Application of a novel linearization method to compare the on–off control strategies modeled by piecewise linear systems

2020 ◽  
Vol 26 (23-24) ◽  
pp. 2125-2135
Author(s):  
Tudor Sireteanu ◽  
Ovidiu Solomon ◽  
Ana-Maria Mitu ◽  
Marius Giuclea
Keyword(s):  
Linear Systems ◽  
Root Mean Square ◽  
Hybrid Control ◽  
Control Strategies ◽  
Piecewise Linear ◽  
Practical Interest ◽  
Dynamic Contact ◽  
Linearization Method ◽  
Mean Square ◽  
Piecewise Linear Systems

In this study, a novel approach for linearization of piecewise linear systems is applied to approximate the root mean square output of a quarter car model with semiactive control. The on–off control strategies, balance logic, skyhook, groundhook, and hybrid are modeled by piecewise linear systems with variable friction. By the proposed method, one can attach, for each output of practical interest, a linear system with the same transmissibility factor. The obtained transmissibility factors are used to approximate the root mean square output of considered semiactive systems using the power spectral density input–output relationships for constant parameter linear systems with stationary random inputs. The method is applied for optimization of hybrid control strategy with respect to a performance index defined in terms of sprung mass acceleration, suspension travel, and dynamic contact force.

A Linearization Method of Piecewise Linear Systems Based on Frequency Domain Characteristics With Application to Semi-Active Control of Vibration

2018 ◽  
Vol 140 (6) ◽  
Author(s):  
Tudor Sireteanu ◽  
Ovidiu Solomon ◽  
Ana-Maria Mitu ◽  
Marius Giuclea
Keyword(s):  
Linear Systems ◽  
Active Control ◽  
Base Isolation ◽  
Piecewise Linear ◽  
Time Integration ◽  
Relative Displacement ◽  
Linearization Method ◽  
Solution Vector ◽  
Piecewise Linear Systems ◽  
Linear Differential

In this paper, a new approach is presented for linearization of piecewise linear systems with variable dry friction, proportional with absolute value of relative displacement. The transmissibility factors of considered systems, defined in terms of root-mean-square (RMS) values, are obtained by numerical time integration of motion equations for a set of harmonic inputs with constant amplitude and different frequencies. A first-order linear differential system is attached to the considered piecewise linear system such as the first component of solution vector of attached system to have the same transmissibility factor as the chosen output of nonlinear system. This method is applied for the semi-active control of vibration with balance logic strategy. Applications to base isolation of rotating machines and vehicle suspensions illustrate the effectiveness of the proposed linearization method.

scholarly journals Limit cycles from a monodromic infinity in planar piecewise linear systems

2021 ◽  
Vol 496 (2) ◽  
pp. 124818
Author(s):  
Emilio Freire ◽  
Enrique Ponce ◽  
Joan Torregrosa ◽  
Francisco Torres
Keyword(s):  
Linear Systems ◽  
Limit Cycles ◽  
Piecewise Linear ◽  
Piecewise Linear Systems

Nondegenerate Piecewise Linear Systems: A Finite Newton Algorithm and Applications in Machine Learning

2012 ◽  
Vol 24 (4) ◽  
pp. 1047-1084 ◽  
Author(s):  
Xiao-Tong Yuan ◽  
Shuicheng Yan
Keyword(s):  
Linear Systems ◽  
Optimization Problems ◽  
Piecewise Linear ◽  
Optimization Methods ◽  
Coefficient Matrix ◽  
Learning Problems ◽  
Support Vector ◽  
Data Sets ◽  
Piecewise Linear Systems ◽  
Vector Machines

We investigate Newton-type optimization methods for solving piecewise linear systems (PLSs) with nondegenerate coefficient matrix. Such systems arise, for example, from the numerical solution of linear complementarity problem, which is useful to model several learning and optimization problems. In this letter, we propose an effective damped Newton method, PLS-DN, to find the exact (up to machine precision) solution of nondegenerate PLSs. PLS-DN exhibits provable semiiterative property, that is, the algorithm converges globally to the exact solution in a finite number of iterations. The rate of convergence is shown to be at least linear before termination. We emphasize the applications of our method in modeling, from a novel perspective of PLSs, some statistical learning problems such as box-constrained least squares, elitist Lasso (Kowalski & Torreesani, 2008 ), and support vector machines (Cortes & Vapnik, 1995 ). Numerical results on synthetic and benchmark data sets are presented to demonstrate the effectiveness and efficiency of PLS-DN on these problems.

scholarly journals Canards in piecewise-linear systems: explosions and super-explosions

2013 ◽  
Vol 469 (2154) ◽  
pp. 20120603 ◽  
Author(s):  
Mathieu Desroches ◽  
Emilio Freire ◽  
S. John Hogan ◽  
Enrique Ponce ◽  
Phanikrishna Thota
Keyword(s):  
Phase Space ◽  
Linear Systems ◽  
Limit Cycles ◽  
Piecewise Linear ◽  
Single Parameter ◽  
Van Der Pol ◽  
Piecewise Linear Systems ◽  
Homoclinic Connections ◽  
Limiting Case

We show that a planar slow–fast piecewise-linear (PWL) system with three zones admits limit cycles that share a lot of similarity with van der Pol canards, in particular an explosive growth. Using phase-space compactification, we show that these quasi-canard cycles are strongly related to a bifurcation at infinity. Furthermore, we investigate a limiting case in which we show the existence of a continuum of canard homoclinic connections that coexist for a single-parameter value and with amplitude ranging from an order of ε to an order of 1, a phenomenon truly associated with the non-smooth character of this system and which we call super-explosion .

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