Recently, the number of people who need powered wheelchairs has been increasing due to aging society. Riding comfort is very important for people who use powered wheelchairs. In addition, wheelchairs must respond well to a velocity command signal with a joystick controller because collision must be avoided. The relation between ride comfort and fast response is a trade-off one. To solve these problems, a suitable reference torque signal should be designed. Thus, we propose a control system for powered wheelchairs that can reduce the vibration caused to the human head and upper body and achieve a fast response. Moreover, to guarantee robustness against parameter variations such as human weight and the friction of joints, a two-degrees-of-freedom control system that consists of feedforward and feedback controllers has been designed. We have designed a feedforward control input that uses the nil-mode-exciting (NME) profiler, which is called a "preshaping profiler". This preshaping profiler has a low-pass-shaped frequency characteristic. Therefore, no residual vibrations are caused at a frequency higher than a certain frequency (the sampling function frequency). In this study, the sampling function frequency has been designed in consideration of both vibration and response. To improve robustness against the variation of model parameters such as weight and friction, we have designed a wheel velocity feedback control added to the feedforward control. To verify the effectiveness of the proposed method, several numerical simulations have been carried out.