Nonminimum Phase Dynamic Inversion for Settle Time Applications

Single-track hard disk drive (HDD) seek performance is measured by settle time, t
_s
. In this paper, we show the effective use of feedforward dynamic inversion, coupled with reference trajectory yd generation, to achieve high performance t
_s
. Models of HDD dynamics are typically nonminimum phase (NMP), and it is well known that the exact tracking solution for 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, y
_d
tracking accuracy, and achievable settle performance. We investigate multiple single-input single-output (SISO) inversion architectures, and we show that the feedforward closed-loop inverse (FFCLI) achieves superior settle performance to the feedforward plant inverse (FFPI) in our application because FFCLI does not excite the closed-loop dynamics. Using the FFCLI architecture, we further investigate numerous NMP inversion algorithms, including both exact inversion schemes with initial condition preloading and stable approximate NMP inverse techniques. We conclude that the settle performance of the zero-order Taylor series stable NMP approximation matches the best performance of the exact inversion techniques in our application, and does so without the high frequency excitation required by the zero magnitude error tracking controller (ZMETC), or the excessive preactuation required by the zero phase error tracking controller (ZPETC). Minimum energy optimal trajectory generation methods show that the system order n is a limiting factor in settle performance. This confirms that the zero-order series method, which is capable of producing settle times in less than n samples, is on par with optimal approaches yet much simpler to implement. Multiple NMP inversion algorithms are experimentally validated on a servo track writer (STW), which reinforces the general trends observed in ideal simulations.