Due to the lack of reliable and/or inexpensive hardware sensors in cement grinding, development of software sensors is particularly significant for control and monitoring purposes. In this study, a nonlinear distribut...
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In this paper, we show how the so-called diffusive representation can be used in order to identify nonlinear Volterra models of the form H (∂ t ) X = f ( u, X ) + v . Several methods are described, all being based on ...
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In this paper, we show how the so-called diffusive representation can be used in order to identify nonlinear Volterra models of the form H (∂ t ) X = f ( u, X ) + v . Several methods are described, all being based on a suitable parameterization of H (∂ t ) by means of its γ-symbol. Following this idea, the complex dynamic nature of H (∂ t ) can be summarized by a few parameters on which the identification of the dynamic part of the model will focus. For illustration, we implement the methods on a concrete numerical example.
This paper deals with large-angle rapid slew maneuvers of a flexible spacecraft, which consists of a rigid central body and a flexible beam attached to it. Dynamic model for the spacecraft described by a coupled nonli...
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This paper deals with large-angle rapid slew maneuvers of a flexible spacecraft, which consists of a rigid central body and a flexible beam attached to it. Dynamic model for the spacecraft described by a coupled nonlinear hybrid system is derived. With the control torque applied to the rigid central body only, a PD control law is presented using the measurements of the attitude angle of the rigid body and its velocity. Based upon the Lyapunov method in infinite dimensional space, it is shown that implementation of the control algorithm results in the slew maneuvering with the simultaneous vibration suppression.
The vertical gradient freeze crystal growth process is the main technique for the production of high quality compound semiconductors that are vital for today's electronic applications. A simplified model of this p...
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The vertical gradient freeze crystal growth process is the main technique for the production of high quality compound semiconductors that are vital for today's electronic applications. A simplified model of this process consists of two 1D diffusion equations with free boundaries for the temperatures in crystal and melt. Both phases are coupled via an ordinary differential equation that describes the evolution of the moving solid/liquid interface. The control of the resulting two-phase Stefan problem is the focus of this contribution. A flatness-based feedforward design is combined with a multi-step backstepping approach to obtain a controller that tracks a reference trajectory for the position of the phase boundary. Specifically, based on some preliminary transformations to map the model into a time-variant PDE-ODE system, consecutive transformations are shown to yield a stable closed loop. The tracking controller is validated in a simulation that considers the actual growth of a Gallium arsenide single crystal.
This work introduces a novel optimal control framework for vibration control of flexible structures, taking into account the spatially distributed nature of the disturbance and structural response. The control framewo...
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This work introduces a novel optimal control framework for vibration control of flexible structures, taking into account the spatially distributed nature of the disturbance and structural response. The control framework is developed by introducing the concept of spatial H 2 norm for systems with spatially distributed input. This approach allows the systematic design of controllers that can perforin optimally in the situation where the disturbance occurs at varying locations over a structure. Simulation studies on a piezoelectric laminate beam are performed by designing spatial H 2 controllers for minimizing structural vibration due to a spatially varying bending moment. The simulation results show that the proposed spatial H 2 controllers can effectively reduce vibration when the bending moment disturbance is applied at various locations over the beam.
The backstepping design of stabilizing state feedback controllers is addressed for bidirectionally coupled ODE-PDE-ODE systems, that naturally arise for infinite-dimensional systems where actuator or sensor dynamics a...
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The backstepping design of stabilizing state feedback controllers is addressed for bidirectionally coupled ODE-PDE-ODE systems, that naturally arise for infinite-dimensional systems where actuator or sensor dynamics are taken into account. A common framework for both linear parabolic and hyperbolic partial differential equations with spatially varying coefficients is presented, that solely relies on the strict feedback form of these systems. Without imposing any limitation on the dimension of the ODEs and PDEs involved, a multi-step design algorithm is suggested, that makes use of classical concepts (such as integrator backstepping and output zeroing) known for the control of ODE systems. By that, backstepping is brought back to its ODE origins and a systematic design of backstepping controllers for ODE-PDE-ODE systems is offered, with a unified treatise for parabolic and hyperbolic PDEs.
An approach to modeling and optimization of controlled dynamical systems with distributed elastic and inertial parameters is considered. The general method of integrodifferential relations (IDR) for solving a wide cla...
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Consider a linear system Ż ( t ) = AZ ( t ), t > 0 in a ililbert space H . When if is finite-dimensional, every state trajetory of the system has a unique backward-time continuation and the set of all finite linear...
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Consider a linear system Ż ( t ) = AZ ( t ), t > 0 in a ililbert space H . When if is finite-dimensional, every state trajetory of the system has a unique backward-time continuation and the set of all finite linear combinations of the generalized eigenvectors of A is dense in H . For infinite-dimensional system, however, both time reversibility and spectral completeness can be absent. This paper reveals the two properties in several elastic systems with boundary damping by the observability method (Liu and Russell, 1998).
In this manuscript, a comparison between the parabolic and hyperbolic partial differential equations for heat diffusion is studied. First, numerical results and an eigenvalue analysis for these two types of equations ...
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In this manuscript, a comparison between the parabolic and hyperbolic partial differential equations for heat diffusion is studied. First, numerical results and an eigenvalue analysis for these two types of equations are shown, which help to understand the difference in the system dynamics. Then, both equations are also considered in a Stefan problem for the melting of an ice block in a one-dimensional setting. The results show that the hyperbolic partial differential equation shows a finite speed of propagation of heat and can represent the system as properly as the parabolic equation.
The paper deals with using optimal control methods for solving inverse problems of mathematical physics. In many cases this problem can be considered as an optimal control problem in which unknown control functions ar...
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The paper deals with using optimal control methods for solving inverse problems of mathematical physics. In many cases this problem can be considered as an optimal control problem in which unknown control functions are smooth elementsof initial or boundary conditions, coefficients of differential operators or right-hand sides of differential equations. A non-classic optimality condition and numerical algorithm for smooth boundary controls in semi-linear first-order hyperbolic systems are presented. The special feature of the general optimization problem for boundary conditions is non-validity of the classic optimality condition of Pontryagin's type. The suggested approach is based on special variations of admissible continuously differentiable controls. These variations can be applied for controls satisfying either restrictions of inclusion type or integral restrictions.
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