A system consists of two electric motors that are coupled by a continuous flexible belt. The belt also passes over a swinging arm that is instrumented to allow measurement of the belt speed and tension. The basic control problem is to regulate the belt speed and tension by varying the motor torques.
An example of a practical system similar to that shown occurs in textile fiber manufacturing processes when yarn is wound from one spool to another at high speed. Between the two spools, the yarn is processed in a way that may require the yarn speed and tension to be controlled within defined limits. A model of the system is shown in Figure P2.32. Find Y2(s)/R1(s), Determine a relationship for the system that will make Y2 independent of R1.
Figure P2.32
A model of the coupled motor drives.

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-H2(3) Gts) Gi(s) GALs) Rj(s) Speed Speed -1 Ggls) G7(t) input Ga(s) Gs(a) Gots) Tension contrnl inpat Tensior Hi(s)