Design and stability analysis of single-input fuzzy logic controller

In existing fuzzy logic controllers (FLCs), input variables are mostly the error and the change-of-error regardless of complexity of controlled plants. Either control input u or the change of control input Deltau is commonly used as its output variable. A rule table is then constructed on a two-dimensional (2-D) space. This scheme naturally inherits from conventional proportional-derivative (PD) or proportional-integral (PI) controller. Observing that 1) rule tables of most FLCs have skew-symmetric property and 2) the absolute magnitude of the control input |u| or |Deltau| is proportional to the distance from its main diagonal line in the normalized input space, we derive a new variable called the signed distance, which is used as a sole fuzzy input variable in our simple FLC called single-input FLC (SFLC). The SFLC has many advantages: The total number of rules is greatly reduced compared to existing FLCs, and hence, generation and tuning of control rules are much easier. The proposed SFLC is proven to be absolutely stable using Popov criterion. Furthermore, the control performance is nearly the same as that of existing FLCs, which is revealed via computer simulations using two nonlinear plants.