The Design of Manipulator System With Pole Placement Approach

1992 ◽  
Author(s):  
Wu DeRong
Keyword(s):  
Transfer Function ◽  
Control Theory ◽  
Complex Plane ◽  
State Equation ◽  
Pole Placement ◽  
Dynamic State ◽  
Controllable System ◽  
Modern Control Theory ◽  
Transfer Function Matrix ◽  
Function Matrix

Abstract The manipulator system is a sequence of mechanisms jointed with each other. It is difficult to establish the dynamic state equation of such a mechanism system. By means of the bond graph method, it is easy to derive the state equation of a mechanism, then one have the transfer function matrix. According to the combined situation of mechanisms for manipulator, whose transfer function matrix may be obtained. Based on the modern control theory, one will find that in a controllable system, it is possible to place the poles anywhere we wish in the complex plane. In this paper one will develop a new procedure concerning system pole assignment within desired places by using two controllers. An example is illustrated.

Error analyses of a Multi-Input-Multi-Output cantilever beam test

2021 ◽  
pp. 107754632110337
Author(s):  
Arup Maji ◽  
Fernando Moreu ◽  
James Woodall ◽  
Maimuna Hossain
Keyword(s):  
Transfer Function ◽  
Frequency Domain ◽  
Cantilever Beam ◽  
Transfer Functions ◽  
Linear Superposition ◽  
Transfer Function Matrix ◽  
Error Analyses ◽  
Pseudo Inverse ◽  
Function Matrix

Multi-Input-Multi-Output vibration testing typically requires the determination of inputs to achieve desired response at multiple locations. First, the responses due to each input are quantified in terms of complex transfer functions in the frequency domain. In this study, two Inputs and five Responses were used leading to a 5 × 2 transfer function matrix. Inputs corresponding to the desired Responses are then computed by inversion of the rectangular matrix using Pseudo-Inverse techniques that involve least-squared solutions. It is important to understand and quantify the various sources of errors in this process toward improved implementation of Multi-Input-Multi-Output testing. In this article, tests on a cantilever beam with two actuators (input controlled smart shakers) were used as Inputs while acceleration Responses were measured at five locations including the two input locations. Variation among tests was quantified including its impact on transfer functions across the relevant frequency domain. Accuracy of linear superposition of the influence of two actuators was quantified to investigate the influence of relative phase information. Finally, the accuracy of the Multi-Input-Multi-Output inversion process was investigated while varying the number of Responses from 2 (square transfer function matrix) to 5 (full-rectangular transfer function matrix). Results were examined in the context of the resonances and anti-resonances of the system as well as the ability of the actuators to provide actuation energy across the domain. Improved understanding of the sources of uncertainty from this study can be used for more complex Multi-Input-Multi-Output experiments.

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