Search results for "Integrator"

A Fractional-Order Control Approach to Ramp Tracking with Memory-Efficient Implementation

2020

We investigate the fractional-order (FO) control of arbitrary order LTI systems. We show that, for ramp tracking or input disturbance rejection, it is advantageous to include an FO integrator to the open-loop if we have to increase the order of integration further than one. With the lower phase-loss of the FO integrator it is easier to guarantee a desired phase margin. Furthermore the flat phase response around the crossover-frequency (iso-damping property) can be achieved for a wider frequency range such that the closed-loop is more robust wrt. amplitude and phase margins. The drawback of the FO approach is the increased implementation effort and the algebraic decay, which slows down the t…

Boosting Signal-to-Noise in Complex Biology: Prior Knowledge Is Power

2011

A major difficulty in the analysis of complex biological systems is dealing with the low signal-to-noise inherent to nearly all large biological datasets. We discuss powerful bioinformatic concepts for boosting signal-to-noise through external knowledge incorporated in processing units we call filters and integrators. These concepts are illustrated in four landmark studies that have provided model implementations of filters, integrators, or both.

On stability issues for IMEX schemes applied to 1D scalar hyperbolic equations with stiff reaction terms

2011

The application of a Method of Lines to a hyperbolic PDE with source terms gives rise to a system of ODEs containing terms that may have very different stiffness properties. In this case, Implicit-Explicit Runge-Kutta (IMEX-RK) schemes are particularly useful as high order time integrators because they allow an explicit handling of the convective terms, which can be discretized using the highly developed shock capturing technology, together with an implicit treatment of the source terms, necessary for stability reasons. Motivated by the structure of the source term in a model problem introduced by LeVeque and Yee in [J. Comput. Phys. 86 (1990)], in this paper we study the preservation of ce…

Multiplicity results for a class of asymmetric weakly coupled systems of second order ordinary differential equations

2005

We prove the existence and multiplicity of solutions to a two-point boundary value problem associated to a weakly coupled system of asymmetric second-order equations. Applying a classical change of variables, we transform the initial problem into an equivalent problem whose solutions can be characterized by their nodal properties. The proof is developed in the framework of the shooting methods and it is based on some estimates on the rotation numbers associated to each component of the solutions to the equivalent system.

Time-Optimal Synthesis for Three Relevant Problems: The Brockett Integrator, the Grushin Plane and the Martinet Distribution

2015

We construct the time-optimal synthesis for 3 problems that are linear in the control and with polytopic constraints in the controls. Namely, the Brockett integrator, the Grushin plane, and the Martinet distribution. The main purpose is to illustrate the steps in solving an optimal control problem and in particular the use of second order conditions. The Grushin and the Martinet case are particularly important: the first is the prototype of a rank-varying distribution, the second of a non-equiregular structure.

Performances Comparison for a Rotating Shaft Suspended by 4-Axis Radial Active Magnetic Bearings via 𝜇 -Synthesis, Loop-Shaping Design, and Sub ( 𝐻…

2011

The control systems applied on active magnetic bearing are several. A perfect levitation is characterized by maintaining the operating point condition that is characterized by the center of stator coincident with the geometric center of shaft. The first controller implemented for this purpose is PID controller that is characterized by an algorithm that leads the amplifier to produce control current until the operating point condition is not reached, this is obtained by an integration operator. The effect of an integrator is essential but not necessary for a centered levitation for example in the robust control characterized by a dynamic model depended on plant of system so that it depends o…

A fully adaptive wavelet algorithm for parabolic partial differential equations

2001

We present a fully adaptive numerical scheme for the resolution of parabolic equations. It is based on wavelet approximations of functions and operators. Following the numerical analysis in the case of linear equations, we derive a numerical algorithm essentially based on convolution operators that can be efficiently implemented as soon as a natural condition on the space of approximation is satisfied. The algorithm is extended to semi-linear equations with time dependent (adapted) spaces of approximation. Numerical experiments deal with the heat equation as well as the Burgers equation.

Indagine sulla supplementazione proteica e sul comportamento alimentare in ambito fitness

2014

Explicit polynomial solutions of fourth order linear elliptic Partial Differential Equations for boundary based smooth surface generation

2011

We present an explicit polynomial solution method for surface generation. In this case the surface in question is characterized by some boundary configuration whereby the resulting surface conforms to a fourth order linear elliptic Partial Differential Equation, the Euler–Lagrange equation of a quadratic functional defined by a norm. In particular, the paper deals with surfaces generated as explicit Bézier polynomial solutions for the chosen Partial Differential Equation. To present the explicit solution methodologies adopted here we divide the Partial Differential Equations into two groups namely the orthogonal and the non-orthogonal cases. In order to demonstrate our methodology we discus…

Iterative Reconstruction of Memory Kernels.

2017

In recent years, it has become increasingly popular to construct coarse-grained models with non-Markovian dynamics to account for an incomplete separation of time scales. One challenge of a systematic coarse-graining procedure is the extraction of the dynamical properties, namely, the memory kernel, from equilibrium all-atom simulations. In this article, we propose an iterative method for memory reconstruction from dynamical correlation functions. Compared to previously proposed noniterative techniques, it ensures by construction that the target correlation functions of the original fine-grained systems are reproduced accurately by the coarse-grained system, regardless of time step and disc…