By Eure K.W.
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Extra info for Adaptive predictive feedback techniques for vibration control
E. Linear Quadratic Regulator (LQR), they may come very close to the optimal solution without the computational burden of solving a Riccati equation. Also, since these finite-horizon controllers have many of the properties of LQR, it may be assumed that both the stability and robustness properties of these controllers closely follow that of LQR. This will become especially true for large prediction horizons. 1 Introduction As shown in Chapter 3, predictive feedback control has been successfully used in the regulation of plate vibrations when no reference signal is available for feedforward control.
P z − p 48 β ( z ) = β 0 + β 1 z −1 + β 2 z −2 ++ β p z − p δ ( z ) = δ 0 + δ 1 z −1 + δ 2 z −2 ++δ p z − p Disturbances which consist of only a single-input periodic signal may be represented by the finite-difference model shown in Eq. 22)41. 22), nd is the disturbance model order and is twice the number of commensurable frequencies in the disturbance signal. 22), results in Eq. 23). 23) where η( z ) = 1 − η1 z −1 − η 2 z −2 −−η nd z − nd Premultiplying Eq. 21) by η( z ) and using Eq. 24) where α~ ( z ) = η( z )α ( z ) = I m − α~1 z −1 − α~ 2 z −2 −−α~ p z − p − nd ~ ~ ~ ~ ~ β ( z ) = η( z )β ( z ) = β 0 − β 1 z −1 − β 2 z −2 −− β p z − p − nd In Eq.
In general, as the value of the control horizon approaches the prediction horizon, better regulation is achieved at the expense of 41 robustness. To gain stability in this case, the value of λ is increased. As the value of the control horizon is made smaller than the prediction horizon, a more robust controller results at the expense of regulation. Also, a shorter control horizon makes the GPC algorithm more computationally efficient in that the matrix pseudo-inverse of Eq. 11) is smaller. The plant model order, prediction horizon, control horizon, and control penalty are all design parameters determined by the user.