arXiv subjects

Thomas Berger

Publications and source records attributed to Thomas Berger.

68 records · Page 4Linked to original sources

arXiv2020

Calibrating GONG Magnetograms with End-to-end Instrument Simulation II: Theory of Calibration

This is the second of three papers describing an `absolute' calibration of the GONG magnetograph using an end-to-end simulation of its measurement process. In the first paper, we described the GONG instrument and our `end-to-end' simulation of its measurement process. In this paper, we consider the theory of calibration, and magnetograph comparison in general, identifying some of the significant issues and pitfalls. The calibration of a magnetograph is a function of whether or not it preserves flux, independent of its spatial resolution. However, we find that the one-dimensional comparison methods most often used for magnetograph calibration and comparison will show dramatic differences between two magnetograms with differing spatial resolution, even if they both preserve flux. Some of the apparent disagreement between magnetograms found in the literature are likely a result of these instrumental resolution differences rather than any intrinsic calibration differences. To avoid them, spatial resolution must be carefully matched prior to comparing magnetograms or making calibration curves. In the third paper, we apply the lessons learned here to absolute calibration of GONG using our `end-to-end' measurement simulation.

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arXiv2020

Tracking with prescribed performance for linear non-minimum phase systems

We consider tracking control for uncertain linear systems with known relative degree which are possibly non-minimum phase, i.e., their zero dynamics may have an unstable part. For a given sufficiently smooth reference signal we design a low-complexity controller which achieves that the tracking error evolves within a prescribed performance funnel. We present a novel approach where a new output is constructed, with respect to which the system has a higher relative degree, but the unstable part of the zero dynamics is eliminated. Using recent results in funnel control, we then design a controller with respect to this new output, which also incorporates a new reference signal. We prove that the original output stays within a prescribed performance funnel around the original reference trajectory and all signals in the closed-loop system are bounded. The results are illustrated by some simulations.

math.OC↗

arXiv2020

The Lunar Lander Neutron and Dosimetry (LND) Experiment on Chang'E 4

Chang'E 4 is the first mission to the far side of the Moon and consists of a lander, a rover, and a relay spacecraft. Lander and rover were launched at 18:23 UTC on December 7, 2018 and landed in the von Kármán crater at 02:26 UTC on January 3, 2019. Here we describe the Lunar Lander Neutron \& Dosimetry experiment (LND) which is part of the Chang'E 4 Lander scientific payload. Its chief scientific goal is to obtain first active dosimetric measurements on the surface of the Moon. LND also provides observations of fast neutrons which are a result of the interaction of high-energy particle radiation with the lunar regolith and of their thermalized counterpart, thermal neutrons, which are a sensitive indicator of subsurface water content.

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arXiv2020

Vector relative degree and funnel control for differential-algebraic systems

We consider tracking control for multi-input multi-output differential-algebraic systems. First, the concept of vector relative degree is generalized for linear systems and we arrive at the novel concept of "truncated vector relative degree", and we derive a new normal form. Thereafter, we consider a class of nonlinear functional differential-algebraic systems which comprises linear systems with truncated vector relative degree. For this class we introduce a feedback controller which achieves that, for a given sufficiently smooth reference signal, the tracking error evolves within a prespecified performance funnel. We illustrate our results by an example of a robotic manipulator.

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arXiv2019

Funnel control in the presence of infinite-dimensional internal dynamics

We consider output trajectory tracking for a class of uncertain nonlinear systems whose internal dynamics may be modelled by infinite-dimensional systems which are bounded-input, bounded-output stable. We describe under which conditions these systems belong to an abstract class for which funnel control is known to be feasible. As an illustrative example, we show that for a system whose internal dynamics are modelled by a transport equation, which is not exponentially stable, we obtain prescribed performance of the tracking error.

math.OC↗

arXiv2019

Learning-based Funnel-MPC for output-constrained nonlinear systems

We exploit an adaptive control technique, namely funnel control, in order to establish both initial and recursive feasibility in Model Predictive Control (MPC) for output-constrained nonlinear systems. Moreover, we show that the resulting feedback controller outperforms the funnel controller both w.r.t. the required sampling rate for a zero-order-hold implementation and required control action. We further propose a combination of funnel control and MPC, exploiting the performance guarantees of the model-free funnel controller during a learning phase and the advantages of the model-based MPC scheme thereafter.

math.OC↗

arXiv2019

Fault tolerant funnel control for uncertain linear systems

We study adaptive fault tolerant tracking control for uncertain linear systems. Based on recent results in funnel control and the time-varying Byrnes-Isidori form, we develop a low-complexity model-free controller which achieves prescribed performance of the tracking error for any given sufficiently smooth reference signal. Within the considered system class, we allow for more inputs than outputs as long as a certain redundancy of the actuators is satisfied. An important role in the controller design is played by the controller weight matrix. This is a rectangular input transformation chosen such that in the resulting system the zero dynamics, which are assumed to be uniformly exponentially stable, are independent of the new input. We illustrate the fault tolerant funnel controller by an example of a linearized model for the lateral motion of a Boeing 737 aircraft.

math.OC↗

arXiv2019

Observers for differential-algebraic systems with Lipschitz or monotone nonlinearities

We study state estimation for nonlinear differential-algebraic systems, where the nonlinearity satisfies a Lipschitz condition or a generalized monotonicity condition or a combination of these. The presented observer design unifies earlier approaches and extends the standard Luenberger type observer design. The design parameters of the observer can be obtained from the solution of a linear matrix inequality restricted to a subspace determined by the Wong sequences. Some illustrative examples and a comparative discussion are given.

