Control of the current profile in tokamak plasmas has been shown to play an important role in achieving advanced scenarios that could enable steady-state operation. The nonlinearity and spatially distributed nature of...
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Control of the current profile in tokamak plasmas has been shown to play an important role in achieving advanced scenarios that could enable steady-state operation. The nonlinearity and spatially distributed nature of the current profile dynamics motivate the use of model-based control designs. In this work, we consider a control-oriented model of the current profile evolution in DIII-D high-confinement (H-mode) discharges, and the problem of regulating the current profile around a desired trajectory. The PDE model is discretized in space with a finite difference method and a backstepping design is applied to obtain a transformation from the original system into a particular target system with desirable properties. The resulting boundary condition control law is complemented with control laws for the available distributed actuators. The combined control strategy uses nonlinear combinations of the total plasma current, total power, and line averaged density as actuators. Simulation and experimental results show the ability of the controller to track desired targets and to reject input disturbances.
Abstract In the present paper we study local input-to-state stability of reaction-diffusion control systems by viewing them as control systems, based on differential equations in abstract spaces. We develop Lyapunov m...
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Abstract In the present paper we study local input-to-state stability of reaction-diffusion control systems by viewing them as control systems, based on differential equations in abstract spaces. We develop Lyapunov methods for verification of local input-to-state stability property and prove linearisation principle, that allows studying of local input-to-state stability of nonlinear systems from the stability properties of linearised systems. We illustrate theory on two examples of linear and nonlinear reaction-diffusion equations.
The purpose of this paper is to show that a distributed-parameter model of a continuous ball mill can be developed by discretizing the particle size continuum into a few size intervals only. Despite this coarse discre...
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The purpose of this paper is to show that a distributed-parameter model of a continuous ball mill can be developed by discretizing the particle size continuum into a few size intervals only. Despite this coarse discretization of the particle size distribution, the ball mill model provides a good representation of the real process, which can be combined with a classifier model to build a complete simulator of a closed-loop grinding circuit. This simplified process representation is compared with a detailed first-principle model previously developed and validated by the authors. The main advantage of the simplified model is that it can be easily incorporated in an on-line control scheme. For illustrative purposes, a NMPC scheme is implemented to regulate the product fineness when variations in the grindability of the raw material occur as a measurable disturbance. The control objective, based on a size interval content, is compatible with traditional fineness measurements.
Concurrent engineering requires designers to share information that can be incomplete or contradictory. Information integrity is even more important when this dynamic network crosses company borders to include custome...
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Concurrent engineering requires designers to share information that can be incomplete or contradictory. Information integrity is even more important when this dynamic network crosses company borders to include customers and suppliers. This paper introduces a new modelling view based upon a parameter approach to maintain data validity and to support network dynamics. We then develop a four part implementation of this approach to co-ordination: a parameter checklist to provide engineering transparency, a parameter checklist with integrated processes for simultaneous engineering workflow, a logged parameter network for engineering change support, and a pre-defined parameter network for engineering organisation. The paper describes these four parts.
This paper, the first of a series of two, deals with the determination of optimal steady-state jacket fluid temperature profiles for dispersive tubular chemical reactors, ranging from plug flow to perfectly mixed reac...
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This paper, the first of a series of two, deals with the determination of optimal steady-state jacket fluid temperature profiles for dispersive tubular chemical reactors, ranging from plug flow to perfectly mixed reactors. According to Pontryagin's minimum principle, the optimal control is of the bang-bang type for the proposed terminal cost criterion. The bang-bang switching position is numerically optimised, by means of a weighted shooting-type procedure for the determination of the reactor profiles, ensuring the Danckwerts boundary conditions are satisfied. Following this procedure the impact of dispersion on the optimised profiles is illustrated. In the second paper, the performance of the obtained optimal control laws will be compared with that of practically more feasible controls. Furthermore, the transient behaviour will be assessed.
Approximate controllability of systems of coupled parabolic partial differential equations has been of interest for a few decades, where the existence of open-loop control laws performing approximate state transitions...
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Approximate controllability of systems of coupled parabolic partial differential equations has been of interest for a few decades, where the existence of open-loop control laws performing approximate state transitions within a finite time is studied. In this work, we specialize to systems of reaction-diffusion equations where the connectivity structure is triangular in the reaction parameters and the controls appear at the boundary. We first generate controllers by combining a decoupling backstepping approach with differential flatness that allow us to generate admissible trajectories for system outputs from a given initial condition. As a byproduct of our approach, we achieve approximate state transitioning for the system within a finite terminal time. We enhance our control law by introducing time-varying error feedback controllers which reject variations in initial conditions within the terminal time. The resulting control law not only performs the approximate control task but also output trajectory tracking, all within the terminal time which can be prescribed independently of initial conditions.
In this paper, we present our recent results which may play a role in improving the situation in the practical implications of mathematical modeling of cancer chemotherapy. We are concerned with control problems for a...
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In this paper, we present our recent results which may play a role in improving the situation in the practical implications of mathematical modeling of cancer chemotherapy. We are concerned with control problems for a model of the dynamics of emergence of resistance of cancer cells to chemotherapy, as understood based on recent progress in molecular biology. In some special cases of this model, their asymptotic behavior and the stability problem for the infinite dimensional case were studied. In the case of finite initial condition the stability conditions were derived by asymptotical analysis of the analytical solution to the system of equations. In the case of initial condition with infinite number of elements the stability verification was based on the spectral properties of the infinitesimal generator of the system.
This paper discusses the boundary stabilization of a beam in free transversal vibration. We consider a nonlinear partial differential equation (PDE) and based on this model construct two linear control laws to stabili...
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This paper discusses the boundary stabilization of a beam in free transversal vibration. We consider a nonlinear partial differential equation (PDE) and based on this model construct two linear control laws to stabilize the system. The first control law guarantees globally convergent of states, while the second control law results into an exponentially stable closed loop. The latter control law is formed by feedbacking slope and velocity of beam’s boundary displacement. Numerical simulations are performed to test each of the control laws. The outcome of simulations are compared and discussed. The novelty of this article is that globally convergece and exponentially stabilization of transversely vibration in a beam is achieved, via boundary control without resorting to truncation of model.
In this paper, the use of computer VlSlon in the feedback stabilization of elastic systems arising in large space structures is explored. In particular, a spaceborne antenna with a large flexible reflector surface is ...
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In this paper, the use of computer VlSlon in the feedback stabilization of elastic systems arising in large space structures is explored. In particular, a spaceborne antenna with a large flexible reflector surface is considered. First, suppose that the reflector is coated with a light reflecting material, and is illuminated by a light source. From the intensity data of the reflector image obtained by a computer vision system, the displacement and velocity of the surface are estimated using a suitable reflectance model. Next, the estimation of surface motion with the aid of special markings is considered. From the image of the deformed markings, the displacement and velocity of the surface are constructed. Various methods for obtaining stabilizing feedback controls from the estimated displacement and velocity of the surface are discussed. The paper concludes with some experimental observations and a discussion of the application of computer vision feedback in controlling other types of distributedsystems
Two approaches to solving the suboptimal Nehari problem are analyzed: the Grassmannian approach and a J -spectral factorization approach. Moreover, using the Grassmannian approach, a solution for the Hankel norm appro...
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Two approaches to solving the suboptimal Nehari problem are analyzed: the Grassmannian approach and a J -spectral factorization approach. Moreover, using the Grassmannian approach, a solution for the Hankel norm approximation problem is presented. The results apply to large classes of infinite-dimensional systems, and in particular to time-delay systems.
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