2005 Fiscal Year Final Research Report Summary
Design of Delayed Feedback for Multi-input Multi-output systems and Its Application
| Project/Area Number |
16560392
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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 |
Control engineering
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| Research Institution | Osaka Prefecture University |
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Principal Investigator |
KOKAME Hideki Osaka Prefecture University, Graduate School of Engineering, Professor, 工学研究科, 教授 (60026341)
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| Co-Investigator(Kenkyū-buntansha) |
HIRATA Kentaro Osaka Prefecture University, Graduate School of Engineering, Lecturer, 工学研究科, 講師 (00293902)
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| Project Period (FY) |
2004 – 2005
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| Keywords | Delayed Feedback / Derivative Feedback / Difference Feedback / Practical Stability / Stabilization / Differential-Difference Equation |
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| Research Abstract |
We have studied the theoretical treatment of the so-called delayed feedback control method, which was invented for the purpose of controlling chaos, with a view to applying it in order to stabilize unstable systems such as the inverted pendulum. Delayed feedback control gives an output which takes the form of difference between the present output and the past output. As such, for stability analysis of feedback systems, it is necessary to cope with resulting differential-difference systems. To stabilize unstable systems by this approach, it seems promising to get a stabilizing derivative feedback and approximate it by a difference counterpart. This prospect is always valid for single input systems. We have pointed out, however, that such is not true for multi-input systems. Thus out task is to provide a useful means to reach a stabilizing difference feedback in the case of multi-input systems. Supposing that a stabilizing dynamic controller which is fed the derivative of output measurements, we have studied the condition under which the closed-loop stability is preserved by an approximate controller which uses difference of output measurements. Applying the obtained result to observer based controller, we have a simple condition for stability preservation, which is written in terms of the observer gain and the state feedback gain. A disadvantage with this approach is that how large delay time in the control input is allowed is not clear. With this point in mind, we have studied a sufficient condition which employs both bounded real lemma and positive real lemma for associated complementary sensitivity transfer matrix. The obtained criterion is useful in that it allows an immediate evaluation of the admissible delay time.
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