Tension and Speed Setpoint Regulation for Axially Moving Materials

Abstract:

During continuous manufacture of axially moving materials such as fiber, paper, foil, and film, accurate speed and tension control are essential. In this project, control torques applied to rollers at the boundaries of an axially moving system regulate the material speed and tension using speed and tension sensors for each roller. Given a distributed parameter model, Lyapunov techniques are used to develop a model-based boundary control system that exponentially stabilizes the material tension and speed at desired setpoints and stabilizes longitudinal vibration. Experimental results compare the tension and speed setpoint regulation provided by the proposed control strategy with proportional plus integral speed control and proportional tension feedback.

Experimental Setup:

The experimental test-stand consists of an elastic rubber belt moving axially over two pulleys actuated by brushed DC motors. The four tension sensors and roller assemblies laterally position the moving material and provide measurements of the forward boundary tensions and the back boundary tensions used by the controller. The brushed DC motors have 1024 counts per revolution encoders that measure the angular displacements of the rotors. The Transducer Techniques' MLP-10 tension sensors (measurement range: 40 [N]) are positioned to ensure maximum surface contact between the material and the pulleys in order to prevent slip. The angles subtended by the material as it approaches and leaves the tension sensor are set equal to produce a resultant force along the measurement axis of the tension sensor, avoiding potential damage to the tension sensor from an induced bending moment.

A Pentium 266 MHz PC running QNX (a real-time, micro-kernel-based operating system) hosts the control algorithm. A graphical user-interface developed in-house, provides an environment to write the control algorithm in the `C' programming language. It also provides features such as on-line graphing and allows the user to vary control gains without having to recompile the program. The MultiQ I/O board provides for the data transfer between computer subsystem and the electrical interface. Two A/D channels are used to sense the currents flowing through the stator windings of the DC motors, and four additional A/D channels are used to read in the tension sensor signals. Two D/A channels output voltages that drive the DC motors. These voltages go through two stages of amplification, consisting of OP07C operational amplifiers and Techron linear power amplifiers, for the first and second stages, respectively. High-gain current feedback ensures that the required torque is applied to the motors. All controllers are implemented using a sampling period of 0.5 [m-sec]. The axial speed of the material and the derivative of the boundary tension at x = 0 are obtained using a filtered backwards difference algorithm.

Experimental Results:

The objective of the experiment is to regulate the material tension at 8 [N] and move the material according to a smooth, exponentially stepped, desired axial speed setpoint trajectory. In order to mimic real-world industrial processes (such as high-speed label printing), the desired speed of the material is aggressively driven to 0 [m/s] and back to 0.75 [m/s] within a time duration of 0.5 [sec] and is repeated every 10 [sec]. Process-line disturbances leading to a sudden change in material tension are also simulated by applying a constant reverse torque on the motor at x = 0 for a duration of 0.5 [sec] at 10 [sec] intervals. The control is initially applied after a one second time delay. Three experiments are performed.

• PI Speed - Constant Bias Torque Control: PI speed controller consists of a constant open-loop bias torque to the motor at x = 0, and PI feedback of the material speed at x=L.
• PI Speed - P Tension Control: Controller consists of a PI speed error feedback at x = L and proportional tension error feedback at x = 0.
• Full-Order Control: Controller consists of PI speed error feedback at x = L, proportional tension error feedback at x = 0, tension and tension rate feedforward terms at x = 0, and boundary coupling terms (i.e., controller at x = 0 contains information from terms at x = L).