Unfalsified Control Approach to Parameter Space Design of PID Controllers

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In this paper, Unfalsified control concept is applied to the parameter space design problem of PID gains for mixed sensitivity control problem, and a new method of drawing unfalsified region on the parameter plane is proposed. This method does not require constructing a mathematical model for design, but draws the unfalsified region directly from the input-output responses of the plant. Therefore, it is expected that this method can be applied to complex nonlinear plants. By numerical experiments, it is found that sufficiently large region cannot be falsified by using a step response data, but can be falsified by using the responses of the plant excited by sinusoidal inputs for many frequencies. If the unfalsified region is empty, it can be concluded that no solution exist. Usefulness is demonstrated by a numerical example for a nonlinear plant with backlash.

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