G. Ron Chen, Ph.D., Associate Professor, UH; Heidar A. Malki, Ph.D., Assistant Professor, UH; Daren Zhang, Doctoral Student, UH; Dave Misir, Doctoral Student, UH
Efforts are underway to extend the new fuzzy PID controllers design that PIs previously developed from single-input single-output control systems to multi-input multi-output (MIMO) systems, with applications to multiple-link robot arm systems for tracking control.
As a result of the large number of potential applications of the fuzzy PID controllers in aerospace engineering and industries, we have rendered the fuzzy PID controllers more robust and suitable for MIMO control systems, such as those suitable for multiple-link robot arms. The new fuzzy PID controllers possess strong robustness against large and sudden changes in the working environment. This extension is not straightforward, since a multiple-link robot arm has a high degree of freedom that can cause serious problems in trajectory planning, multiple-link cooperation, and redundance avoidance. Some of these issues have been taken into account in the new design and have been completely or partially resolved.
The objectives accomplished in this project include:
Figure 1 shows a typical two-link robot arm structure with two flexible joints, where m and J are mass and inertia, respectively, and k is the flexibility coefficient. As is well known, a mathematical model for this arm is complicated; hence, it is generally difficult to design a simple but effective controller to handle a robot-arm structure. Our resulting fuzzy PID controller has a simple PD-type structure with explicit control formulas resulting from six triangular membership functions, nine simple IF-THEN rules, and a standard center-of-mass defuzzification formula.
Figure 2 shows a typical tracking performance of the arm-tip that follows a reference curve (dotted-curve is the target; solid-curve is the tip trajectory), where the slight off-set is caused naturally by the joint flexibility, as expected.
References
1G. R. Chen and D. Zhang. "Back-Driving a Truck with Suboptimal
Distance Trajectories: A Fuzzy Logic Control Approach," IEEE Trans. on Fuzzy Systems,
1995. (Accepted for publication.)
2G. R. Chen and D. Zhang. "Backing a Truck-Trailer with Suboptimal Distance
Trajectories," Proc., FUZZ-IEEE Conf., New Orleans, LA, Sept. 8-11, 1996.
3P. Sooraksa and G. R. Chen. "Fuzzy PI+D Control for Flexible Robot Arms,"
Proc., IEEE Int'l Conf. on Control Appl., Dearborn, MI, Sept. 15-18, 1996.
4H. A. Malki and Y. C. Hsu. "Multiple Input Multiple Output Fuzzy Logic Controllers
Design and Analysis," IEEE Trans. on Fuzzy Systems, 1996. (Submitted for
publication.)
Albert M. K. Cheng, Ph.D., Assistant Professor & Director, Real-Time Systems Lab, UH; Xiao Chen, Research Assistant, UH; Fred Wong, Research Assistant, UH
Real-time image and video transmission are required in many aerospace applications. These applications include transmission of images from autonomous spacecraft to earth stations and video communication between airplanes or space shuttles. There are severe constraints in time, distance, bandwidth, and processing power in aerospace environments. Furthermore, the communicating parties are usually mobile and not connected by physical links. Current precise image and video transmission techniques work well if sufficient processing power, network bandwidth, and transmission time are available, but do not adapt properly to a reduction in one or more of these resources. A precise algorithm must be executed in its entirety before an output can be produced, whereas the execution of an imprecise (approximate) algorithm can be ended at any time prior to normal completion, and a usable output can still be produced. The objective of the project is to apply imprecise computation techniques to yield a balanced tradeoff between the quality of the image/video transmitted and the available resources for transmission.
Our research project builds on highly promising results[1] obtained in a project initiated late last year and partially supported by a University of Houston Institute for Space Systems Operations (ISSO) award. The project also benefits from related accomplishments[2] in research supported by Texas-ARP and NSF awards.
Methodology
Images and videos are among the most demanding multimedia information to process and
transmit. Several algorithms are currently being used to reorganize image data, transmit
them progressively, and then reconstruct a single image by incrementally increasing its
resolution at the destination. A well-known technique constructs a hierarchical structure
of images with increasing resolution from top to bottom. It is adopted and further
extended to reorganize the image data and transmit the details of the image in a
non-increasing order of their significance.
