1998 Fiscal Year Final Research Report Summary
Computer Aided Design of Robust Control Systems Using Polygon Interval Arithmetic
| Project/Area Number |
09650474
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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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 Faculty of Engineering Professor, 工学部, 教授 (80111772)
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| Co-Investigator(Kenkyū-buntansha) |
MASUBUCHI Izumi Kobe University Faculty of Engineering Research Associate, 工学部, 助手 (90283150)
FUJISAKI Yasumasa Kobe University Faculty of Engineering Associate Professor, 工学部, 助教授 (30238555)
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| Project Period (FY) |
1997 – 1998
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| Keywords | Robust Control / Polygon Interval Arithmetic / Uncertain Systems / Frequency Domain / Value Sets / PID Control |
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| Research Abstract |
The main results obtained through the research are summarized as follows.
1. Value sets estimate for functions which have no totally decomposable expression.
We consider a problem to compute good estimate of value sets when a given analytic function f(p) has no totally decomposable expression, where each parameter p1 of p belongs to a polygon, and showed that the boundary of the value set of f is included by the image of edges of polygons. Using this result, we proposed two methods to compute estimates of value sets. One is for the functions which are given by the ratio of affine functions of p. The other is for the functions which are multi-affine functions of p.
2. Development of CAD system for robust control systems.
We developed a CAD system which design PID controllers, lead compensators, lag compensators and 2 degree of freedom PID controllers, which satisfy several robust performances. This system compute value sets of plants using NPIA and feasible regions of parameters of controllers using operations on sets (union, intersection and difference set). Since it computes feasible regions, it gives global optimum solution even if optimization problems are not convex.
3. Stability analysis of nonlinear systems.
We analyze stability of Lur'e systems which have uncertainties in not only for the nonlinear part but also the linear part. Value sets of transfer function corresponding to the linear part are computed using NPIA and stability is analyzed applying Popov criterion.
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