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doi:10.1016/j.biosystemseng.2006.11.015 
Copyright © 2006 IAgrE Published by Elsevier Ltd.
Feedback Approach for Reproduction of Field Measurements on a Hydraulic Four Poster
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J. Anthonis1, D. Vaes2, K. Engelen1, H. Ramon1 and J. Swevers2
Received 14 January 2006;
The study of vibrations in agriculture is performed to assess the efficiency of machinery, lifetime of components, drivers’ comfort, damage of crop during harvest and transport. An important source of vibrations is the soil. Owing to the stochastic character and visco-elastic behaviour of the soil, it is very difficult to create repeatable testing conditions. Experiments on vibration test rigs, also called shakers, in combination with time waveform replication (TWR) can solve this problem. The objective of TWR is to determine the inputs to the shakers in order to obtain the same sensor readings as during the field experiments. The classical TWR method consists of an iterative procedure that can be time consuming. This paper presents a feedback approach, thereby reducing the number of iterations. As in general, several sensor signals need to be reproduced, a multiple-input multiple-output (MIMO) controller needs to be designed, which is often a time consuming and difficult process. A methodology based on static decoupling is introduced such that the MIMO controller design reduces to the synthesis of several single-input, single-output (SISO) controllers. Experiments on a tractor indicate that with the present procedure, compared to the classical TWR procedure, the number of iterations can be reduced and a better accuracy can be achieved.
Notation
- C(ω)
- feedback controller signal
- diagonal matrix with the diagonal elements of
on its diagonal
- E(ω)
- Fourier transform of the error signals, m/s2
- the relative difference between the decoupled frequency response matrix and its diagonal approximation
- G(s)
- system matrix
- Gd(s)
- transformed system matrix TyG(s)T(u)
- Gm(ω)
- measured frequency response matrix of the system
- transformed measured frequency response matrix of the system
- I
- identity matrix
- P(ω)
- true plant
- Q
- gain matrix
- R(ω)
- Fourier transform of the target signals, m/s2
- S(ω)
- sensitivity matrix
- T(ω)
- complementary sensitivity matrix
- Tu
- input transformation matrix
- Ty
- output transformation matrix
- Uff(ω)
- Fourier transform of the drive signals, V
- W(ω)
- weighting function
- Wo
- robustness weight
- Wp
- performance weight
- e(t)
- error signals, m/s2
- r(t)
- target signals, m/s2
- s
- Laplace variable
- t
- time
- uff(t)
- drive signals, inputs, V
- uT
- transformed input, V
- y(t)
- response signal, m/s2
- yT
- transformed outputs, m/s2
- ΔG(ω)
- the relative difference between the true plant P(ω) and the measured Gm(ω)
- ω
- circular frequency, Hz
- j
- iteration number
