Stabilization of a solid propellant rocket instability by state feedback

Bošković, Dejan M.; Krstić, Miroslav

doi:10.1002/rnc.732

Cited by 58 publications

(18 citation statements)

References 10 publications

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“…Because the transformation is invertible for an arbitrary grid choice, it can be concluded that the discretized version of the original system is asymptotically stable and we obtain a nonlinear feedback boundary control law for the density in the original set of coordinates. This technique, which avoids linearization of the model, has already been successfully applied to other physical applications in [8], [9], [10]. Numerical simulations of the resulting control laws show that the response time of density profiles is greatly improved with just one step of backstepping, or, in other words, with a single sensor measurement of the densities from within the plasma.…”

Section: Introductionmentioning

confidence: 90%

Simultaneous control of effective atomic number and electron density in non-burning tokamak plasmas

Boyer

Schuster

2010

Proceedings of the 2010 American Control Conference

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The control of plasma density profiles is one of the most fundamental problems in fusion reactors. During reactor operation, the density profiles of hydrogen ions and heavier impurity ions must be precisely regulated, and while the uncontrolled open-loop behavior of these profiles is stable in non-burning plasmas, the system response time may be very slow. In this work, a controller is sought to improve the response of ion density profiles in a non-burning plasma and to track reference profiles for the electron density and effective atomic number, a set of coupled variables that are directly dependent on the hydrogen and impurity ion density profiles. A one-dimensional approximation of the transport equation for ion densities is represented in cylindrical coordinates by a partial differential equation (PDE). To control the density profiles, the PDE is discretized in space using a finite difference method and a backstepping design is applied to obtain a discrete transformation from the original system into an asymptotically stable target system. Numerical simulations of the resulting control law show that density profiles can be successfully controlled with just one step of backstepping. Tracking of electron density and effective atomic number profiles is then simulated by first transforming the profiles into corresponding ion density profiles for use by the backstepping controller. Simulations show the successful tracking of reference profiles.

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Section: Introductionmentioning

confidence: 90%

Simultaneous control of effective atomic number and electron density in non-burning tokamak plasmas

Boyer

Schuster

2010

Proceedings of the 2010 American Control Conference

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“…This equation is partly motivated by the model of unstable burning in solid propellant rockets [2]. But the most important reason to consider this plant is that it often appears as a part of the control design for more complicated systems (see Sections VIII and IX).…”

Section: B Other Spatially Causal Plantsmentioning

confidence: 99%

Infinite-dimensional backstepping and applications to flows in electromagnetic fields

Krstić

Smyshlyaev

Vázquez

2008

2008 16th Mediterranean Conference on Control and Automation

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Numerous physical processes are modeled by partial differential equations and are often instrumented with boundary actuators and sensors. A major new effort has been underway in recent years to develop constructive designs of boundary control laws for unstable PDE systems. This development draws upon the ideas of "backstepping" synthesis for nonlinear ODEs from the 1990s and is an infinite-dimensional, continuum extension of backstepping. Initial efforts on infinitedimensional backstepping focused on linear PDEs and produced a set of methodologies, for all of the major classes of PDEs, that results in elegant formulae for the gain functions of the feedback laws, which do not require the solution of operator Riccati equations. The most recent efforts pushed even further, into developing an adaptive control approach for PDEs, with unknown functional parameters and output feedback, and into developing feedback linearizing control designs for nonlinear PDEs. The most significant application-driven results in this expanding area of research have so far been for turbulent and magnetohydrodynamic flows, such as those that arise in aerodynamics applications, and in plasma and liquid metal flow problems in tokamak fusion reactors. This talk will present highlights of various methods and applications of infinitedimensional backstepping.

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“…Using the above backstepping approach, the problem of finding the coordinate transformation (5) and the corresponding stabilizing boundary control (3) requires two steps.…”

Section: Open Problemmentioning

confidence: 99%

“…Superlinear nonlinearities can imply finite time blow-up for the uncontrolled case [6,7,9,10]. However, numerical results in a series of papers by Boskovic and Krstic [3,4,5] show promise for the applicability of the infinite dimensional backstepping to nonlinear problems, at least for finite-grid discretizations. In this note, we present the open problem of convergence of nonlinear backstepping schemes as the discretization grid becomes infinitely refined.…”

Section: Introductionmentioning

confidence: 97%