H∞ design of 2D controller for batch processes with uncertainties and interval time-varying delays

Based on robust feedback incorporated with iterative learning control scheme, this paper proposes a 2D controller design for a kind of batch process with uncertainties and interval time-varying delay. The batch process is first transformed into a two-dimensional Fornasini—Marchsini (2D-FM) model with a delay varying in a range. Then the design of 2D controller scheme is cast as a robust H∞ control problem for uncertain 2D systems. Based on the 2D control system theory, a design framework of 2D controller is formulated, which consists of two control actions: a robust feedback control for ensuring the performances over time and a P-type iterative learning control (P-type ILC) for improving the tracking performance from cycle to cycle. The proposed control law can guarantee closed-loop convergence along both the time and the cycle directions to satisfy H∞ performance. Conditions for the existence of the proposed 2D control design scheme are given in terms of linear matrix inequalities. The minimum H∞ norm bound γγ is obtained by solving linear objective optimization problems. The generality of the proposed design method is shown by the results converted to constant delay case. Application to injection velocity control demonstrates the effectiveness and advantages of the proposed approach.