1995 Fiscal Year Final Research Report Summary
Relaxing the Assumptions of Standard H_* Control
| Project/Area Number |
06650453
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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 | TOKYO INSTITUTE OF TECHNOLOGY (1995)
Chiba University (1994) |
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Principal Investigator |
MITA Tsutomu TOKYO INSTITUTE OF TECHNOLOGY, 工学部, 教授 (60092102)
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| Project Period (FY) |
1994 – 1995
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| Keywords | H_* control / Servo controller / Nonstandard H_* control / Zeros / スペクトル分解 |
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| Research Abstract |
The H_* control is a theory giving fundamental design method of robust control systems. However, several relatively strong conditions are imposed on applicable control problems such that :
1.(A,B_2) is stabilizable and (A,C_2) is detectable.
2.G_<12> (s) and G_<21> (s) have no jomega zeros.
3.D_<12> is of full column rank and D_<21> is of row full rank.
In order to avoid these conditions, the following results are gained in this research.
a.Typical control problems violating the first and second conditions include the servo problem, where unstable weighting functions are introduced to implement the internal model principle into the H_* control problem setting. In order to give a solution to this problem, introducing a notion of essential stability and additional condition which guarantees for the controller to have the internal model, we firstly solved the H_* servo problem. Our further investigation even solved the problem without assuming the additional condition. However, the proof of the obtained theory was rather complicated. Therefore, to simplify the proof, we next introduced a notion of comprehensive stability and tried to solve the problem by an alternative procedure.
b.The second and third conditions are violated when placement of inputs and outputs is unbalanced. This includes an H_* control problem where real plants have poles on the jomega axis. In order to get around the difficulties, we firstly introduced descriptor representation and analyzed spectral factorization problem for plants having zeros on the imaginary axis as well as at infinity. Then, based on this spectral factorization, we derived nonstandard H_2 control as well as H_* control solutions.
Effectiveness of the proposed H_* servo design method was proven by several industrial applications. The theoretical results obtained here give foundation of researches on nonstandard H_* control problems.
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