OPERATION ON SETS AND IT'S APPLICATIONS TO COMPUTER AIDED DESIGN OF ROBUST CONTROL SYSTEMS
| Project/Area Number |
63550311
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Research Field |
計測・制御工学
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| Research Institution | KOBE UNIVERSITY |
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Principal Investigator |
OHTA Yuzo KOBE UNIVERSITY, ELECTRONICS DEPARTMENT, ASSOCIATE PROFESSOR, 工学部, 助教授 (80111772)
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| Co-Investigator(Kenkyū-buntansha) |
KIMURA Shinji KOBE UNIVERSITY, ELECTRONICS DEPARTMENT, ASSISTANT PROFESSOR, 工学部, 助手 (20183303)
HANEDA Hiromasa KOBE UNIVERSITY, ELECTRONICS DEPARTMENT, PROFESSOR, 工学部, 教授 (10031113)
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| Project Period (FY) |
1988 – 1989
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| Project Status |
Completed (Fiscal Year 1989)
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| Budget Amount *help |
¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 1989: ¥700,000 (Direct Cost: ¥700,000)
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| Keywords | OPERATION ON SETS / UNCERTAINTY / ROBUST CONTROL / COMPUTATIONAL GEOMETRY / COMPUTER AIDED DESIGN / ROBUST STABILITY / 凸包問題 / 制御系のCAD |
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| Research Abstract |
Because of variation and uncertainty of system parameters, mathematical models Invariably give an imperfect description of real systems. Therefore, robustness is one of the most fundamental requirements for control systems. Main results of this research project may be summarized as follows:
1. Polygon Interval Arithmetic. To treat uncertainty, we defined operations (addition, multiplication, and reversion) on sets consisting of all the convex polygons, which we call polygon interval arithmetic. We derived several important properties of polygon interval arithmetic. We also proposed an efficient algorithm to calculate addition of convex polygons.
2. Robust Stability Analysis. (1)Stability of feedback systems can be analyzed by examining determinants of return differential matrix at every frequencies. A method based on the mapping theorem was used to calculate it, but it is very much time consuming. We proposed to use a method based on both polygon interval arithmetic and the mapping theorem to calculate determinants. (2)Stability of (nonlinear) systems can be examined by using Liapunov functions. We proposed a method to construct a Liapunov function via computational geometric technique to calculate convex hulls.
3. RSRD(Robust Sequential Return Difference) method. We proposed RSRD method to design robust control systems, which uses polygon interval arithmetic, and which makes possible to design controllers of each loops "independently", and to guarantee the integrity.
4. CAD(Computer Aided Design) System. We developed a CAD system to design robust control systems based on RSRD method. We also implemented a program to calculate stability margin of multi-input multi-output systems.
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Report
(3 results)
Research Products
(16 results)