A video consists of a sequence of images. To transmit a video, we perform motion estimation and temporal interpolation of skipped frames. By dividing the entire video into several frame pieces, carefully scheduling the progressive data transmission, and reconstructing frames by motion prediction, the video can be gradually recovered. The commercial product InPerson running on Silicon Graphics workstations provides tools for teleconferencing between two or more parties connected by a computer network. It takes a live video and transmits it to the other party; at the same time, it receives and displays the video sent from the other party. However, if the network traffic becomes heavy, the images from the remote site or sites become fuzzy. If the rate of motion of the video increases, the continuity as well as the quality of the transmitted video decreases. This software implements the progressive video transmission technique in a practical product. However, it does not perform any time-quality trade-off to enforce the continuity of the video.
Since progressive transmission results in partially transmitted images, it can be modeled by the imprecise computation framework. The purpose of imprecise computation is to utilize the partial results in case of insufficient execution time. Thus, real-time video transmission may apply this idea and automatically adjust the accuracy of the transmitted video according to the processing time available.
Imprecise Computation
For conventional precise algorithms, the correctness of the output is either 0 or 1,
meaning that either no result or a perfect result is generated from the computation. When
the time T required for completing the execution of an algorithm is available, the
correctness of the output is always 1. If the available time is insufficient, the
correctness is always 0 and no result can be produced.
The correctness function for imprecise algorithms is continuous in the time range [0, T]. At any moment between 0 and T when the computation is stopped, the partial result produced has a correctness valued between 0 and 1. More precisely, the correctness function for imprecise algorithms executing in a computer system is a staircase function. The width of a stair is the execution time for a small piece of source code, and the height is the improved correctness after the execution of this code section. Imprecise computation makes it possible to reduce the amount of time used on a job and obtain a partial result in order to meet the specified deadline. Recent work on imprecise computation in real-time systems proposed two imprecise approaches to utilize partial results in case of insufficient resources.
The milestone approach periodically records intermediate results and outputs the latest set of program values as the final result when the deadline is encountered. The basic assumption of this approach is that the longer a computation executes, the more accurate is the result it produces. The time Ts is the setup time necessary for the computation to produce useful results, and Tc is the time needed to produce fully correct results, where T = Ts + Tc. The sieve approach skips certain predefined source code sections when the deadline approaches and produces a result as soon as possible. The optional sections are called sieve functions whose purpose is to refine the partial results and make them more precise. Whether they are executed or not should not violate the correctness of the algorithm. However, the quality of the partial results may be significantly reduced if these sieve functions are not performed.
We employed both approaches to yield imprecise image/video transmission algorithms. For instance, when the computation takes the form of incremental refinement of the final results, it can be divided into a sequence of sieve functions. The milestone approach is used to save intermediate results after distinct stages of the computation.
Image Progressive Transmission
Before an image is sent, its data should be reorganized in descending order of their
contribution to the reconstruction of the image. The hierarchical method is one of the
popular reorganization methods. It decomposes the original image into a pyramid of
sub-images. The top-level sub-image contains the basic information of the original image,
and the lower-level sub-images contain the details. Among a variety of data reorganization
formats, the Laplacian/Gaussian pyramid is the most popular because of its low
computational cost and satisfactory results.
Content-driven progressive approaches divide the transmission of the Laplacian pyramid into a number of steps. In each step, the entire pyramid is scanned from top to bottom, level by level. More informative parts are therefore identified by some parameters and then given higher priorities in the transmission. The decision parameters are updated for every step, and the process is repeated for further improvement. At the destination, the Laplacian pyramid becomes clearer as more data are transmitted. Eventually it is restored and then the Gaussian pyramid can be calculated. The imprecise image/video transmission technique to be investigated in this project is different from this approach in several aspects. The transmission of the Laplacian pyramid is performed level by level from top to bottom. The more informative part of the image at each level is sent before the less important part. The Gaussian pyramid can be reconstructed from top to bottom as soon as one level of the Laplacian pyramid is received. If there is insufficient transmission time for the entire Laplacian pyramid, the lowest-level image in the Gaussian pyramid obtained so far is expanded to estimate the bottom-level image, which is the original one.
