Figure P11.35 a is the circuit diagram of a speed-control system in which the dc motor voltage va is supplied by a generator driven by an engine. This system has been used on locomotives whose diesel engine operates most efficiently at one speed. The efficiency of the electric motor is not so sensitive to speed and thus can be used to drive the locomotive at various speeds. The motor voltage va is varied by changing the generator input voltage vf. The voltage va is related to the generator field current if by va = Kjif.
Figure P11.35 b is a diagram of a feedback system for controlling the speed by measuring it with a tachometer and varying the voltage uf. Use the following values in SI units.
Lf = 0.2 Rf = 2 Kt = 1
La = 0.2 Ra = 1 Kb = KT = 0.5
Kf = 50 I = 10 c = 20
Develop a state variable model of the plant that includes the generator, the motor, and the load. Include the load torque TL as a disturbance.
Develop a proportional controller assuming all the state variables can be measured. Analyze its steady-state error for a step command input and for a step disturbance.
Figure P11.35