بر اساس کنترل یادگیری تکراری بر اساسIMC برای فرآیندهای دسته ای با تاخیر زمانی نامشخص

Based on the internal model control (IMC) structure, an iterative learning control (ILC) scheme is proposed for batch processes with model uncertainties including time delay mismatch. An important merit is that the IMC design for the initial run of the proposed control scheme is independent of the subsequent ILC for realization of perfect tracking. Sufficient conditions to guarantee the convergence of ILC are derived. To facilitate the controller design, a unified controller form is proposed for implementation of both IMC and ILC in the proposed control scheme. Robust tuning constraints of the unified controller are derived in terms of the process uncertainties described in a multiplicative form. To deal with process uncertainties, the unified controller can be monotonically tuned to meet the compromise between tracking performance and control system robust stability. Illustrative examples from the recent literature are performed to demonstrate the effectiveness and merits of the proposed control scheme.

Significant progress has been made for both technologies and applications of iterative learning control (ILC) in the past decade for batch processes, e.g., chemical distillation/crystallization reactors, industrial injection molding machines, and robotic manipulators [1], owing to that this type of control technique can progressively improve system performance for setpoint tracking and load disturbance rejection using historical cycle data [2]. As surveyed in the recent papers [1] and [3], quite an amount of ILC control methods have been well developed in both continuous- and discrete-time domains that can realize perfect tracking for linear or nonlinear batch processes. Presently, the challenges for practical applications of ILC are mainly associated with robust convergence and stability against process uncertainties. Recently, a number of references have presented robust ILC methods to cope with structured and unstructured process uncertainties for delay-free or known time delay batch processes. In frequency domain, a robust ILC design method [4] was proposed for delay-free linear time-invariant (LTI) batch processes based on the linear fractional transformation (LFT) analysis of robust control theory [5]; Gorinevsky [6] extended the loop shaping method [7] for ILC design with phase/magnitude margin; using the Smith predictor control structure, which is well known for superior control of time delay processes with a priori knowledge of the time delay, several ILC algorithms [8] and [9] were proposed to improve tracking performance of ILC for batch processes with obvious time delay; Tan et al. [10] developed an ILC tuning of proportional-integral-derivative (PID) controller in the framework of the conventional unity feedback structure to enhance load disturbance rejection; an ILC strategy for tuning a dual-mode controller was recently proposed for optimal heating of exothermic batch reactors [11]; to deal with output delay of a non-minimum phase plant, a reference shift algorithm was suggested based on a double-loop ILC structure [12]. In time domain, Park et al. [13] proposed an ILC method in terms of a holding mechanism for the control input during the estimated time delay for operation of batch processes with time delay; from a two-dimensional (2D) view (i.e., time-wise and batch-wise) for batch process control design [14], a state-space ILC method was presented in terms of using a 2D linear continuous-discrete Roesser’s model [15]. Equivalent convergence conditions for ILC design in either frequency or time domain were analyzed in the recent papers [16], [17] and [18]. Meanwhile, in discrete-time domain, robust ILC methods for batch processes with model uncertainties or unmodeled dynamics have also been proposed by comparison. Using historical data to modify output prediction from cycle to cycle, on-line adaptive ILC methods [19] and [20] were presented to deal with model mismatch. Based on a 2D system description, a series of ILC methods [21], [22], [23] and [24] have been developed using a linear quadratic optimal control criterion and robust stability conditions of linear matrix inequalities to deal with a variety of model uncertainties. To accommodate for implemental constraints, model predictive control (MPC) based ILC schemes were proposed in the recent papers [25], [26], [27], [28] and [29]. Using the real-time feedback information to modify the ILC parameters, Chin et al. [30] presented an improved strategy for independent disturbance rejection. With an inherent lag compensation in the updating law, Tan et al. [31] proposed an ILC algorithm for batch processes with input delay or phase lag. Based on estimating the minimum variance bound and the achievable variance bounds from batch to batch, Chen and Kong [32] developed an ILC method for progressively improving operation of time delay batch processes. In view of that time delay mismatch is commonly associated with other process uncertainties during operation of a time delay batch process in engineering practice, this paper proposes a robust ILC method based on the internal model control (IMC) structure [33] to deal with such difficulties. Sufficient conditions to guarantee the convergence of ILC are derived for time delay batch processes with or without model uncertainties. To facilitate the controller design, a unified controller structure in terms of the standard IMC controller form is proposed for implementation of IMC in the initial run and the subsequent ILC in the proposed control scheme. An important merit is that both IMC and ILC can be independently designed to deal with the process uncertainties. Moreover, the unified controller can be monotonically tuned to meet the compromise between tracking performance and control system robust stability. For practical applications with measurement noise, denoising strategies are given to enhance convergence robustness. The paper is organized as follows: Section 2 introduces the proposed IMC-based ILC scheme and the general transfer function form of time delay batch processes studied in this paper. In Section 3, an IMC design for the initial run of the proposed control scheme is given in terms of the general transfer function, together with a robust tuning constraint for maintaining the control system stability against process uncertainties. In Section 4, sufficient conditions to guarantee the convergence of ILC in the proposed control scheme are derived, and correspondingly, a unified controller form is proposed for the convenience of implementing both IMC and ILC in the proposed control scheme. Denoising strategies are presented in Section 5 to enhance convergence robustness against measurement noise associated with practical applications. Illustrative examples are given in Section 6 to demonstrate the effectiveness and merits of the proposed control scheme. Finally, conclusions are drawn in Section 7.

To deal with time delay uncertainty often encountered in engineering practices for operation of batch processes, this paper has proposed an IMC-based ILC method for practical applications. Relative independence is therefore obtained for designing the IMC control law to maintain the control system robust stability and the ILC control law to realize perfect tracking, respectively. Sufficient conditions to guarantee the convergence of ILC have been derived. It is a notable merit that the developed characteristic equation of the ILC transfer function connecting the tracking errors from cycle to cycle is free of delay, which may facilitate the controller design. For the convenience of implementation, a unified controller form has been proposed for implementing IMC in the initial run and the subsequent ILC for perfect tracking. To cope with process uncertainties, robust tuning constraints of the unified controller have been derived, respectively for maintaining the control system stability and the convergence for tracking a desired trajectory. It is convenient for practice that the unified controller can be monotonically tuned through only one adjustable parameter to meet the compromise between tracking performance and the control system robust stability. The application to two examples from the recent literature has evidently demonstrated the merits of the proposed control scheme.