By Germán A. Ramos
The tracking/rejection of periodic signs constitutes a large box of analysis within the keep an eye on conception and functions sector. Repetitive regulate has confirmed to be an effective method to face this subject. besides the fact that, in a few functions the frequency of the reference/disturbance sign is time-varying or doubtful. This motives an incredible functionality degradation within the typical Repetitive regulate scheme. This publication provides a few suggestions to use Repetitive keep watch over in various frequency stipulations with no loosing steady-state functionality. it's also an entire theoretical improvement and experimental ends up in consultant structures. The provided recommendations are geared up in complementary branches: various sampling interval Repetitive keep an eye on and excessive Order Repetitive regulate. the 1st strategy permits facing huge diversity frequency diversifications whereas the second one permits facing small variety frequency diversifications. The booklet additionally provides functions of the defined recommendations to a Rota-magnet plant and to an influence energetic filter out device.
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Additional resources for Digital Repetitive Control under Varying Frequency Conditions
Synthesis of a sampling period dependent controller using LPV approach. In: Proceedings of the 5th IFAC Symposium on Robust Control Design, Toulouse, France (2006) 7. : An H∞ LPV design for sampling varying controllers: experimentation with a T inverted pendulum. IEEE Transactions on Control Systems Technology 18(3), 741–749 (2010) 8. : Computer control under time-varying sampling period: An LMI gridding approach. Automatica 41(12), 2077–2082 (2005) 9. : Robust Systems Theory and Applications.
9), which yields the following condition M ∑ wl = 1. 8) is the same as that obtained using just one delay element. To show how the derivatives of W (e jω ) and Ihodd (e jω ) with respect to ω are related, the chain rule can be used: thus, for the first derivative one has ∂ Ihodd (e jω ) ∂ω = ∂ Ihodd (e jω ) ∂ W (e jω ) ∂ω ∂ W (e jω ) = ∂ W (e jω ) −1 ∂ω (1+W (e jω ))2 , while for the second derivative it is ∂ 2 Ihodd (e jω ) ∂ ω2 = = ∂ 2 Ihodd (e jω ) ∂ W 2 (e jω ) 2 (1+W(e jω ))3 ∂ W (e jω ) 2 (e jω ) ∂ 2W (e jω ) + ∂ ∂Ihodd ∂ω W (e jω ) ∂ ω2 ∂ W (e jω ) 2 ∂ 2W (e jω ) −1 + (1+W (e jω ))2 ∂ ω 2 .
M − 1. 14) yields w1 + 2w2 + 3w3 = 0, w1 + 4w2 + 9w3 = 0, which renders w1 = 3, w2 = −3, and w3 = 1. In the same way, one gets w1 = 2 and w2 = −1 for M = 2. The procedure described here attains the same conditions found in . 8). At the same time, the properties obtained from each method are preserved. 14) can be put together in the following compact form: M ∑ l p wl = l=1 1 if p = 0 0 if p = 1, . . , M − 1. 2. 17) √ −1 with multiplicity M. N/2 Proof. By straightforward calculation. 1 and using the same reasoning as before, it is immediate that the odd-harmonic internal models that can be obtained adapting the procedures  and  would yield the same (open loop) stability issues as those in the original version.