Wave-Based Modeling and Control of Flexible Structures

2018 ◽  
Vol 141 (3) ◽  
Author(s):  
Paul F. Curran
Keyword(s):  
Linear Time ◽  
Flexible Structures ◽  
Modeling And Control ◽  
Linear Time Invariant ◽  
Stability Robustness ◽  
Objective Control ◽  
Upper Stage ◽  
The Face ◽  
Linear Time Invariant Systems ◽  
And Control

The relatively new concept of wave-based control is extended to general, finite-dimensional, linear, time-invariant systems, with or without damping. The new models offer an explanation for how systems of springs and masses although lumped, and therefore, technically having no delay appear to have delay nonetheless. The principal contribution is a fairly systematic, multi-input multi-output, multi-objective control design methodology. The method yields controllers which in general deliver good closed-loop tracking, good disturbance rejection, and good stability robustness in the face of parameter uncertainty. In particular, but not exclusively, the method is applicable to the control of flexible structures as demonstrated by several examples including mitigation of sloshing of liquid-fuel in a simplified model of an upper-stage Vega rocket.

Design of a Compliant Based Biomimetic Planar Locomotive Mechanism

2020 ◽  
Author(s):  
Dillon Loupe ◽  
Hanseul Kim ◽  
Ayse Tekes ◽  
Coskun Tekes ◽  
Amir Ali Amiri Moghadam
Keyword(s):  
Nonlinear Dynamics ◽  
Linear Time ◽  
High Mobility ◽  
Performance Bounds ◽  
Design Development ◽  
Modeling And Control ◽  
Linear Time Invariant ◽  
Time Domains ◽  
Linear Time Invariant Systems ◽  
And Control

Abstract This paper presents the design, development, modeling and control of a biomimetic multi degree of freedom compliant locomotive mechanism that can follow a prescribed trajectory. The research objective of this study is the design of a high mobility and flexible planar locomotive mechanism incorporating large deflecting compliant hinges. The actuation is realized using servo motors. Mechanism is consisted of five sliding carts, rail, 3D-printed supplementary pieces to house motors and pins. Carts are connected by monolithically designed two arm links joined by a large deflecting flexure. Four servo motors are mounted on the driven carts. Since sliding carts are identical, forward motion is achieved by changing the friction of carts through the connecting pins. Dynamical model is created in Matlab Simulink using Euler’s laws of motion principle, pseudo rigid body modeling (PRBM), vector closure-loop equations and kinematic constraints. To robustly control the position of the mechanism, first its nonlinear dynamics replaced with a family of linear time invariant systems which have parameter uncertainty. Then a robust controller is designed based on the Quantitative Feedback Theory (QFT) for the desired robust tracking and stability bounds. QFT is one of the most powerful robust control techniques which can take into account both phase and magnitude information of the system and enables the designer to minimize the cost of feedback by clearly observing the design constraints through robust performance bounds. Finally, the performance of the designed controller is validated though nonlinear simulations using the nonlinear dynamics of the mechanism. It has been shown that the mechanism can consistently track the desired inputs both in frequency and time domains.

Some Issues of Structure and Control for Linear Time-Invariant Systems

2004 ◽  
Vol 37 (21) ◽  
pp. 7-18
Author(s):  
Michel Malabre
Keyword(s):  
Linear Time ◽  
Linear Time Invariant ◽  
Linear Time Invariant Systems ◽  
And Control ◽  
Time Invariant

Stability Analysis of LTI Systems With Three Independent Delays—A Computationally Efficient Procedure

2009 ◽  
Vol 131 (5) ◽  
Author(s):  
Rifat Sipahi ◽  
Hassan Fazelinia ◽  
Nejat Olgac
Keyword(s):  
Linear Time ◽  
Numerical Procedure ◽  
Computationally Efficient ◽  
Linear Time Invariant ◽  
Characteristic Roots ◽  
Stability Robustness ◽  
Linear Time Invariant Systems ◽  
The Stability ◽  
Operation Results ◽  
Time Invariant

A practical numerical procedure is introduced for determining the stability robustness map of a general class of higher order linear time invariant systems with three independent delays, against uncertainties in the delays. The procedure is based on an efficient and exhaustive frequency-sweeping technique within a single loop. This operation results in determination of the complete description of the kernel and the offspring hypersurfaces, which constitute exhaustively the potential stability switching loci in the space of the delays. The new numerical procedure corresponds to the first step in the overarching framework, called the cluster treatment of characteristic roots. The results of this treatment can also be represented in another domain (called the spectral delay space) within a finite dimensional cube called the building block, which is much simpler to view and analyze. The paper also offers several case studies to demonstrate the practicality of the new numerical methodology.

Modeling and path-tracking control of a mobile wheeled robot with a differential drive

Robotica ◽  
1995 ◽  
Vol 13 (4) ◽  
pp. 401-410 ◽  
Author(s):  
R. M. DeSantis
Keyword(s):  
Tracking Control ◽  
Linear Time ◽  
Path Tracking ◽  
Modeling And Control ◽  
Differential Drive ◽  
Linear Time Invariant ◽  
Wheeled Robot ◽  
And Control ◽  
Time Invariant ◽  
Kinematic Properties

SummaryTopics relevant to modeling and control of mobile wheeled robots with a differential drive are discussed by assuming a motion that is planar and free from lateral and longitudinal slippages, and by taking into account dynamic and kinematic properties of the vehicle. Based on the concept of geometric path-tracking, a controller is designed that is a memoryless function of the lateral, heading, and velocity path-tracking offsets. If these offsets are kept small and the assigned tracking velocity is constant, then this controller may be given a linear, time-invariant and decoupled PID (Proportional + integral + derivative) structure.

Integral Sliding-Mode Observation and Control for Switched Uncertain Linear Time Invariant Systems: a Robustifying Strategy

2017 ◽  
Vol 20 (4) ◽  
pp. 1551-1565 ◽  
Author(s):  
Rosalba Galván-Guerra ◽  
Leonid Fridman ◽  
Rafael Iriarte ◽  
Juan-Eduardo Velázquez-Velázquez ◽  
Martin Steinberger
Keyword(s):  
Sliding Mode ◽  
Linear Time ◽  
Integral Sliding Mode ◽  
Linear Time Invariant ◽  
Linear Time Invariant Systems ◽  
And Control ◽  
Time Invariant

Some issues of structure and control for linear time-invariant systems

2006 ◽  
Vol 30 (2) ◽  
pp. 131-141 ◽  
Author(s):  
Michel Malabre
Keyword(s):  
Linear Time ◽  
Linear Time Invariant ◽  
Linear Time Invariant Systems ◽  
And Control ◽  
Time Invariant

A new approach for simplification and control of linear time invariant systems

2018 ◽  
Vol 25 (2) ◽  
pp. 599-607 ◽  
Author(s):  
Rajul Goyal ◽  
Girish Parmar ◽  
Afzal Sikander
Keyword(s):  
Linear Time ◽  
New Approach ◽  
Linear Time Invariant ◽  
Linear Time Invariant Systems ◽  
And Control ◽  
Time Invariant
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