Development and application of a gradient descent method in adaptive model reference fuzzy control

This pager presents an adaptive model-reference fuzzy controller (AMRFC) to control the water level of a water tank. It derives the AMRFC and compares its performance with the more conventional methods of proportional-integral (PI) control and model-reference adaptive control (MRAC). The gradient descent method is chosen to adapt the AMRFC. Unlike most of the papers reviewed, which use the error and error change as inputs to the fuzzy system, this paper uses the theoretical background developed for MRAC in choosing these inputs. Although the controller uses many inference rules (441 rules), it is shown that the required mathematical calculations are not much, making implementation on a low-end microcontroller feasible. The control algorithm is implemented in simulation and real-time using an 8-bit microcontroller. It is found that the AMRFC and MRAC have approximately similar performance, however they compare favorably to the PI controller. This similarity in performance is due to the linearity of the plant, and it is expected that the AMRFC would have a much performance if the plant had a stronger non-linearity.