A precision speed control system (Figure P7.12) is required for a platform used in gyroscope and inertial system testing where a variety of closely controlled speeds is necessary. A direct-drive DC torque motor system was utilized to provide (1) a speed range of 0.01°/s to 600°/s, and (2) 0.1% steady-state error maximum for a step input. The direct-drive DC torque motor avoids the use of a gear train with its attendant backlash and friction. Also, the direct-drive motor has a high-torque capability, high efficiency, and low motor time constants. The motor gain constant is nominally Km = 1.8, but is subject to variations up to 50%. The amplifier gain Ka is normally greater than 10 and subject to a variation of 10%.
(a) Determine the minimum loop gain necessary to satisfy the steady-state error requirement.
(b) Determine the limiting value of gain for stability.
(c) Sketch the roots locus as Ka varies from 0 to ˆž.
(d) Determine the roots when Ka = 40, and estimate the response to a step input.
Figure P7.12
Speed control.

Disturbance Controller R(s) is) Speed (s2) L.H Tachometer