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An Adaptive Fuzzy PID Controller with Genetic Algorithm (GA) to tune its parameters is proposed by this paper. The task of the controller is to track the trajectory of a nonlinear system as best as it could. The Lyapunov's direct method is used as a tool for nonlinear system analysis and design. In which, the Lyapunov's linearization method is proven here to be useful for linear control. The paper relies on linearization method and the direct method to formulate its stability theory. The controller has two states, a learning state and a controlling state where GA performs on-line tuning of the controller's parameters. The GA method has the effect of tuning PID parameters to meet operation time constraint and system performance. In the controlling state, there are a supervisory controller designed to ensure system stability and a compensator appended to compensate for modeling error and disturbance. Overall performance of the controller is not compromised by the fact that it has only three parameters to work with.