Control systems for maintaining constant tension on strip steel in a hot strip finishing mill are called "loopers." A typical system is shown in Figure P7.16. The looper is an arm 2 to 3 feet long with a roller on the end; it is raised and pressed against the strip by a motor [18]. The typical speed of the strip passing the looper is 2000 ft/min. A voltage proportional to the looper position is compared with a reference voltage and integrated where it is assumed that a change in looper position is proportional to a change in the steel strip tension. The time constant Ñ‚ of the filter is negligible relative to the other time constants in the system.
(a) Sketch the root locus of the control system for 0 (b) Determine the gain Ka that results in a system whose roots have a damping ratio of ζ = 0.707 or greater.
(c) Determine the effect of Ñ‚ as Ñ‚ increases from a negligible quantity.
Figure P7.16
Steel mill control system.

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