math.OC↗

arXiv2019

Funnel cruise control

We consider the problem of vehicle following, where a safety distance to the leader vehicle is guaranteed at all times and a favourite velocity is reached as far as possible. We introduce the funnel cruise controller as a novel universal adaptive cruise control mechanism which is model-free and achieves the aforementioned control objectives. The controller consists of a velocity funnel controller, which directly regulates the velocity when the leader vehicle is far away, and a distance funnel controller, which regulates the distance to the leader vehicle when it is close so that the safety distance is never violated. We provide a rigorous proof for the feasibility of the overall controller design. The funnel cruise controller is illustrated by a simulation of three different scenarios which may occur in daily traffic.

math.OC↗

arXiv2018

On a class of non-Hermitian matrices with positive definite Schur complements

Given a positive definite matrix $A\in \mathbb{C}^{n\times n}$ and a Hermitian matrix $D\in \mathbb{C}^{m\times m}$, we characterize under which conditions there exists a strictly contractive matrix $K\in \mathbb{C}^{n\times m}$ such that the non-Hermitian block-matrix \[ \left[ \begin{array}{cc} A & -AK \\ K^*A & D \end{array} \right] \] has a positive definite Schur complement with respect to its submatrix~$A$. Additionally, we show that~$K$ can be chosen such that diagonalizability of the block-matrix is guaranteed and we compute its spectrum. Moreover, we show a connection to the recently developed frame theory for Krein spaces.

math.FA↗

arXiv2017

Quiescent prominence dynamics observed with the Hinode Solar Optical Telescope . II. Prominence Bubble Boundary Layer Characteristics and the Onset of a Coupled Kelvin-Helmholtz Rayleigh-Taylor Instability

We analyze solar quiescent prominence bubble characteristics and instability dynamics using Hinode/Solar Optical Telescope (SOT) data. We measure bubble expansion rate, prominence downflows, and the profile of the boundary layer brightness and thickness as a function of time. The largest bubble analyzed rises into the prominence with a speed of about 1.3 km/s until it is destabilized by a localized shear flow on the boundary. Boundary layer thickness grows gradually as prominence downflows deposit plasma onto the bubble with characteristic speeds of 20 - 35 km/s. Lateral downflows initiate from the thickened boundary layer with characteristic speeds of 25 - 50 km/s, "draining" the layer of plasma. Strong shear flow across one bubble boundary leads to an apparent coupled Kelvin-Helmholtz Rayleigh-Taylor (KH-RT) instability. We measure shear flow speeds above the bubble of 10 km/s and infer interior bubble flow speeds on the order of 100 km/s. Comparing the measured growth rate of the instability to analytic expressions, we infer a magnetic flux density across the bubble boundary of ~10^{-3} T (10 gauss) at an angle of ~70 degrees to the prominence plane. The results are consistent with the hypothesis that prominence bubbles are caused by magnetic flux that emerges below a prominence, setting up the conditions for RT, or combined KH-RT, instability flows that transport flux, helicity, and hot plasma upward into the overlying coronal magnetic flux rope.

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arXiv2012

Simulations of Buoyant Plumes in Solar Prominences

Observations of solar prominences reveal a complex, dynamic flow field within them. The flow field within quiescent prominences is characterized by long ``threads'' and dark ``bubbles'' that fall and rise (respectively) in a thin sheet. The flow field in active prominences display more helical motions that travel along the axis of the prominence. We explore the possible dynamics of both of these with the aid of 2.5D MHD simulations. Our model, compressible plasma possesses density and temperature gradients and resides in magnetic field configurations that mimc those of a solar prominence. We present results of various configurations and discuss the nonlinear behavior of the resulting dynamics.

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arXiv2011

Numerical Simulations of the Magnetic Rayleigh-Taylor Instability in the Kippenhahn-Schlüter Prominence Model

The launch of the Hinode satellite has allowed unprecedented high resolution, stable images of solar quiescent prominences to be taken over extended periods of time. These new images led to the discovery of dark upflows that propagated from the base of prominences developing highly turbulent profiles. As yet, how these flows are driven is not fully understood. To study the physics behind this phenomena we use 3-D magnetohydrodynamic (MHD) simulations to investigate the nonlinear stability of the Kippenhahn-Shlüter prominence model to the magnetic Rayleigh-Taylor instability. The model simulates the rise of a buoyant tube inside a quiescent prominence, where the upper boundary between the tube and prominence model is perturbed to excite the interchange of magnetic field lines. We found upflows of constant velocity (maximum found 6\,km\,s$^{-1}$) and a maximum plume width $\approx 1500$\,km which propagate through a height of approximately 6\,Mm in the no guide field case. The case with the strong guide field (initially $B_y=2B_x$) results in a large plume that rises though the prominence model at $\sim 5$\,km\,s$^{-1}$ with width $\sim 900$\,km (resulting in width of 2400\,km when viewed along the axis of the prominence) reaching a height of $\sim 3.1$\,Mm. In both cases nonlinear processes were important for determining plume dynamics.

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arXiv2009

Service-Mode Observations for Ground-Based Solar Physics

There are significant advantages in combining Hinode observations with ground-based instruments that can observe additional spectral diagnostics at higher data rates and with greater flexibility. However, ground-based observations, because of the random effects of weather and seeing as well as the complexities data analysis due to changing instrumental configurations, have traditionally been less efficient than satellite observations in producing useful datasets. Future large ground-based telescopes will need to find new ways to optimize both their operational efficiency and scientific output. We have begun experimenting with service-mode or queue-mode observations at the Dunn Solar Telescope using the Interferometric Bidimensional Spectrometer (IBIS) as part of joint Hinode campaigns. We describe our experiences and the advantages of such an observing mode for solar physics.

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