Project Results
For aerospace applications, we have made significant progress in imprecise image/video
transmission[3-6] as well as in imprecise image magnification.[7]
References
1T. Lee and A. M. K. Cheng. "Multiprocessor Scheduling of
Independent Hard-Real-Time Periodic Tasks with Task Migration Constraints," Proc.,
IEEE-CS Workshop on Real-Time Computing Systems and Applications (Dec. 1994).
2J.-R. Chen and A. M. K. Cheng. "Response Time Analysis of EQL Real-Time Rule-Based
Systems," IEEE Trans. on Knowledge and Data Engineering 7.1 (Feb. 1995): 26-43.
3C. Wong and A. M. K. Cheng. "An Approach for Imprecise Transmission of TIFF Image
Files Through Congested Real-Time ATM Networks," 1996. (Submitted for publication.)
4A. M. K. Cheng and X. Huang. "An Imprecise Real-Time Video Transmission
Algorithm," Proc., Int'l Computer Science Conf., Hong Kong, Dec. 1995.
5A. M. K. Cheng and X. Huang. "Improving Real-Time Image and Video Transmission with
Imprecise Algorithms," IEEE Trans. on Computers, 1995. (Submitted for publication.)
6L. N. Nguyen and A. M. K. Cheng. "An Imprecise Real-Time Image Magnification
Algorithm," Proc., Int'l Symp. on Multimedia Systems, Yokohama, Japan, Mar. 1996.
William E. Fitzgibbon, III, Ph.D., Professor, UH
Although it is one of the most challenging problems in modern engineering science, the understanding of complex speed compressible fluid flows is critical to the design of experimental military and civilian aircraft. The extremity of the physical conditions in these flow regimes renders the task of reproducing these flows in a controlled experimental environment both difficult and expensive. In the case of hypersonic flows, little experimental data are available. On the other hand, the task of numerically simulating the aerothermal environment of vehicles traveling at or well beyond the speed of sound is and will continue to be one of the challenging problems confronting modern computational science. Therefore, the cross validation of physical results and computational simulation is currently an active issue in fluid mechanics, and practitioners seek to validate numerical simulations with results produced by qualified fluid dynamics experiments. Computational algorithms are validated by comparison with experimental data when available or otherwise by comparison with other computational methods.
The modeler faces multi-fold difficulties because of the many complex physical processes which may be present. At hypersonic speeds, aero-chemistry must not be ignored. Here, chemical non-equilibrium is highly significant. In many high speed environments, temperatures, velocities, and enthalpy are high while densities are low. This makes it extremely difficult, if not impossible, to reproduce the processes in ground based experiments. Shock/shock interaction and shock/surface phenomena must be accounted for. In various flow regimes, the governing equations can be of Boltzman, Navier-Stokes, or compressible Euler type. Turbulence effects can play a significant role. The computational difficulties are profound. The fluid time scales and the chemical time scales differ radically, and, therefore, these systems exhibit a high degree of stiffness. While modern shock-capturing schemes allow for the accurate resolution of shocks, the accurate description of slip surfaces remains a challenging task. The description of boundary layers and shock boundary interactions is formidable. Turbulence modeling is still at best an art form. Other difficulties include the rapid calculation of steady states, the robust calculation of wake flow, and the optimal utilization of state-of-the-art computer hardware.
Under the ISSO grant entitled "Workshop and Database on Compressible High Speed Flow," we are establishing a permanent database archiving computational results for a battery of test case problems which have been selected to explore identified critical issues of high speed flow including transition to turbulence, rarefied flows, non-equilibrium flows, real gas effects with complex chemistry, catalytic gas, and air breathing propulsion surface as well as other characteristics. Only simple two- and three-dimensional geometric configurations are used for test case problems. All test cases are supported by high quality experimental data.
