Oscillations-Induced Transitions and Their Application in Control of Dynamical Systems

1990 ◽  
Vol 112 (3) ◽  
pp. 313-319 ◽  
Author(s):  
J. Bentsman
Keyword(s):  
Dynamical Systems ◽  
Parabolic Equations ◽  
Closed Loop ◽  
Distributed Parameter ◽  
Control Laws ◽  
Loop Control ◽  
Finite Dimensional ◽  
Analytical Tools ◽  
Semilinear Parabolic ◽  
Qualitative Changes

Studies of the use of oscillations for control purposes continue to reveal new practically important properties unique to the oscillatory open and closed loop control laws. The goal of this paper is to enlarge the available set of analytical tools for such studies by introducing a method of analysis of the qualitative changes in the behavior of dynamical systems caused by the zero mean parametric excitations. After summarizing and slightly refining a technique developed previously for the finite dimensional nonlinear systems, we consider an extension of this technique to a class of distributed parameter systems (DPS) governed by semilinear parabolic equations. The technique presented is illustrated by several examples.

scholarly journals Accurate Motion Control of a Pneumatic Linear Peristaltic Actuator

Actuators ◽  
2020 ◽  
Vol 9 (3) ◽  
pp. 63 ◽  
Author(s):  
João Falcão Carneiro ◽  
João Bravo Pinto ◽  
Fernando Gomes de Almeida
Keyword(s):  
Closed Loop ◽  
Low Cost ◽  
Dynamic Performance ◽  
Control Law ◽  
Control Loop ◽  
Control Laws ◽  
Loop Control ◽  
Error Band ◽  
Short Service Life ◽  
High Mechanical Stress

Pneumatic linear peristaltic actuators can offer some potential advantages when compared with conventional ones. The low cost, virtually unlimited stroke and easy implementation of curved motion profiles are among those benefits. On the downside, these actuators suffer high mechanical stress that can lead to short service life and increased leakage among chambers during the actuator lifetime. One way to cope with this problem is to impose the force—instead of the displacement—between rollers, as this has been shown to improve the endurance of the hose while reducing leakage during the actuator lifetime. This paper presents closed control loop results using such a setup. Previous studies with linear peristaltic actuators have revealed that, although it is possible to reach zero steady state error to constant references with closed loop control, the dynamic response obtained is very slow. This paper is mainly focused on this topic, namely on the development of several control laws to improve the dynamic performance of the system while avoiding limit cycles. The new developed control law leads to an average time of 1.67 s to reach a 0.1 mm error band in an experiment consisting of a series of 16 steps ranging from 0.02 to 0.32 m in amplitude.

scholarly journals Formulation and Simulations of the Conserving Algorithm for Feedback Stabilization on Rigid Body Rotations

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Yong-Ren Pu ◽  
Thomas A. Posbergh
Keyword(s):  
Rigid Body ◽  
Closed Loop ◽  
Numerical Algorithms ◽  
Open Loop ◽  
Rigid Bodies ◽  
Feedback Stabilization ◽  
Conserved Quantities ◽  
Control Laws ◽  
Loop Control ◽  
Closed Loop Systems

The problem of stabilization of rigid bodies has received a great deal of attention for many years. People have developed a variety of feedback control laws to meet their design requirements and have formulated various but mostly open loop numerical algorithms for the dynamics of the corresponding closed loop systems. Since the conserved quantities such as energy, momentum, and symmetry play an important role in the dynamics, we investigate the conserved quantities for the closed loop control systems which formally or asymptotically stabilize rigid body rotation and modify the open loop numerical algorithms so that they preserve these important properties. Using several examples, the authors first use the open loop algorithm to simulate the tumbling rigid body actions and then use the resulting closed loop one to stabilize them.

Shaped Time-Optimal Feedback Controllers for Flexible Structures

2004 ◽  
Vol 126 (1) ◽  
pp. 173-186 ◽  
Author(s):  
Lucy Y. Pao ◽  
Chanat La-orpacharapan
Keyword(s):  
Phase Plane ◽  
Closed Loop ◽  
Flexible Structures ◽  
Input Shaping ◽  
Feedback Controllers ◽  
Control Laws ◽  
Loop Control ◽  
Flexible Mode ◽  
Time Optimal ◽  
Acceleration And Deceleration

This paper describes the design of closed-loop control laws for servomechanisms with one dominant flexible mode. An input shaping technique is employed to alter the rigid body phase-plane trajectory that is used in time-optimal servomechanisms. The resulting controllers lead to near time-optimal performance without unwanted residual vibrations. After the basic technique is outlined for a system with one undamped flexible mode, extensions are given considering different acceleration and deceleration capabilities, damping, and slew rate limits.

CONTROLLING IDEAL TURBULENCE IN TIME-DELAYED CHUA'S CIRCUIT: STABILIZATION AND SYNCHRONIZATION

2010 ◽  
Vol 20 (05) ◽  
pp. 1351-1363 ◽  
Author(s):  
MASAYASU SUZUKI ◽  
NOBORU SAKAMOTO
Keyword(s):  
Wave Equations ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Conditions ◽  
Distributed Parameter ◽  
Distributed Parameter System ◽  
Parameter System ◽  
Equilibrium Solutions ◽  
Control Laws ◽  
Finite Dimensional ◽  
Steady Solutions

We try to stabilize steady solutions of a physical model described by wave equations with nonlinear boundary conditions. This system is a distributed parameter system in which ideal turbulence, introduced by Sharkovsky et al., occurs. Although the behavior of the system is quite intricate both in time and space, by using d'Alembert's solution, the analysis of the dynamic characteristics can be reduced to that of a finite-dimensional difference equation. In this report, based on this analytical method using d'Alembert's solution, we design control laws to stabilize steady solutions (equilibrium solutions and periodic solutions) and synchronize a pair of identical systems.

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