Brian P. Rigney

Nonminimum Phase Dynamic Inversion for Settle Time Applications

Single-track hard disk drive (HDD) seek performance is measured by settle time, ts. In this paper, we show the effective use of feedforward dynamic inversion, coupled with reference trajectory yd generation, to achieve high performance ts. 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, yd 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.

Model Inversion Architectures for Settle Time Applications with Uncertainty

We compare two common model inversion architectures, plant inverse (PI) and closed-loop inverse (CLI), by evaluating their ability to achieve settle time performance improvements. The plant models of interest are discrete-time, single-input single-output (SISO), linear time-invariant (LTI), nonminimum phase (NMP), and uncertain. We use a simple algebraic analysis to show that PI and CLI yield the same desired to actual output dynamics if the plant is minimum phase. Using a stable inverse approximation when the plant is certain but NMP, the same algebraic analysis shows that CLI achieves superior settle time performance relative to PI when the settle boundaries are tight. Simulation and experimental data are used to derive conclusions when the plant is NMP and uncertain. We show that CLI has superior performance over PI for our plant dynamics of interest when low frequency parametric uncertainty is present. For higher frequency unstructured uncertainty, the distinction between the two inversion architectures is negligible

Discrete-Time Exact and Approximate Dynamic Inversion for Settle Performance

Abstract Single-track hard disk drive (HDD) seek performance is measured by settle time, t s , 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 y d , 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).

Adaptive inverse control for settling performance improvements

Single-track hard disk drive (HDD) seek performance is measured by settling 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. Previous work has shown feedforward dynamic inversion, coupled with an aggressive desired trajectory yd, is capable of achieving high performance settling times when the closed-loop dynamics are time-invariant and accurately modeled. In contrast, we describe an adaptive inversion procedure in this paper which removes the requirement for accurate initial models and tracks the position-variant dynamics present in our Servo Track Writer (STW) experimental apparatus. The proposed indirect adaptive inversion algorithm relies on a recursive least squares (RLS) estimate of the closed-loop dynamics. Pre-filtering of the RLS input signals and covariance resetting are necessary additions to the baseline adaptive algorithm in order to achieve fast settling times. Compared to the nonadaptive solution with accurate system identification, we show the adaptive algorithm achieves a 22% reduction in average settling time and a 53% reduction in settling time standard deviation.