Dynamic matrix control of the lateral position of a moving web

Abstract

The lateral motion of the web is one of the most common problems in roll-to-roll (R2R) systems, which results in degraded product quality, waste, or even processing interruption. An industrial proportional-integral-derivative (PID) controller with fixed gain is mostly used for lateral position control. In fact, the model parameters of the web lateral dynamics such as the tension and the transport velocity of the web are seldom exact. Variations of these parameters could significantly affect the lateral web dynamics. A dynamic matrix control (DMC) strategy is adopted in the offset pivot web guide to control the lateral position of the web, which does not depend on accurate model. Simulations of the DMC controller and the PID controller was carried out with a sinusoidal disturbance in different web conditions. The results show that DMC controller performs much better than PID controller with good disturbance rejection. It is observed that the lateral position of the DMC controller is less than a half of that of the PID controller. As the web velocity decreases or the web tension increases, the lateral position becomes smaller.

Model‐free hierarchical control with fractional‐order sliding surface for multisection web machines

“…Based on Euler-Bernoulli theory, studies successfully modeled the lateral web dynamics. [4][5][6][7][8] Specifically, a mathematical model of a web span [4][5][6]8 was represented as the fourth-order partial differential equation (PED) combined with boundary conditions. Besides, the authors showed a two-span roll-to-roll (R2R) system model based on the second-order PED with three dynamic response modes.…”

“…Recent investigations on modeling of rewinding systems have been investigated, divided into two trends: lateral and longitudinal models. Based on Euler–Bernoulli theory, studies successfully modeled the lateral web dynamics 4‐8 . Specifically, a mathematical model of a web span 4‐6,8 was represented as the fourth‐order partial differential equation (PED) combined with boundary conditions.…”

Adaptive Model Predictive Controller for Web Transport Systems

“…More recently, the investigations in ( [10] and [17]) proposed the use of model predictive controllers (MPC) for WTS. The MPC uses the model of the web transport system, estimate of disturbance and an optimization routine to optimize the product quality and energy consumption in the WTS.…”

Supervisory GPC and Evolutionary PI Controller for Web Transport Systems

“…Design of WTC has received considerable attention of researchers in the past two decades owing their wide applications and economic benefits. The available results can be broadly classified into five categories, they are: (i) conventional controllers (see, [9], [12], [16], [17], [27], [30], [31] and [34]), (ii) robust controllers (for e.g., [5], [8], [13] and [17]) (iii) adaptive controllers ( [1] and [23]), (iv) optimizing controllers [33]. A comparison of these controllers highlighting their advantages and limitations is shown in Table 1.…”

“…To reach our first objective of optimizing the quality and energy cost, the investigation proposes to use model predictive controller (MPC) that not only combines the advantages of the existing results in adaptive and robust controller such as using models, disturbance attenuation, and dealing with model uncertainties, but also overcomes their shortcomings such as the need for accurate models, online estimation of model parameters and being not optimal. Recently, Dynamic Matrix Controller (DMC) for WTS proposed in [33] uses the model of the process along with constraints, estimate of the disturbance and an optimization routine to compute the future control moves in receding horizon manner to enhance the product quality and reduce energy cost. But, step response based computation in DMC involves intensive computations for multivariable process.…”