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This paper presents the design and implementation of a new fuzzy proportional-integration plus fuzzy proportional-derivative control scheme, named the fuzzy P$^2$ID controller hereafter, for controlling the handlebar of a bicycle robot with time-varying load (disturbance). The fuzzy P$^2$ID controller combines some advantages of the fuzzy PI controller and the ones of the fuzzy PD controller, which can compensate their individual shortcomings. Detailed design is described, along with the implementation of the integrated computer-aided designed bicycle control system. Functionally, the controller is a nonlinear controller with variable gains, providing the expected fast response and robustness. Structurally, it is an embedded version of a conventional PI controller and a PD controller, which has an additional fuzzy control block, where a switching rule of control signal is also implemented. Experimental results show the effectiveness of the new control scheme for controlling the handlebar of a bicycle robot, built from "off-the-shelf" parts with completely unknown hardware parameters. Comparison tests among several existing fuzzy controllers as well as the conventional PID controller have been conducted, so as to evaluate the superior performance of the new scheme. This new control scheme can be directly applied to general robotic systems and other industrial processes under similar physical conditions.