The establishment of a well-behaved fuzzy model implies the completion of two major tasks: generation of fuzzy rule base and selection of membership function parameters. In this document, a time domain state space fuzzy identifier of an inverted pendulum is presented. First, rule base is generated by using cell to cell mapping method, in which the rules are generalized from the actual system trajectories. Then, a supervised learning method is used to fine tune the parameters of the membership functions. The learning method is derived directly from the gradient descent approach. Training data are collected from the actual system input-output behavior, and three training techniques are presented: the fixed learning rate method, the time-variant learning rate method, and the conjugate-gradient method. The learning results of all the methods are presented and compared.