Consider the elementary motor-speed regulator scheme shown in Figure P16.2.23 for a separately excited dc motor, whose armature is supplied from a solid-state controlled rectifier. The motor speed is measured by means of a dc tachometer generator, and its voltage et is compared with a reference voltage ER. The error voltage ER −et is amplified and made to control the output voltage of the power-conversion equipment, so as to maintain substantially constant speed at the value set by the reference voltage. Let the armature-circuit parameters be Ra and La, and the speed–voltage constant of the motor be Km, with units of V·s/rad. Assume that the combination of A and P is equivalent to a linear controlled voltage source vs = KA (error voltage), with negligible time lag and gain KA. Assume also that the load torque TL is independent of the speed, with zero damping. Neglect no-load rotational losses.
(a) Develop the block diagram for the feedback speed-control system with ER/Kt, the steady state no-load speed setting, as input, and Ωm as output. Kt is the tachometer speed–voltage constant in V/(r/min).
(b) With TL = 0, evaluate the transfer function Ωm/ER.
Save your time - order a paper!
Get your paper written from scratch within the tight deadline. Our service is a reliable solution to all your troubles. Place an order on any task and we will take care of it. You won’t have to worry about the quality and deadlinesOrder Paper Now
(c) With ER = 0, obtain the transfer function Ωm/TL.
(d) Find the expressions for the under damped natural frequency ωn, the damping factor α, and the damping ratio ξ = α/ωn.
(e) For a step input ∆ER, obtain the final steady state response ∆ωm(∞), i.e., evaluate ∆ωm(∞)/∆ER.
(f) Evaluate ∆ωm(∞)/∆TL for the step input ∆T=of a load torque.