Cross-directional Controllers Research Articles

The Robustness and Design of Constrained Cross-Directional Control Via Integral Quadratic Constraints

A robust stability test for a class of constrained cross-directional controllers is found. Under special circumstances, the stability test is executed on a mode-by-mode basis and greatly simplified to a frequency-domain criterion. The test is also exploited to develop tuning algorithms. The control system involves a quadratic program embedded within an internal model control antiwindup structure and achieves optimal steady-state performance when the plant is known. Both the nonlinearity in the controller and the plant uncertainty satisfy certain integral quadratic inequalities. This allows us to obtain conditions for robust stability that can be expressed as linear matrix inequalities via the Kalman-Yakubovich-Popov lemma.

Modeling and Control of a Plastic Film Manufacturing Web Process

This paper is concerned with the modeling of a plastic film manufacturing process and the development and implementation of a model-based Cross-Directional (CD) controller. The model is derived from first-principles and some empirical relationships. The final validated nonlinear model could provide a useful offline platform for developing control and monitoring algorithms. A new controller is designed which has a similar structure to that of Internal Model Control (IMC) with the addition of an observer whose gain is designed to minimize process and model mismatch. The observer gain is obtained by solving a multiobjective optimization problem through the application of a genetic algorithm. The controller is applied to the nonlinear model and simulation results are presented demonstrating improvements that can be achieved by the proposed controller over two existing CD controllers.

Detecting Mismapping in Cross-Directional Control Systems

Cross-directional (CD) control systems regulate product properties in industrial web processes by manipulating the inputs to arrays of actuators. In many of these processes, the product wanders or undergoes transformations such as stretching that introduce lateral shifts in the location of the actuator responses. The spatial position of the center of the response of each actuator is known as the actuator mapping and for CD controllers to operate effectively, it is important that this is known accurately. Actuator mapping is one of the main sources of uncertainty in the model that is used to design CD controllers and mismapping can lead to closed-loop instability, so CD controllers are often designed conservatively to provide robustness to this uncertainty. Because CD controllers can operate with a significant level of mismapping, both the dynamic and steady-state responses of the closed-loop system are often degraded. In practice, it is difficult to detect the presence of mismapping, but this brief describes an online diagnostic technique based on a vector auto regression (VAR) representation of the closed-loop response of the actuator inputs, which derives a statistic from existing plant data that can be used in a hypothesis test to detect the presence of mismapping. The performance of the technique is demonstrated by results from an implementation on a plastic film process.

Discussion on: Design of Cross-Directional Controllers with Optimal Steady State Performance

Discussion on: Design of Cross-Directional Controllers with Optimal Steady State Performance

Design of Cross-Directional Controllers with Optimal Steady State Performance*

Actuator constraint handling is necessary for many cross-directional controllers. We discuss how optimal steady state performance can be guaranteed by modifying an internal model control structure with a non-linear element. For the simple dynamics associated with most web processes this also gives good closed-loop dynamic behaviour. Thus unconstrained control design techniques may be applied directly to the constrained control problem.

Discussion on: “Design of Cross-Directional Controllers with Optimal Steady State Performance”

Discussion on: “Design of Cross-Directional Controllers with Optimal Steady State Performance”

Feedback controller design for a spatially distributed system: the paper machine problem

This paper reports on the development and implementation of an algorithm for the design of spatially distributed feedback controllers for the wide variety of physical processes that are included in cross-directional (CD) control of industrial paper machines. The spatial and temporal structure of this class of process models is exploited in the use of the 2D frequency domain for analysis and 2D loop shaping design of feedback controllers. This algorithm forms the basis of a software tool that has recently been implemented in a commercial product and its use is illustrated for tuning CD controllers on two different industrial paper machines. The first example describes the use of the tool in stabilizing an unstable closed-loop system by retuning the distributed controller. The second paper machine example exposes an underperforming controller. Subsequent retuning of the controller resulted in a dramatic performance improvement.

Analysis of steady-state performance for cross-directional control

The authors analyse the steady-state behaviour of a class of cross-directional controllers that are pertinent to general web-forming processes. Their analysis is framed in terms of the controllable space prescribed by the interaction matrix and general discrete orthonormal basis descriptions of both the input and output space under the assumption of closed-loop stability. The specific choice of controller defines (whether explicitly or implicitly) an additional assumed controlled space. It is well known that the controllable space determines a lower bound on output variation. They examine the implications of integral action and provide sufficient conditions for the steady-state output variation to achieve this lower bound. They confirm some intuitive results that connect the optimal constrained and unconstrained steady-state solutions for model-based control with no model mismatch. Model mismatch is usually detrimental to steady-state performance. This effect is interpreted in terms of leakage between the controllable and assumed controlled spaces, as well as their respective orthogonal complements.