Noncausal inverses for linear systems

Hunt, L. R.; Meyer, George E.; Su, Renjeng

doi:10.1109/9.489285

Cited by 186 publications

(80 citation statements)

References 4 publications

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“…An important practical disadvantage is that they do not provide an approach for designing an appropriate trajectory. Various examples of this approach can be found in [2,4,g,IO,II,14,15,16].…”

Section: Introductionmentioning

confidence: 99%

Trajectory planning and feedforward design for electromechanical motion systems

Lambrechts

Boerlage

Steinbuch

2005

Control Engineering Practice

283

197

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This report considers trajectory planning with given design constraints and design of an appropriate feedforward controller for single axis motion control. A motivation is given for using fourth order feedfonvard with fourth order trajectories. An algorithm is given for calculating hqjher order trajectories with bounds on all considered derivatives for point to point moves. It is shown that these trajectories are time-optimal in the most relevant cases. All required eqmtions for third and fourth order trajectory planning are explicitly derived. Implementation, discretization and quantization effects are considered. Simulation results show the effectiveness of fourth order feedfonvard in comparison with lower order feedforward.

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Section: Introductionmentioning

confidence: 99%

Trajectory planning and feedforward design for electromechanical motion systems

Lambrechts

Boerlage

Steinbuch

2005

Control Engineering Practice

283

197

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“…Direct inversion methods attempt to use the unstable model-inverse directly but maintain bounded plant inputs by either pre-loading the initial conditions [11], using noncausal plant inputs [8], [10], [12], or adjusting the desired reference trajectory [13]. Alternatively, approximate inversion techniques replace the unstable inverse system with a stable approximation [14]- [18].…”

Section: Nmp Inversion Algorithmsmentioning

confidence: 99%

Model Inversion Architectures for Settle Time Applications with Uncertainty

Rigney

Pao²,

Lawrence³

2006

Proceedings of the 45th IEEE Conference on Decision and Control

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Abstract-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 discretetime, 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.

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“…This design is complicated by the presence of NMP zeros in the closed-loop dynamics. It is well known that the exact tracking solution for NMP systems requires noncausal preactuation of the closedloop system to maintain bounded internal signals [Devasia et al, 1996], [Hunt et al, 1996], [Marconi et al, 2001]. Unlike the tracking applications discussed in these references, anticipation of a seek command is unrealistic in the specific HDD operating modes of interest.…”

Section: Introductionmentioning

confidence: 99%

“…The authors of [Devasia et al, 1996] and [Hunt et al, 1996] derive a continuous-time noncausal input r(t) over the preactuation interval t ∈ (−∞, t 0 ] which drives the state of H CL from rest to the required x(t 0 ) while maintaining y(t) = 0. A similar procedure is detailed in [Marconi et al, 2001] for a noncausal input r(k) in discrete-time, which we briefly review here.…”

Section: Infinite Preactuationmentioning

confidence: 99%

“…2) to maintain bounded r while still achieving delayed exact tracking. The authors of [Devasia et al, 1996], [Hunt et al, 1996], and [Marconi et al, 2001] derive additional preactuation sequences of length k 0 that preload the required initial conditions of H CL . In this case, the total preactuation is k p = k 0 + p. Similar in spirit to [Marconi et al, 2001], we review a discrete-time polynomial development of the required initial conditions, simplified for SISO LTI system dynamics.…”

Section: Exact Nmp Dynamic Inversionmentioning

confidence: 99%

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