Stability impact of small delays in proportional–derivative state feedback

Vyhlídal, Tomáš; Michiels, Wim; Zı́tek, Pavel; McGahan, Paul

doi:10.1016/j.conengprac.2008.09.001

Cited by 32 publications

(18 citation statements)

References 24 publications

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“…Thus, apart from the usual engineering objection of using the 'noisy' acceleration signals in feedback loops, the control design of such systems requires additional care. The complexities of NFDEs have fuelled an enormous mathematical literature [7,[32][33][34]; however, there have been few practical applications (for notable exceptions, see recent studies [35][36][37][38]). Here, we show that the stability criteria for the NFDE that arises in the setting of an inverted pendulum stabilized by a corrective torque can be readily determined.…”

Section: Introductionmentioning

confidence: 99%

Acceleration feedback improves balancing against reflex delay

Insperger

Milton

Stépàn

2013

J. R. Soc. Interface.

122

111

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A model for human postural balance is considered in which the time-delayed feedback depends on position, velocity and acceleration (proportionalderivative-acceleration (PDA) feedback). It is shown that a PDA controller is equivalent to a predictive controller, in which the prediction is based on the most recent information of the state, but the control input is not involved into the prediction. A PDA controller is superior to the corresponding proportional-derivative controller in the sense that the PDA controller can stabilize systems with approximately 40 per cent larger feedback delays. The addition of a sensory dead zone to account for the finite thresholds for detection by sensory receptors results in highly intermittent, complex oscillations that are a typical feature of human postural sway.

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Section: Introductionmentioning

confidence: 99%

Acceleration feedback improves balancing against reflex delay

Insperger

Milton

Stépàn

2013

J. R. Soc. Interface.

122

111

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“…In [1,2], it is shown that, if the system (5.11) is controllable, and det(A) = 0, then all the characteristic roots of the closed-loop system can be assigned at arbitrary positions in C \ {0}. However, results described in [30] indicate that stability of the state derivative feedback control may not be robust against small feedback delays. This issue is investigated in what follows.…”

Section: = (2 H)mentioning

confidence: 64%

“…In [6,18,22] boundary controlled partial differential equations are described that lead to a closed-loop system of neutral type, where the delays in the model are particular linear combinations of (physical) feedback delays and delays induced by propagation phenomena. In [30,31] the robustness against small feedback delays of linear systems controlled with state derivative feedback is addressed, motivated by vibration control applications. There, the closed-loop system can again be written in the form (1.1), where the delays τ k are combinations of actuator and sensor delays in input and output channels.…”

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confidence: 99%

Strong Stability of Neutral Equations with an Arbitrary Delay Dependency Structure

Michiels¹,

Vyhlídal²,

Zı́tek³

et al. 2009

SIAM J. Control Optim.

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Abstract. The stability theory for linear neutral equations subjected to delay perturbations is addressed. It is assumed that the delays cannot necessarily vary independently of each other, but depend on a possibly smaller number of independent parameters. As a main result necessary and sufficient conditions for strong stability are derived along with bounds on the spectrum, which take into account the precise dependency structure of the delays. In the derivation of the stability theory results from realization theory and determinantal representations of multivariable polynomials play an important role. The observations and results obtained in the paper are first illustrated and validated with a numerical example. Next, the effects of small feedback delays on the stability of a boundary controlled hyperbolic partial differential equation and of a control system involving state derivative feedback are analyzed.Key words. neutral system, strong stability, spectral theory Notations.C set of complex numbers [27] in mechanical engineering. Equations of neutral type also arise in boundary controlled hyperbolic partial differential equations subjected to small feedback delays [22,6] and in implementation schemes of predictive controllers for time-delay systems [7,25]. In this paper we discuss stability properties of the linear neutral equatioṅ

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“…Those approximations were based on low-pass filters, and it was found that most of the robustness benefits of SSD were then lost. It has also been shown that SSD controllers may be fragile, in the sense that arbitrarily small time delays may destroy stability [32], and that small uncertain feedback delays cannot always be safely neglected if state derivatives are used in the feedback [33]. This occurs when such delays lead to neutral, rather than retarded, DDE's.…”

Section: Introductionmentioning

confidence: 95%

Time-Delayed Control of SISO Systems for Improved Stability Margins

Ulsoy

2014

Journal of Dynamic Systems, Measurement, and Control

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While time delays typically lead to poor control performance, and even instability, previ-ous research shows that time delays can, in some cases, be beneficial. This paper presents a new benefit of time-delayed control (TDC) for single-input single-output (SISO) linear time invariant (LTI) systems: it can be used to improve robustness. Time delays can be used to approximate state derivative feedback (SSD), which together with state feedback (SF) can reduce sensitivity and improve stability margins. Additional sensors are not required since the state derivatives are approximated using available measurements and time delays. A systematic design approach, based on solution of delay differential equa-tions (DDEs) using the Lambert W method, is presented using a scalar example. The method is then applied to both single- and two-degree of freedom (DOF) mechanical sys-tems. The simulation results demonstrate excellent performance with improved stability margins. [DOI: 10.1115/1.4028528]

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Stability impact of small delays in proportional–derivative state feedback

Cited by 32 publications

References 24 publications

Acceleration feedback improves balancing against reflex delay

Acceleration feedback improves balancing against reflex delay

Strong Stability of Neutral Equations with an Arbitrary Delay Dependency Structure

Time-Delayed Control of SISO Systems for Improved Stability Margins

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