Vibration Control of a Probe-and-Drogue Refueling Hose System with Prescribed Bound
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We develop a boundary control strategy for vibration suppression mission of a probe-and-drogue refueling hose (PDRH) system with prescribed bound in this study. Based on the distributed parameter system theory, the PDRH is modeled by partial differential equations (PDEs) because of its characteristic of infinite dimension. No violation of the time-varying boundary constraint during operation is warranted by the barrier Lyapunov function. Signals of closed-loop system are demonstrated to be uniformly bounded via Lyapunov's direct method. By choosing parameters appropriately, system state is proven to converge to a small neighborhood of zero. The feasibility of the proposed control law is verified by simulation results.Keywords:
Distributed parameter system
In many systems the physical quantity of interest depends on several independent variables. For instance, the temperature of an object depends on both position and time, as do structural vibrations and the temperature and velocity of water in a lake. When the dynamics are affected by more than one independent variable, the equation modeling the dynamics involves partial derivatives and is thus a partial differential equation (PDE). Since the solution of the PDE is a physical quantity, such as temperature, that is distributed in space, these systems are often called distributed parameter systems (DPS). The state of a system modeled by an ordinary differential equation evolves on a finite-dimensional vector space, such as $${\mathbb R}^n.$$ In contrast, the solution to a partial differential equation evolves on an infinite-dimensional space. For this reason, these systems are often called infinite-dimensional systems. The underlying distributed nature of the physical problem affects the dynamics and controller design.
Distributed parameter system
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Partial derivative
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This paper addresses a systematic method for the reconstruction and the prediction of a distributed phenomenon characterized by partial differential equations, which is monitored by a sensor network. In the first step, the infinite-dimensional partial differential equation, i.e. distributed-parameter system, is spatially and temporally decomposed leading to a finite-dimensional state space form. In the next step, the state of the resulting lumped-parameter system, which provides an approximation of the solution of the underlying partial differential equations, is dynamically estimated under consideration of uncertainties both occurring in the system and arising from noisy measurements. By using the estimation results, several additional tasks can be achieved by the sensor network, e.g. optimal sensor placement, optimal scheduling, and model improvement. The performance of the proposed model-based reconstruction method is demonstrated by means of simulations.
Distributed parameter system
Partial derivative
State-space representation
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We develop a boundary control strategy for vibration suppression mission of a probe-and-drogue refueling hose (PDRH) system with prescribed bound in this study. Based on the distributed parameter system theory, the PDRH is modeled by partial differential equations (PDEs) because of its characteristic of infinite dimension. No violation of the time-varying boundary constraint during operation is warranted by the barrier Lyapunov function. Signals of closed-loop system are demonstrated to be uniformly bounded via Lyapunov's direct method. By choosing parameters appropriately, system state is proven to converge to a small neighborhood of zero. The feasibility of the proposed control law is verified by simulation results.
Distributed parameter system
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Distributed parameter system
Partial derivative
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Distributed parameter system
Parameter identification problem
Realization (probability)
Smoothing
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Time-varying ISS-Lyapunov functions for impulsive systems provide a necessary and sufficient condition for ISS. This property makes them a more powerful tool for stability analysis than classical candidate ISS-Lyapunov functions providing only a sufficient ISS condition. Moreover, time-varying ISS-Lyapunov functions cover systems with simultaneous instability in continuous and discrete dynamics for which candidate ISS-Lyapunov functions remain inconclusive. The present paper links these two concepts by suggesting a method of constructing time-varying ISS-Lyapunov functions from candidate ISS-Lyapunov functions, thereby effectively combining the ease of construction of candidate ISS-Lyapunov functions with the guaranteed existence of time-varying ISS-Lyapunov functions.
Lyapunov optimization
Control-Lyapunov function
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Partial derivative
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Abstract : Optimal control, observability, and controllability of linear systems governed by simultaneous sets of ordinary and partial differential equations are investigated. Such systems are called mixed distributed and lumped parameter systems. The interaction on the spatial boundary between the lumped and the distributed subsystems provides a convenient criterion for their classification. Three common types of mixed distributed and lumped parameter systems are identified and practical examples are referenced. Optimal sampled-data control of mixed systems is studied. (Modified author abstract)
Observability
Distributed parameter system
Distributed element model
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Distributed parameter system
Base (topology)
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