# For a paper processing plant, it is important to maintain a constant tension on the continuous sheet

## Question:

Figure P4.10

Paper tension control.

Therefore, the measure of the tension is described by the relation 2T(s) = k1y, where y is the deviation from the equilibrium condition, and T(s) is the vertical component of the deviation in tension from the equilibrium condition. The time constant of the motor is Ñ‚ = La/Ra, and the linear velocity of the wind-up roll is twice the angular velocity of the motor, that is, v0(t) = 2w0(t). The equation of the motor is then

where Î”T = a tension disturbance.

(a) Draw the closed-loop block diagram for the system, including the disturbance Î”T(s).

(b) Add the effect of a disturbance in the wind-off roll velocity Î”V1(s) to the block diagram. (c) Determine the sensitivity of the system to the motor constant Km.

(d) Determine the steady-state error in the tension when a step disturbance in the input velocity, Î”V1(s) = A/s, occurs.

## Step by Step Answer:

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