Database development is being performed by Dr. Richard Sanders, Associate Professor of Mathematics, and Dr. Eric Morano who currently holds an appointment as a UH/NASA-JSC Postdoctoral Fellow. The test case problems were selected by a panel of experts from the United States, Western Europe, Russia, and Japan. This project is a collaborative venture with a team centered at the Institut National de Réserche en Informatique et en Automatique (INRIA-SA) in France. Professor W. E. Fitzgibbon of the Department of Mathematics, University of Houston, and Dr. J. A. Desideri, Directeur de Réserche, INRIA-SA, have overall responsibility for the coordination and management of the project.
Computational simulations of the test case problems deemed acceptable will be entered into the database. Criteria for acceptance of solutions to test case problems will include accuracy, robustness, and originality or, perhaps, revelation of prior unseen phenomena. The database will be documented and accessible to the research and industrial communities. The documentation will include reports, books and an on-line browser. It will be stored on a devoted hard disk attached to an Internet accessible node. The database will contain experimental data and general information as well as the simulations. General information will include the definition of the test cases, the formats used to write the solutions, grids available for solutions, a graphic software, and a chart defining the read access rules. The contributed solutions will be organized into directories. Besides digitized flowfields, the base will contain abstracts providing the essential feature of the employed computational method and information on its efficiency and the computer system used. This feature will enable one to compare the results for various computational methods applied to the same problem and to compare the computation with experiments. One will be able to focus on critical regions of the flow (to zoom in on them), to post process critical quantities, and to obtain a detailed comparative analysis of the flow as well as the efficiency of the methodology. A preview demonstration of the database is available on the Internet at the following address: math.uh.edu/~hsff/hhsfd.html.
The database project was officially launched with the U. S.-Europe Conference on High Speed Flow Fields and the First U. S.-Europe High Speed Flow Field Database Workshop held at the University of Houston, November 6-9, 1995. In January 1996, W. E. Fitzgibbon and J. A. Desideri made a presentation to the Fluid Dynamics Technical Committee of the AIAA (American Institute of Aeronautics and Astronautics at the annual Reno meeting of the AIAA.. In the Summer of 1997 the project will be showcased at the summer meeting of the AIAA in Colorado. In November 1997, a second workshop will be held to review the database. The second round workshop will be hosted by the Centro Italiano Recherche Aerospaziali (CIRA) in Capua, Italy.
Karolos M. Grigoriadis, Ph.D., Assistant Professor, UH; Alexander Mayzus, Graduate Student, UH
The focus of this project is the development of novel control design techniques for vibrational systems described by vector second-order differential equations. A vector second-order differential equation description of vibrational systems with respect to its generalized coordinates follows from physical modeling of lumped-parameter mechanical systems or finite element discretization of distributed-parameter structural systems. This vector second-order representation has the following form
where q is the generalized coordinate vector, u is the input excitation vector, B is the input matrix, and M, D and K are the generalized mass, damping and stiffness matrices of the vibrational system, respectively.
However, modern control design theory largely ignores the special mathematical form of these systems since this theory has been developed for system models in first-order (state-space) differential equation form. Consequently, the application of existing control design tools to vibrational systems requires a first-order state-space description of these systems in terms of the state-space vector x
where the structural system parameters are imbedded in a nonlinear fashion in the state-space system matrices, resulting in high-order controllers, loss of physical insight, increased dimension and complexity, and loss of information about the special structure of the vibrational control problem.
Following a recently developed Linear Matrix Inequality (LMI) representation of the control design problem, researchers have chosen to address two objectives in the project:
For structural systems with collocated sensors and actuators, analytical solutions of static output feedback robust control design problems were obtained in terms of the structural system matrices. This is a significant improvement compared to the complicated existing computational design techniques for solving the static output feedback control design problem using a state-space representation of the system in terms of the augmented matrices. The proposed techniques have been recently extended to solve integrated structural design and control design problems that provide improved performance and robustness for controlled structural systems. The design of controlled rotating and translating elastic systems (such as rotors, saws, and transmission belts), flexible robotic arms, and smart structures controlled by piezoelectric sensors and actuators could benefit from the progress of this project.
ISSO * 1995-1996 * Annual Report
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