Optimal output-transitions for linear systems

Stable inversion based precise tracking for continuous‐time square or nonsquare non‐minimum phase systems is studied. However, high precision trajectory tracking of non‐minimum phase systems can be obtained by the stable inversion method but requiring large enough extended time interval. In order to solve this problem of large extended time restriction, a novel approach to precise trajectory tracking of non‐minimum phase systems is proposed, it is called the improved stable inversion (ISI) method, using an optimal integration of the pre‐actuation and the optimal state transition (OST) techniques. The ISI method can obtain precise trajectory tracking with a smaller extended time interval as compared to the stable inversion method. The proposed method achieves better validation through numerical simulations for the non‐minimum phase system.

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“…Due to d (t), when t → −∞ in the delimiting situation [16], the input Eq. (39) and the antistable subsystem equation in (40) are changed as…”

Section: Pre-action Processmentioning

confidence: 99%

Precise Tracking for Continuous‐Time Non‐Minimum Phase Systems

Zhang

Zhu

Xiong

2018

Asian Journal of Control

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“…Delimiting state. The delimiting state [21] is defined as the system state x = [ ] ⊤ satisfyingẋ = Ax = 0 as time t tends to infinity.…”

Section: Pre-actuationmentioning

confidence: 99%

Pre‐Actuation and Optimal State Transition Based Precise Tracking for Maximum Phase System

Zhang¹,

Liu²

2016

Asian Journal of Control

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Precise trajectory tracking for the maximum phase system can be achieved by the stable inversion method. However, its side effect is requiring the sufficient extended zero trajectory. To overcome this drawback, firstly, this paper introduces the concept of stable initial state which is of vital importance to achieve precise output tracking. And then several methods have been presented to obtain the stable initial state. Both the standard method and the pre-actuation method can be seen as the simplified stable inversion method under certain conditions, but the two methods only perform approximate output tracking. To achieve precise trajectory tracking, the optimal state transition method and the combination method consisting of the pre-actuation and the optimal state transition are introduced. Finally, the optimal combination method is proposed to obtain the best overall tracking effect. In brief, different methods are fit for different situation but the optimal combination method is the finest method in practical situation. The effectiveness of the proposed methods are verified through numerical simulations for the maximum phase system.

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“…It is easy to see that E(y(k)) is given by the r.h.s. of (11) and E(e t (k)) is given by the r.h.s. of (12) wherẽ z(k) is obtained replacing x(0) with x 0 .…”

Section: The Stochastic Casementioning

confidence: 99%

“…In this regard, many methods are based on the model stable inversion [3][4][5], which allows exact tracking through an infinite preactuation interval. The practical infeasibility of this solution motivated the use of approximated preview-based inversion techniques with preactuation [6][7][8][9][10][11]. All the above papers assume that the system is hyperbolic, namely without zeros on the boundary of the stability region (the imaginary axis or the unitary Manuscript received February 28, 2014; revised July 21, 2014; accepted October 10, 2014.…”

Section: Introductionmentioning

confidence: 99%

Spline Based Pseudo‐Inversion of Sampled Data Non‐Minimum Phase Systems for an Almost Exact Output Tracking

Jetto¹,

Orsini²,

Romagnoli³

2014

Asian Journal of Control

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This paper considers the problem of achieving a very accurate tracking of a pre-specified desired output trajectorỹ y(k), k ∈ ∠ Z + , for linear, multiple input multiple output, non-minimum phase and/or non hyperbolic, sampled data, and closed loop control systems. The proposed approach is situated in the general framework of model stable inversion and introduces significant novelties with the purpose of reducing some theoretical and numerical limitations inherent in the methods usually proposed. In particular, the new method does not require either a preactuation or null initial conditions of the system. The desiredỹ(k) and the corresponding sought input are partitioned in a transient component (ỹ t (k) and u t (k), respectively) and steady-state (ỹ s (k) and u s (k), respectively). The desired transient componentỹ t (k) is freely assigned without requiring it to be null over an initial time interval. This drastically reduces the total settling time. The structure of u t (k) is a priori assumed to be given by a sampled smoothing spline function. The spline coefficients are determined as the least-squares solution of the over-determined system of linear equations obtained imposing that the sampled spline function assumed as reference input yield the desired output over a properly defined transient interval. The steady-state input u s (k) is directly analytically computed exploiting the steady-state output response expressions for inputs belonging to the same set ofỹ s (k). Key Words:Model stable inversion, sampled data non-minimum phase systems, optimal transient tracking.

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Optimal output-transitions for linear systems

Cited by 97 publications

References 15 publications

Precise Tracking for Continuous‐Time Non‐Minimum Phase Systems

Precise Tracking for Continuous‐Time Non‐Minimum Phase Systems

Pre‐Actuation and Optimal State Transition Based Precise Tracking for Maximum Phase System

Spline Based Pseudo‐Inversion of Sampled Data Non‐Minimum Phase Systems for an Almost Exact Output Tracking

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