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# Tachometer Feedback in a Reel To Reel Control System

IP.com Disclosure Number: IPCOM000083123D
Original Publication Date: 1975-Apr-01
Included in the Prior Art Database: 2005-Mar-01
Document File: 3 page(s) / 47K

IBM

## Related People

Hansen, NH: AUTHOR

## Abstract

The system, as depicted herein, describes a reel-to-reel control system with control loops for enabling low-speed operation (i.e., speed below 20 RPM of the DC motors. DC motors generally operate at speeds of 100 to 5,000 RPM. At speeds below 20 RPM, DC motors are susceptible to speed variations resulting from parameter changes such as drag and torque constant fluctuations. The speed of a DC motor may be described by the following differential equations: (i) e = L di over dt + Ri + K(m)w (ii) Kmi = J dw over dt + Bw + T(L) where: K(m) is the motor constant. B is the viscous motor drag. T(L) is the load torque.

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Tachometer Feedback in a Reel To Reel Control System

The system, as depicted herein, describes a reel-to-reel control system with control loops for enabling low-speed operation (i.e., speed below 20 RPM of the DC motors. DC motors generally operate at speeds of 100 to 5,000 RPM. At speeds below 20 RPM, DC motors are susceptible to speed variations resulting from parameter changes such as drag and torque constant fluctuations. The speed of a DC motor may be described by the following differential equations: (i) e = L di over dt + Ri + K(m)w (ii) Kmi = J dw over dt + Bw + T(L) where: K(m) is the motor constant. B is the viscous motor drag. T(L) is the load torque.

At normal speeds, the back EMF (K(m)w) of Equation (i) accounts for a substantial part of the applied voltage e. This back EMF gives the motor some speed control. At low speeds, however, the back EMF is negligible, which means small load torque can cause large speed variations. At high speeds, motor inertia has a speed-stabilizing effect similar to that of the back EMF.

For low-speeds operation, consider Fig. 1 where e = k (v-K(T)W). Using this in Equation i, provides: (iii) K(v) = L di over dt + Ri + (KK(t) + K(m))w where KK(t) represents loop gain of a feedback system.

The loop gain has the same velocity-stabilizing effect on the motor as does the back EMF. If the loop gain could be increased without limit, the motor speed would be controlled only by the tachometer signal in a feedback loop. However, it may be shown that motor resonance is the limiting factor for the loop gain.

The loop speed operation of the motor can be further improved by selecting the proper compensating circuit to be used, as shown in Fig. 2. Many compensating circuits could be used. In selecting the proper one, first the gain and phase margin of the loop needs to be checked for stability; then the speed- torque transfer function is investigated for loop sensitivity to torque disturbances.

The low-speed control loop is incorporated in Fig. 2. Reel-to-reel transport 10 having supply spool 26 and take-up spool 28 is driven by DC motor 14 and DC motor 12, respective...