Robust PID based indirect-type iterative learning control for batch processes with time-varying uncertainties

Abstract

Based on the proportional-integral-derivative (PID) control structure widely used in engineering applications, a robust indirect-type iterative learning control (ILC) method is proposed for industrial batch processes subject to time-varying uncertainties. An important merit is that the proposed ILC design is independent of the PID tuning that aims primarily to hold robust stability of the closed-loop system, owing to the fact that the ILC updating law is implemented through adjusting the setpoint of the closed-loop PID control structure plus a feedforward control to the plant input from batch to batch. According to the robust H infinity control objective, a robust discrete-time PID tuning algorithm is given in terms of the plant state-space model description to accommodate for time-varying process uncertainties. For the batchwise direction, a robust ILC updating law is developed based on the two-dimensional (2D) control system theory. Only measured output errors of current and previous cycles are used to implement the proposed ILC scheme for the convenience of practical application. An illustrative example from the literature is adopted to demonstrate the effectiveness and merits of the proposed ILC method.

Quasi-Newton-type optimized iterative learning control for discrete linear time invariant systems

“…Assume that the tracking errors {e k } are generated by SR1-ILC algorithm (6)- (11) and (15), then the following conclusions hold.…”

“…Lemma 1 Suppose that the sequence of the gradient difference vectors {ẽ j } k+1 j=1 and the searching direction vectors {Δu j } k+1 j=1 are generated by the SR1-ILC algorithm (6)- (11) and (15) satisfying (Δu k+1 − H kẽk+1 ) Tẽ k+1 0. Then, the following secant equations are true:…”

“…Suppose that the sequence of the gradient difference vectors {ẽ j } and the searching direction vectors {Δu k } are generated by SR2-ILC algorithm (6)- (11) and (16). Then, the searching direction vectors Δu 1 , Δu 2 , .…”

“…As one of the important theoretical issues, the convergence analysis has been discussed by Amann et al [2], Xu [3], and Meng et al (2-D analysis approach) [5] and Ruan et al [6,7]. In addition, the robustness has been discussed from many aspects, such as stochastic noise in [8], iteration-varying disturbances in [9], model uncertainty in [10] and time-delay uncertainty in [11], etc., stability and initial state learning have been researched in [12] and [13], respectively. Another significant contribution to ILC theory is optimal ILC algorithms in articles [14][15][16][17][18][19].…”

Two-dimensional generalized predictive control (2D-GPC) scheme for the batch processes with two-dimensional (2D) dynamics

“…Based on the stability theory of 2D system, Wang et al (2012Wang et al ( , 2013a proposed an advanced PI learning control and presented stability analysis for the multi-input and multi-output linear batch processes. By using LMI technique for 2D systems, Wang et al (2013b, c) developed a design method of the 2D ILC for the batch process with time delay and uncertainties, Liu et al (2014) proposed a design method of indirect-type ILC system with a PID control as the inner control loop for the batch processes, Hladowski et al (2010) proposed a design method of robust ILC scheme for a class of repetitive processes with uncertainty in trial dynamic and applied it on a gantry robot performing pick and place operations, and Cichy et al (2014) proposed to use a 2D system setting in the form of repetitive process stability theory to design an ILC law that is robust against model uncertainties. Although all of these research works provide solutions from different viewpoints of the control problems, there are still some basic problems remained in this field.…”