Resolution of Output

First, there is the resolution of the output. Since most robots are controlled by pulse-width-modulation (PWM), the output is an adjustment of the duty cycle of the PWM signal. The real question is, then, the resolution of PWM.

Obviously, a resolution of 2 (1 bit) is not sufficient. That would be the same as on-off control. On the other hand, a resolution of 1024 (10 bits) is too much because most mechanical systems have errors that exceed 0.1%. For a mechanical system that has an inherent error of 1%, 128 divisions for the PWM is enough. We will use $r_{k}$ to represent the number of bits to represent the output.