Optimal Control of Linear Systems of Arbitrary Fractional Order

Matychyn, Ivan; Onyshchenko, Viktoriia

doi:10.1515/fca-2019-0011

Cited by 10 publications

(3 citation statements)

References 16 publications

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“…The aircraft of interest in this paper is the Boeing 747 100/200 series, flying at the altitude of 4000 m with 0.567 Mach number corresponding to 185 m/s speed [53]. Non-minimum phase behavior is typically encountered when pitching up an aircraft to increase its altitude.…”

Section: Non-minimum Phase Problemmentioning

confidence: 99%

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Robust Control for Non-Minimum Phase Systems with Actuator Faults: Application to Aircraft Longitudinal Flight Control

et al. 2021

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This study is concerned with developing a robust tracking control system that merges the optimal control theory with fractional-order-based control and the heuristic optimization algorithms into a single framework for the non-minimum phase pitch angle dynamics of Boeing 747 aircraft. The main control objective is to deal with the non-minimum phase nature of the aircraft pitching-up action, which is used to increase the altitude. The fractional-order integral controller (FIC) is implemented in the control loop as a pre-compensator to compensate for the non-minimum phase effect. Then, the linear quadratic regulator (LQR) is introduced as an optimal feedback controller to this augmented model ensuring the minimum phase to create an efficient, robust, and stable closed-loop control system. The control problem is formulated in a single objective optimization framework and solved for an optimal feedback gain together with pre-compensator parameters according to an error index and heuristic optimization constraints. The fractional-order integral pre-compensator is replaced by a fractional-order derivative pre-compensator in the proposed structure for comparison in terms of handling the non-minimum phase limitations, the magnitude of gain, phase-margin, and time-response specifications. To further verify the effectiveness of the proposed approach, the LQR-FIC controller is compared with the pole placement controller as a full-state feedback controller that has been successfully applied to control aircraft dynamics in terms of time and frequency domains. The performance, robustness, and internal stability characteristics of the proposed control strategy are validated by simulation studies carried out for flight conditions of fault-free, 50%, and 80% losses of actuator effectiveness.

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Section: Non-minimum Phase Problemmentioning

confidence: 99%

“…The longitudinal state-space dynamics of the Boeing 747-100/200 model obtained through Jacobian linearization at the trim point as reported in [53] can be expressed in state-space form as, .…”

Section: Aircraft Dynamicsmentioning

confidence: 99%

Robust Control for Non-Minimum Phase Systems with Actuator Faults: Application to Aircraft Longitudinal Flight Control

et al. 2021

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“…Explicit solutions to linear systems of differential equations provide a basis to solve control problems. Analytical solutions of the linear systems of fractional differential equations with constant coefficients were derived in the papers [8,9] and then applied to solving control problems and differential games in [10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

Analytical Solution of Linear Fractional Systems with Variable Coefficients Involving Riemann–Liouville and Caputo Derivatives

Matychyn

2019

Symmetry

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This paper deals with the initial value problem for linear systems of fractional differential equations (FDEs) with variable coefficients involving Riemann–Liouville and Caputo derivatives. Some basic properties of fractional derivatives and antiderivatives, including their non-symmetry w.r.t. each other, are discussed. The technique of the generalized Peano–Baker series is used to obtain the state-transition matrix. Explicit solutions are derived both in the homogeneous and inhomogeneous case. The theoretical results are supported by examples.

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A Study on Linear Prabhakar Fractional Systems with Variable Coefficients

Aydin,

Mahmudov

2024

Qual. Theory Dyn. Syst.

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The focus of this paper is on addressing the initial value problem related to linear systems of fractional differential equations characterized by variable coefficients, incorporating Prabhakar fractional derivatives of Riemann–Liouville and Caputo types. Utilizing the generalized Peano–Baker series technique, the state-transition matrix is acquired. The paper presents closed form solutions for both homogeneous and inhomogeneous cases, substantiated by illustrative examples.

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Optimal Control of Linear Systems of Arbitrary Fractional Order

Cited by 10 publications

References 16 publications

Robust Control for Non-Minimum Phase Systems with Actuator Faults: Application to Aircraft Longitudinal Flight Control

Robust Control for Non-Minimum Phase Systems with Actuator Faults: Application to Aircraft Longitudinal Flight Control

Analytical Solution of Linear Fractional Systems with Variable Coefficients Involving Riemann–Liouville and Caputo Derivatives

A Study on Linear Prabhakar Fractional Systems with Variable Coefficients

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