lee, C.-H., and Juang, J.-N.., “Deterministic Bilinear System Identification”, To appear in The Journal of the Astronautical Sciences, 2013, Special Issue: the Jer-Nan Juang Astrodynamcs Symposium.
4. Juang, J.-N., and Wu, W.-S., A Hybrid Parameter Estimation Algorithm for S-system Model of Gene Regulatory Networks, To appear in The Journal of the Astronautical Sciences, 2013, Special Issue: the Jer-Nan Juang Astrodynamcs Symposium.
5. Chih-Chao Hsu, Tzone-I Wang, “Enhancing Concept Comprehension in a Web-based Course Using a Framework Integrating the Learning Cycle with Variation Theory,” Asia Pacific Education Review.
SCI Publications (Submitted)
6. Chih-Chao Hsu, Tzone-I Wang , “Real Time Context Switch Between Two Identical Embedded Systems with Shared Memories.” Reliability Engineering and System Safety.
SCI Publications (To Be Submitted)
7. Huang, Y-R., Juang, J.-N., Hung, C.-H., and Wilkie, W. K., “Dynamics of a Coupled Pendulum Model of a Heliogyro Membrane Blade”, Third International Symposium on Solar Sailing, University of Strathclyde, Glasgow, Scotland, June 11-13, 2013
8. Juang, J.-N., Lu, H.-H., Horta, L. G., and Wilkie, W. K., “Challenge Associated with System Identification and Control of a Heliogyro Membrane Blade”, Third International Symposium on Solar Sailing, University of Strathclyde, Glasgow, Scotland, June 11-13, 2013
9.
W. Keats Wilkie, Jerry E. Warren, Jer-Nan Juang, Lucas G. Horta, Karen H. Lyle, Justin D.Littell, and Robert G. Bryan, Mark W. Thomson, Phillip E. Walkemeyer, Daniel V. Guerrant, Dale A. Lawrence, S. Chad Gibbs, and Earl H. Dowell, “Heliogyro Solar Sail Research at NASA”, Third International Symposium on Solar Sailing, University of Strathclyde, Glasgow, Scotland, June 11-13, 2013
Summary of the above publications is provided in the following table.
Technical Publications (Proceedings and Journal)
No. Title/Symposium/Journal Results and Discussion
1 Dynamics of a Coupled demonstration, meaningful ground test experiments are necessary for predicting the linear and nonlinear structural dynamics of the heliogyro membrane blades in flight. This paper describes analytical comparisons of linear and nonlinear behavior of a multi-link discrete model of a heliogyro blade under 1-g gravitational and centrifugal loads, and one setup for experimental validation of 1-g out-of-plane motion. Linear system-identification is performed on the multi-link experimental data to validate the 1-g multi-link model of a heliogyro membrane blade. We were motivated by hoping to replace some experiments in the spinning setting by experiments in the gravitational setting, which is more plausible to perform on earth. The bending (out-of-plane) motions of a coupled pendulum model of a heliogyro blade were studied analytically and experimentally. Although our efforts to make this conversion were not as expected, we discovered some interesting properties on the motion of the multi-link coupled pendulum, namely, the linearized (motion in small angles) system of the twisting and bending motions give identical frequencies. This means that resonance is likely to occur in small angle movements once either type of motion is present in conjunction with offset centers of structural geometry and external force. We derived the equations of motion by using the Lagrangian equations, and provided computer simulations and experimental results to support our studies. significant nonlinearities in the equations of motion. The objective of this paper is to demonstrate a system identification method applicable for describing the dynamic behavior of a Heliogyro membrane blade and to use it for control design. The approach is to use simulation data generated from linear and nonlinear models of a spinning membrane to identify linear models using time and frequency domain techniques. A simplified model of a spinning membrane using discrete lump masses has been used to create simulated time history data for system identification and control studies. A frequency response approach has been implemented to envelope nonlinear effects for stability assessments of the control system. An example was presented where simulated time history data from the out-of-plane/bending response was used to identify a nominal model, to design a controller, and quantify the nonlinearities in terms of system uncertainty. A full state feedback control system was implemented to increase damping while maintaining stability under nonlinearities. With this control
system, it is demonstrated that the achievable level of damping is diminished by the system nonlinearities
3 Heliogyro Solar Sail NASA-sponsored heliogyro technology advancement activities. Several key examples of such activities were also presented. Our initial efforts have been encouraging and lead us to conclude that a credible, near-term heliogyro technology demonstration mission is possible at an affordable cost. Performance characteristics in the range needed for many science missions enabled by solar sail propulsion technology should also be achievable. This high performance is largely made possible by advances in small satellite and CubeSat technologies since the 1970s, which permit a small scale heliogyro solar sail to be flown with very lightweight bus system. Our renewed analytical investigations into the coupled structural dynamics of heliogyro membrane blades have also revealed no intractable stability and control issues, although to what degree major damping augmentation systems will be needed to ensure solarelastic stability and damping of blade transient responses remains a subject for future work. The subject of future work is the development of higher-fidelity blade deployment mechanisms. Development of these systems to high technology readiness levels should be possible with standard flight systems engineering practices and well designed ground tests. High altitude, balloon tests could also be used to experimentally validate deployment reel mechanisms at HELIOS-like full-scales, although without rotational dynamics. Ultimately, an actual spaceflight validation mission will be needed to prove feasibility of the heliogyro solar sail concept and retire risk. Fortunately, this appears possible at an affordable, non-flagship mission cost. Given a near term effort to advance the technology readiness of critical systems, most notably blade dynamics simulation capabilities, deployment mechanisms, solarelastic flutter dynamics and control systems including damping augmentation, and relevant ground test demonstrations, a HELIOS or HELIOS-like, low-cost heliogyro flight demonstration could be ready for launch in as few as five years.
4 System identification for a general class of observable continuous-time bilinear systems. The method uses a special input sequence in conjunction with a Hankel-like matrix constructed by carefully selected output data. A key feature of the method is that the order reduction problem is overcome by a two-stage coordinate transformation based on the notion of common null space among related system matrices. This novel identification algorithm eliminates the drawback of its predecessors that require the observability of the linear part of
a bilinear system, i.e. the pair (state matrix Ac, output matrix C) to be observable. Numerical examples showed good correspondence between the identified bilinear models and the original nonlinear systems.
5 Deterministic Bilinear System Identification / To appear in the Journal of the Astronautical Sciences, 2013, Special Issue: the Jer-Nan Juang
Astrodynamcs Symposium
A unified system identification method has been developed to realize a general class of deterministic CBS (continuous-time system) and DBS (discrete-time system) models. A key procedure of the method is the transformation of a bilinear system model to a LTV (linear time-varying) system model.
A special input sequence consisting of a repeated random signal is used to drive the transformed LTV system model and a general Hankel matrix is constructed using carefully selected output data. Incorporating an orthogonal projection on the general Hankel matrix and the least-squares solution of combined outputs, all system matrices can be identified.
A special input sequence consisting of a repeated random signal is used to drive the transformed LTV system model and a general Hankel matrix is constructed using carefully selected output data. Incorporating an orthogonal projection on the general Hankel matrix and the least-squares solution of combined outputs, all system matrices can be identified.