Transfer Matrix Modeling of Systems With Noncollocated Feedback

2010 ◽  
Vol 132 (6) ◽  
Author(s):  
Ryan W. Krauss ◽  
Wayne J. Book
Keyword(s):  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Transfer Functions ◽  
Flexible Structures ◽  
Control Design ◽  
Feedback Loops ◽  
Flexible Robot ◽  
Matrix Modeling ◽  
Primary Contribution

The transfer matrix method (TMM) can be a powerful tool for modeling flexible structures under feedback control. It is particularly well suited to modeling structures composed of serially connected elements. The TMM is capable of modeling continuous elements such as beams or flexible robot links without discretization. The ability to incorporate controller transfer functions into the transfer matrix model of the system makes it a useful approach for control design. A limitation of the traditional formulation of the TMM is that it can only model feedback where the actuators and sensors are strictly collocated. The primary contribution of this paper is an algorithm for modeling noncollocated feedback with the TMM. Two cases of noncollocated sensors are considered (upstream and downstream). The approach is experimentally verified on a flexible robot that has one upstream and one downstream sensor in its feedback loops.

Infinite-Dimensional Pole-Optimization Control Design for Flexible Structures Using the Transfer Matrix Method

2013 ◽  
Vol 9 (1) ◽  
Author(s):  
Ryan W. Krauss
Keyword(s):  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Closed Loop ◽  
Flexible Structures ◽  
Three Dimensional ◽  
Control Design ◽  
Optimization Procedure ◽  
Step Response ◽  
Infinite Dimensional

This paper presents an approach to control design for flexible structures based on the transfer matrix method (TMM). The approach optimizes the closed-loop pole locations while working directly on the infinite-dimensional TMM model. The approach avoids spatial discretization, eliminating the possibility of modal spillover. The design strategy is based on an iterative process of optimizing the closed-loop pole locations using a Nelder-Mead simplex algorithm and then performing hardware-in-the-loop experiments to see how the pole locations are affecting the closed-loop step response. The evolution of the cost function used to optimized the pole locations is discussed. Contour plots (three dimensional Bode plots) in the complex s-plane are used to visualize the pole locations. A computationally efficient methodology for finding the closed-loop pole locations during the optimization is presented. The technique is applied to a single-flexible-link robot and experimental results show that the optimization procedure improves upon an initial, Bode-based compensator design, leading to a lower settling time.

Active Vibration Control Design of Multi-Rigid-Flexible-Body Systems Based on Transfer Matrix Method for Multibody Systems

2018 ◽  
Author(s):  
Gangli Chen ◽  
Xiaoting Rui ◽  
Yuanyuan Ding ◽  
Hanjing Lu
Keyword(s):  
Vibration Control ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Multibody Systems ◽  
Active Vibration Control ◽  
Control Design ◽  
Flexible Body ◽  
Global Dynamics ◽  
Active Vibration

A new approach for active vibration control design of multi-rigid-flexible-body systems based on transfer matrix method for multibody systems (MSTMM) is presented in this paper. The vibration characteristics are computed by solving homogeneous linear algebraic equations. Then, the augmented eigenvector and body dynamics equation are adopted to derive the state space representation by combining modal superposition method. Furthermore, Linear Quadratic Gaussian (LQG) control strategy is employed to design the control law. Compared with the conventional methods, the proposed method has the following features: without system global dynamics equation, high programming, low order of system matrix and high computational speed. Formulations as well as a numerical example are given to validate the proposed method.

Modified Finite Element Transfer Matrix Method for Eigenvalue Problem of Flexible Structures

2010 ◽  
Vol 78 (2) ◽  
Author(s):  
Bao Rong ◽  
Xiaoting Rui ◽  
Guoping Wang
Keyword(s):  
Finite Element ◽  
Eigenvalue Problem ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Eigenvalue Problems ◽  
Flexible Structures ◽  
System Matrix ◽  
Element Transfer ◽  
High Computational Efficiency

The speedy computation of eigenvalue problems is the key point in structure dynamics. In this paper, by combining transfer matrix method and finite element method, the modified finite element-transfer matrix method and its algorithm for eigenvalue problems are presented. By using this method, the speedy computation of eigenvalue problem of flexible structures can be realized, and the repeated eignvalue problem can be solved simply and conveniently. This method has the low order of system matrix, high computational efficiency, and stability. Formulations of this method, as well as some numerical examples, are given to validate the method.

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