Discrete-Time Exact and Approximate Dynamic Inversion for Settle Performance

Single-track hard disk drive (HDD) seek performance is measured by settle time, ts, defined as the time from the arrival of a seek command until the measured position reaches and stays within an acceptable distance from the target track. In this paper, we show the effective use of feedforward dynamic inversion, coupled with an aggressive desired trajectory yd, to achieve high performance settle times. It is well known that the exact tracking solution for nonminimum phase (NMP) systems requires noncausal preactuation to maintain bounded internal signals. In the specific HDD operating modes of interest, anticipation of a seek command is unrealistic, and thus preactuation adds to the overall computation of settle time. Unlike many dynamic inversion tracking applications, this negative effect of preactuation leads to interesting trade-offs between preactuation delay, tracking accuracy, and achievable settle performance. We show that, surprisingly, very little preactuation is desirable when truncating the exact tracking solution and applying it to our NMP HDD model. For comparison, we also review the stable Taylor series approximate inverse, and show that a zero-order series’ settle performance is comparable to truncated exact inversion while being easier to compute and implement. We experimentally validate this conclusion on a Servo Track Writer (STW).