Hard disk drive bandwidth limitations due to sampling frequency and computational delay

The improvements in track density and performance expected of future disk drives require increased servo bandwidths. The mechanics are often cited as a bandwidth limiter, but sampling frequency and computational delay also play a part in reducing the achievable bandwidth. To isolate the effects of the sampling frequency and the computational delay, the higher frequency resonances often found in disk drives were ignored, and a simple double-integrator plant model was used for the controller designs. The maximum bandwidths (assuming fixed stability margins) were calculated using two controller types, a second-order lead-lag filter and an H_∞ controller, for a range of sampling frequencies and computational delays. The results are summarized in a scaling law that relates the bandwidth to the sampling period, delay time, and an empirically determined constant. The effects of sampling and delay on the sensitivity function, and the implications of the Bode integral theorem, are also discussed