Fuzzy-Adaptive Control with Gain and Phase Margins

This paper presents a fuzzy-adaptive control method that results in the same gain and phase margins as a known linear control. The method uses fuzzy switching to transition between a traditional fuzzy-adaptive control and the linear control. Our novel switching algorithm changes the structure of the fuzzy approximator itself, so that the fuzzy approximator completely transforms into a pure integrator e.g. becoming the integral term in a PID control. The fuzzy inference takes both state error and adaptive-parameter drift as the inputs, so as to detect possible instabilities resulting from unmodeled dynamics, disturbances, and/or adaptive-parameter drift. The fuzzy inference determines how close the error and adaptive-parameter drift are to imposed limiting parameters. In our simulation we find that when the limiting parameters are tuned for peak performance, the proposed method doubles the performance compared to the traditional robust adaptive weight update methods of deadzone, leakage, and e-modification. Moreover, the limiting parameters can be tuned to find this peak performance by trial-and-error without fear of instability, unlike with traditional robust update methods.