2005 Fiscal Year Final Research Report Summary
Control of mechanical systems with friction
| Project/Area Number |
16560383
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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 University |
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Principal Investigator |
OHTA Yoshito Osaka University, Mechanical Engineering, Professor, 大学院工学研究科, 教授 (30160518)
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| Co-Investigator(Kenkyū-buntansha) |
HIRATA Kenji Osaka University, Mechanical Engineering, Assistant Professor, 大学院工学研究科, 助手 (40314364)
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| Project Period (FY) |
2004 – 2005
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| Keywords | invariant set / duality / output admissible set / reachable set / friction / switching control / input constraint |
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| Research Abstract |
In this study, a new method for switching control of mechanical systems with friction is proposed. The proposed method switches the feedback gain based on the invariant set called maximal output admissible set. The method can be applied to the situation where mechanical control systems such as positioning systems are driven by step-wise reference signals and non-zero steady error is caused in presence of friction. First, this research studies fundamental properties of invariant sets and proposes how to construct such sets. Second, a switching rule is proposed for the control of mechanical systems.
The maximal output admissible sets and the reachable sets are invariant sets of control systems. In this research, we study and establish (1) construction and approximation methods of such sets for linear systems, (2) non-conservative construction of the maximal output admissible set for uncertain linear systems, (3) exact determinations of the maximal output admissible set for a class of nonlinear systems, and (4) the duality relations between the maximal output admissible sets and the reachable sets.
Using the maximal output admissible sets, a switching rule for the state feedback gains is proposed for systems with friction. The idea is to set up gains in such a way that maximal output admissible sets are nested, and to use the gain when the trajectory of the system is inside the corresponding maximal output admissible set. If gains are designed appropriately, we can avoid using unnecessarily high gains and at the same time achieve fast convergence to the steady state with a small steady error.
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