Cross Directional Control of Web Forming Processes - Interaction and Simple PID Control
Summary
Web forming processes represent a wide class of industrial processes with relevance in many different production areas such as paper making, plastic film extrusion, steel rolling, coating and laminating.
These are large scale processes, involving complex machinery, which exhibit some challenging difficulties for the design of efficient control systems. Web forming processes are multivariable high dimensional systems which must operate subject to tight constraints.
These systems are a quintessential example of a difficult industrial control problem and are therefore an ideal case study for a virtual laboratory.
Figure 12.1: Screenshot of Program
The Physical Apparatus
Web forming processes represent a wide class of industrial processes with relevance in many different production areas such as paper making, plastic film extrusion, steel rolling, coating and laminating [6, 4, 11, 7]. These are large scale processes, involving complex machinery [3], which exhibit some challenging difficulties for the design of efficient control systems. As such, they have been the object of much investigation by many researchers [3, 2].
Web forming processes are multivariable high dimensional systems which must operate subject to tight input constraints. It is not uncommon to have Several hundred actuators. Thus these systems are a quintessential example of a difficult industrial control problem and are therefore an ideal case study for a virtual laboratory.
Description of the Process
In a general setup, web forming processes (also known as film and sheet forming processes) are characterized by raw material entering one end of the process machine and a thin web or film being produced at the other end of the machine - see Figure 12.2. The raw material is fed into the machine continuously or semicontinuously.
Sheet and film processes are effectively two dimensional spatially distributed processes [13]. Several properties of the sheet material vary in the direction in which the sheet runs - known as the machine direction (MD) - and in the direction across the sheet - known as the cross direction (CD).
The main objective of the control applied to sheet and film processes is to maintain both the MD and CD profiles of the sheet as flat as possible, in spite of multiple disturbances including:
- Variations in the composition of the raw material fed to the machine.
- Uneven distribution of the material in the cross direction.
- Deviations in the cross directional profile.
Usually the average properties of the web are controlled in the machine direction, whilst deviations from this average are compensated in the cross direction. Properties of interest include weight, moisture and caliper (in papermaking applications), thickness (in polymer extrusion) and tension (in steel rolling applications) [6].
Figure 12.2 shows the main components of a general web forming process. In order to control the cross directional profile of the web, an array of actuators are evenly distributed along the cross direction of the sheet. The number of actuators can vary from as few as 30 up to as many as 300. The film properties, on the other hand, are either measured via an array of sensors placed in a downstream position or via a scanning sensor that moves back and forth in the cross direction. The number of measurements taken by a single scan of the sensor can be up to 1000, but we will assume that the number of measurements is equal to the number of actuators and that actuators are aligned with the sensing points.
Figure 12.2: Generic Web Forming Process
The control in the cross direction is generally more difficult than the control in the machine direction [6]. Some of the difficulties associated with the cross directional control problem include:
- the high dimensionality of the cross directional system;
- the high cross directional spatial interaction between actuators;
- the uncertainty in the model;
- the limited control authority of the actuators.
Prerequisites
This virtual laboratory assumes familiarity with several concepts and tools of Systems and Control Engineering. Whenever possible we have tried to include illustrative examples of key issues that the students are encouraged to fully understand to achieve the learning objectives of this virtual laboratory.
The background knowledge that students are assumed to have include:
- Design of PI controllers
- Basic matrix analysis; including matrix manipulation, transpose and inverse of a matrix
- Singular value analysis
Learning Objectives
The learning objectives of this virtual laboratory are:
- Exposure to a realistic multivariable control problem.
- Study the interaction between actuators which is typical of web forming processes.
- Study of the longitudinal dynamics (also known as Machine Direction dynamics) of the process.
- Application of naive PI SISO control to a MIMO plant.
- Decoupling and diagonalised PI control for MIMO plants.
This laboratory would be suitable for people who have taken, or who are currently taking, a course on multivariable control.
