scholarly journals A Single Differential Equation for First-Excursion Time in a Class of Linear Systems

2011 ◽  
Vol 133 (6) ◽  
Author(s):  
Matthew B. Greytak ◽  
Franz S. Hover
Keyword(s):  
Structural Dynamics ◽  
Closed Loop ◽  
Damping Ratio ◽  
Robotic Systems ◽  
Time Varying ◽  
Stochastic Environments ◽  
Closed Loop Systems ◽  
Time Varying Systems ◽  
Major Application ◽  
Excursion Time

First-excursion times have been developed extensively in the literature for oscillators; one major application is structural dynamics of buildings. Using the fact that most closed-loop systems operate with a moderate to high damping ratio, we have derived a new procedure for calculating first-excursion times for a class of linear continuous, time-varying systems. In several examples, we show that the algorithm is both accurate and time-efficient. These are important attributes for real-time path planning in stochastic environments, and hence the work should be useful for autonomous robotic systems involving marine and air vehicles.

The Swing Control of Cranes with Variable Rope Length Based on Linear Time Varying System Theory

2012 ◽  
Vol 461 ◽  
pp. 763-767
Author(s):  
Li Fu Wang ◽  
Zhi Kong ◽  
Xin Gang Wang ◽  
Zhao Xia Wu
Keyword(s):  
State Feedback ◽  
Closed Loop ◽  
Linear Time ◽  
Feedback Stabilization ◽  
Time Varying ◽  
Closed Loop System ◽  
Overhead Cranes ◽  
Time Varying Systems ◽  
Time Invariant ◽  
Time Invariant System

In this paper, following the state-feedback stabilization for time-varying systems proposed by Wolovich, a controller is designed for the overhead cranes with a linearized parameter-varying model. The resulting closed-loop system is equivalent, via a Lyapunov transformation, to a stable time-invariant system of assigned eigenvalues. The simulation results show the validity of this method.

Observer and Controller Design Using Time-Varying Gains: Duality and Distinctions

2004 ◽  
Vol 127 (2) ◽  
pp. 267-274
Author(s):  
Vladimir Polotski
Keyword(s):  
State Feedback ◽  
Closed Loop ◽  
Dual Problem ◽  
Controller Design ◽  
Time Varying ◽  
Feedback Controllers ◽  
Observer Error ◽  
Time Varying Systems ◽  
Error Dynamics ◽  
Time Invariant

Stabilization of linear systems by state feedback is an important problem of the controller design. The design of observers with appropriate error dynamics is a dual problem. This duality leads, at first glance, to the equivalence of the responses in the synthesized systems. This is true for the time-invariant case, but may not hold for time-varying systems. We limit ourselves in this work by the situation when the system itself is time invariant, and only the gains are time varying. The possibility of assigning a rapidly decaying response without peaking is analyzed. The solution of this problem for observers using time-varying gains is presented. Then we show that this result cannot be obtained for state feedback controllers. We also analyze the conditions under which the observer error dynamics and the response of the closed loop time-varying controllers are equivalent. Finally we compare our results to recently proposed observer converging in finite time and Riccati-based continuous observer with limited overshoots.

scholarly journals Damping Effects Induced by a Mass Moving along a Pendulum

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
E. Gandino ◽  
S. Marchesiello ◽  
A. Bellino ◽  
A. Fasana ◽  
L. Garibaldi
Keyword(s):  
Linear Time ◽  
Damping Ratio ◽  
System Response ◽  
Time Varying ◽  
Simple Method ◽  
Equivalent Damping ◽  
Stochastic Subspace Identification ◽  
Time Varying Systems ◽  
Instantaneous Frequencies ◽  
Short Time

The experimental study of damping in a time-varying inertia pendulum is presented. The system consists of a disk travelling along an oscillating pendulum: large swinging angles are reached, so that its equation of motion is not only time-varying but also nonlinear. Signals are acquired from a rotary sensor, but some remarks are also proposed as regards signals measured by piezoelectric or capacitive accelerometers. Time-varying inertia due to the relative motion of the mass is associated with the Coriolis-type effects appearing in the system, which can reduce and also amplify the oscillations. The analytical model of the pendulum is introduced and an equivalent damping ratio is estimated by applying energy considerations. An accurate model is obtained by updating the viscous damping coefficient in accordance with the experimental data. The system is analysed through the application of a subspace-based technique devoted to the identification of linear time-varying systems: the so-called short-time stochastic subspace identification (ST-SSI). This is a very simple method recently adopted for estimating the instantaneous frequencies of a system. In this paper, the ST-SSI method is demonstrated to be capable of accurately estimating damping ratios, even in the challenging cases when damping may turn to negative due to the Coriolis-type effects, thus causing amplifications of the system response.

Time-Varying Modal Analysis by SDOF Wavelets

2000 ◽  
Author(s):  
Arata Masuda ◽  
Akira Sone
Keyword(s):  
Matching Pursuit ◽  
Damping Ratio ◽  
Identification Problem ◽  
Mode Shapes ◽  
Time Varying ◽  
Identification Method ◽  
Time Varying Systems ◽  
Single Input ◽  
Expansion Coefficients ◽  
The Time Domain

Abstract The purpose of this paper is to provide a modal expression of a time-varying MDOF system and to develop an identification method for it. The single-input-multi-output relation of a time-varying N-DOF system is expressed as a superposition of N time-varying SDOF subsystems in the time domain, where the expansion coefficients represent the time-varying mode-shapes, and the natural frequency and the damping ratio of each subsystem represent the time-varying modal parameters of each mode. Then we define the SDOF wavelets, which correspond to the time-varying impulse responses of SDOF subsystems and show that the output of the entire system can be expressed by a superposition of SDOF wavelets. Then, the identification problem is reduced to an atomic decomposition problem of choosing the nearly best set of SDOF wavelets and determining the expansion coefficients. We develop a modified matching pursuit algorithm, called modal pursuit, to solve the problem. Basic examples are numerically examined to show that the proposed modal representation and the identification method are applicable to track the modal characteristics of time-varying systems.

Stabilization of linear time-varying systems using proportional-derivative state feedback

2017 ◽  
Vol 40 (7) ◽  
pp. 2100-2115 ◽  
Author(s):  
Taha HS Abdelaziz
Keyword(s):  
Degrees Of Freedom ◽  
State Feedback ◽  
Linear Time ◽  
State Feedback Control ◽  
Time Varying ◽  
Closed Loop Systems ◽  
Continuous Time Systems ◽  
Time Varying Systems ◽  
Small Gain ◽  
Time Systems

This paper presents the stabilization approach for linear time-varying continuous-time systems using proportional-derivative (PD) state feedback control. The solvability conditions for the problem are considered. The general analytical expressions for the PD controller gains are derived, which describe the available degrees of freedom offered by PD state feedback. The non-uniqueness of the controller gains is utilized to obtain closed-loop systems with small gain elements. Two numerical examples are introduced to demonstrate the effectiveness of the proposed approach.

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