Robust PD-type iterative learning control design for uncertain batch processes subject to nonrepetitive disturbances

Abstract

This paper develops PD-type iterative learning control schemes for a class of uncertain batch processes subject to nonrepetitive disturbances. By means of two-dimensional/repetitive setting the conditions for batch-to-bach error convergence and H ∞ disturbance attenuation are formulated and analyzed. Subsequently, the procedure for computing the desired control law matrices is formulated in terms of solvability of linear matrix inequalities. The proposed control law is able to fulfil the imposed design specifications, i.e., they are suitable for the batch processes with time-varying uncertainties as well as non-repetitive disturbances. An illustrative example is used to validate the proposed control scheme and demonstrates a possible applicability of the developed results.

Improved LMI-based conditions for designing of PD-type ILC laws for linear batch processes over two-dimensional setting

“…The resulting controlled system represented as Roesser model is structurally stable and hence batch-to-batch error convergence occurs. This can be verified in Figure 2 where the RMSE of the tracking error is shown and compared to the previously presented results in [7,10]. From comparison in Figure 2, the RMSE of the proposed method is lower when comparing with [7,10].…”

“…This can be verified in Figure 2 where the RMSE of the tracking error is shown and compared to the previously presented results in [7,10]. From comparison in Figure 2, the RMSE of the proposed method is lower when comparing with [7,10]. Obviously, the effectiveness of the presented ILC design is apparent.…”

“…and G(λ) * P (λ)G(λ) − P (λ) ≺ 0, (10) where the matrices P and P (λ) satisfy P ≻ 0 and P (λ) ≻ 0 ∀λ ∈ ∂ l D. Equivalently, the inequality (9) implies that ρ(A 22 ) ≤ 1 and (10) can be transformed into ρ(G(λ)) ≤ 1 ∀λ ∈ ∂ l D. However, in practice it is desirable to increase the speed of batch-to-batch error convergence. Therefore, we are interested in placing the eigenvalues of A 22 and G(λ) inside the open disc centered at the origin with radius r 1 satisfying 0 < r 1 ≤ 1.…”