Control Design and Robustness Analysis of Linear Time-Periodic Systems

Kalender, S.; Flashner, Henryk

doi:10.1115/1.2960481

Cited by 6 publications

(4 citation statements)

References 23 publications

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“…The perturbation matrices above are also periodic in time with the orbital period (that is, B i (t) = B i (t + T )), and denoting δ 1 = cos μ, δ 2 = sin μ, one has |δ 1 | 1, |δ 2 | 1. Thus, the momentum unloading magnetic control system is a special case of a parametrically perturbed LPTV system given in the following form (see for a detailed study of robust control of this type of systems by the authors in reference [15])…”

Section: Linearized Modelmentioning

confidence: 99%

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Design of Spacecraft Momentum Unloading Using Discrete-Time Formulation

Kalender

Flashner

2011

Proceedings of the Institution of Mechanical Engineers, Part G:

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An approach for the design of a momentum unloading system for a spacecraft controlled by momentum exchange actuators is proposed. The approach is based on formulating momentum unloading as a control problem of a parametrically perturbed periodic system. An equivalent discrete-time robust control design problem is formulated using a point-mapping-based numerical algorithm. Established robust control analysis can then be used to develop and analyse the robustness of the unloading control law. The method is demonstrated on an Earth-pointing satellite with magnetic torquers serving as unloading actuators. Earth's magnetic field is modelled as a tilted dipole that consists of a periodic term and bounded perturbations. A discrete-time representation of the system is used to develop an unloading control law and the structured singular value theory is employed to analyse its robustness to parametric uncertainties.

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Section: Linearized Modelmentioning

confidence: 99%

“…In this article, a new approach for control design of perturbed LPTV systems [14,15] to develop momentum unloading control laws is presented. In this approach, the perturbed LPTV control design problem is formulated as a discrete-time robust control design problem.…”

Section: Introductionmentioning

confidence: 99%

Design of Spacecraft Momentum Unloading Using Discrete-Time Formulation

Kalender

Flashner

2011

Proceedings of the Institution of Mechanical Engineers, Part G:

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“…For instance, a matrix polynomial approach in Reference 17 and the method of first integrals in Reference 18 were employed to analyze the periodic piecewise systems. The problems of periodic piecewise systems with uncertainty and disturbances were discussed in References 19 and 20. By far, the investigations of continuous‐time periodic systems have achieved ample results but received scanty attention to the networked control.…”

Section: Introductionmentioning

confidence: 99%

Event‐based output feedback control of periodic systems: A piecewise impulsive method

Yang

Gao

Feng

et al. 2021

Intl J Robust & Nonlinear

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In this article, an event‐triggered control with periodic time‐varying parameters is designed to stabilize a class of periodic systems with exogenous disturbances in a network environment. The continuous‐time periodic system is approximated by some linear subsystems with finite‐number constant matrices based on a piecewise method. It can thus reduce the complexity of theoretical analysis. To tackle the reduction of unnecessary data transmission between the sensor (or controller) and the controller (or actuator), new event‐triggering mechanisms are designed via output feedback. Special parameters are designed to eliminate Zeno behavior, and the minimum triggering interval is obtained according to the designed condition. Then, an event‐triggered periodic piecewise system is modeled as an impulsive periodic piecewise system. The bounded stability, as well as the L∞ performance of the impulsive periodic piecewise system, are analyzed. Furthermore, the gains of the event‐triggered controller are obtained by a method of variable substitution. Finally, the validity of the proposed control is demonstrated by an application example.

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“…In [13], the parametric robustness analysis of LTP systems is considered using a truncated point mapping technique and µ-analysis. the other in such systems was not studied.…”

mentioning

confidence: 99%

Robustness Analysis of Helicopter Ground Resonance with Parametric Uncertainties in Blade Properties

Sanches

Alazard

Michon

et al. 2013

Journal of Guidance, Control, and Dynamics

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This paper presents a stability robustness analysis of the helicopter ground resonance phenomenon. By using the lifting procedure, the uncertain Linear Time-Periodic (LTP) model of the helicopter is transformed into an augmented uncertain Linear-Time-Invariant (LTI) model that allows the application of µ-analysis tools. The lifting procedure involves a periodic switching LTI piecewise model computed using oversampling of the system period. The representativeness of the lifted model for various oversampling period values and discretization methods is discussed and compared with a Floquet analysis for several parametric congurations. A µ-analysis is then applied to nd the worst case parametric conguration for a given rotor angular rate. The parametric uncertainties taken into account are the dynamic characteristics (stiness and damping) of each blade hinge. A signicant advantage of the proposed approach is that it enables performing ground resonance analysis for a rotor with dissimilar blade properties due to aging eects. Considering uncertainties on the four blade hinge sti-1 PhD. student.

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Control Design and Robustness Analysis of Linear Time-Periodic Systems

Cited by 6 publications

References 23 publications

Design of Spacecraft Momentum Unloading Using Discrete-Time Formulation

Design of Spacecraft Momentum Unloading Using Discrete-Time Formulation

Event‐based output feedback control of periodic systems: A piecewise impulsive method

Robustness Analysis of Helicopter Ground Resonance with Parametric Uncertainties in Blade Properties

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