A robust feedback integrated with iterative learning control (FILC) scheme for batch processes with uncertain perturbations and interval time-varying delay is developed. The batch process is modeled as a two-dimensional (2D) Rosser system with a delay varying in a range. The design of FILC scheme is transformed into a robust control problem of uncertain 2D system. New delay-range-dependent stability criteria and stabilization conditions are derived in terms of linear matrix inequalities (LMIs), which depend on not only the difference between the upper and lower delay bounds but also the upper delay bound of the interval time-varying delay. Parameterized characterizations for stabilizing the controller are given in terms of the feasibility solutions to the LMIs. Applications to injection velocity control show that the proposed FILC achieve the design objectives well.
Studies on batch process control have attracted considerable attention because batch processes are the preferred manufacturing choice for low-volume and high-value products, and batch processing is widely used in chemical industries [1]. Iterative learning control (ILC) has been used widely to exploit the repetitive nature of batch processes. The challenges for practical applications of ILC are mainly associated with robust convergence and stability against process uncertainties. Recently, a number of robust ILC methods have been presented to cope with structured and unstructured process uncertainties for batch processes. In time domain, by using a LMI approach, Nguyen et al. [2] present the design of iterative learning control based on quadratic performance criterion for linear systems subject to additive uncertainty. From a two-dimensional (2D) view (i.e., time-wise and batch-wise) for batch process control design, a state-space ILC method was presented in terms of using a 2D linear continuous-discrete Roesser's model [3]. Equivalent convergence conditions for ILC design in frequency or/and time domain were analyzed in the recent papers [4]. Meanwhile, in discrete-time domain, robust ILC methods have also been proposed for batch processes with model uncertainties or unmodeled dynamics. On-line adaptive ILC methods [5] were presented to deal with model mismatch using historical data to modify output prediction from cycle to cycle. Based on a 2D system description, a series of ILC methods [6], [7] and [8] have been developed using a linear quadratic optimal control criterion and robust stability conditions in terms of linear matrix inequalities to deal with a variety of model uncertainties. Model predictive control (MPC) based ILC schemes was proposed to accommodate for implemental constraints in the recent papers [9] and [10].
Time-delay is a common phenomenon in chemical and other industrial processes, which may give rise to instability of the system. How to deal with time delays has been a hot topic in control community [11]. Recently, the research has been extended to dynamical systems with time-varying delay that varies in a range for which the lower bound is not restricted to be zero for continuous processes [12] and [13]. Like continuous processes, batch process sufferers also from time-delay, and the delay is typically varying in a range. Very limited results on this topic have been available up to now. In frequency domain, using the Smith predictor control structure, which is known for superior control of time delay processes with a priori knowledge of the time delay, an ILC algorithm [14] was proposed to improve tracking performance of ILC for batch processes with known and fixed time delay; 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 [15]. To deal with output delay of a non-minimum phase plant, a reference shift algorithm was suggested based on a double-loop ILC structure [16]. In time domain, Park et al. [17] 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. In these existing results, only known and fixed delay is considered and conventional ILC methods are used. Time-delay may result in instability of a system. Conventional ILC methods in time domain are likely to cause system performance degradation and even make the system state divergent. It remains as a challenge to find a control method for a batch process with time-varying delay. It has been shown that the feedback control incorporated with ILC technique is an effective tool for studying stability criteria of batch process without time-delay based on 2D system [6], [7] and [8]. However, to the best of our knowledge, no such results on batch process with time-delay have been available up to now.
This article proposes a robust feedback integrated with ILC design scheme for batch processes with uncertain perturbations and interval time-varying delay. A two-dimensional (2D) Rosser model with a delay varying in a range serves as the foundation of the proposed design. Based on 2D system theory, here a FILC law is designed to guarantee the considered systems asymptotically stable along both the time and the cycle directions. With two lemmas and a new Lyapunov functional proposed, new delay-range-dependent stability criteria and stabilization conditions are derived in terms of linear matrix inequalities, which depend on not only the difference between the upper and lower delay bounds but also the upper delay bound of the interval time-varying delay. Parameterized characterizations for stabilizing the controller are given in terms of the feasibility solutions to the LMIs. The feasibility and effectiveness of the proposed FILC method are demonstrated with injection velocity control
Based on integrating an iterative learning control with a feedback control, a feedback and iterative learning control (FILC) scheme has been proposed for a batch process with interval time-varying delay. The process has been transformed to a two-dimensional Rosser model. The design of FILC scheme is transformed into a robust control problem of uncertain 2D time-delayed system. By defining a 2D Lyapunov function, new delay-range-dependent stability and stabilization conditions are established in terms of linear matrix inequalities. Parameterized characterization of the feedback and iterative learning control law is given in terms of the feasibility solutions to the LMIs. The results on injection velocity control have clearly illustrated the feasibility and effectiveness of the proposed design.
