2006 Fiscal Year Final Research Report Summary
Construction of a data driven control design method for nonlinear complex systems based on unfalsified control
| Project/Area Number |
16560384
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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 | Hiroshima University |
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Principal Investigator |
SAEKI Masami Hiroshima University, Graduate School of Engineering, Professor, 大学院工学研究科, 教授 (60144325)
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| Project Period (FY) |
2004 – 2006
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| Keywords | unfalsified control / PID control / parameter space method / nonlinear complex system / frequency response / multivariable PID control / numerical optimization / stability region |
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| Research Abstract |
1) A design method of the PID controller is constructed based on unfalsified control theory. This method is a data-driven model-free design method, and the system information used for the design is just the input-output responses of the plant. In this method, the set of PID gains that do not satisfy the performance index of the mixed sensitivity control is drawn on the parameter plane. We have proposed to apply many bandpass filters with different frequency bands to filtering the input-output data, and to use the filtered data to our method. This method enables us to tune the PID gain easily from an input-output data obtained in the normal operation. Therefore, this is a practical tuning method that can be applied to wide variety of systems, which may contain nonlinear complex systems.
2) A design method of the multivariable PID controller using the frequency response of the plant is proposed. Frequency response is also a nonparametric model of the plant as the input output response is,
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and such a method that uses the frequency response is easy to be applied to practical problems. A numerical optimization method of multivariable PID controllers that satisfy the performance index of the standard H-infinity control problem is given. Since the problem is described as a bilinear matrix inequality of PID gains for each frequency, a new method of obtaining a sufficient condition in the form of a linear matrix inequality is proposed. The PID gain converges by solving the LMI problem iteratively starting from a stabilizing PID controller, while the H-infinity norm decreases monotonically. Controller structure constraints such as decentralized control can be readily treated in the framework.
3) The properties of the PID gain set for which all the closed-loop poles lie in the left half complex plane are given on the parameter plane. A new method of determining the number of increase of unstable poles when the gain crosses the boundary of stability regions is proposed. This method is useful for determining the number of unstable poles in each region. These results are extended to Gamma-stability based on conformal mapping. This method is useful to determine the stability region on the complex plane from the frequency response directly instead of computing the number of unstable poles. Less
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