A pulley with a torque drive is shown in Figure 1.25. The goal is to maintain the prescribed profile of the torque of the pulley so that the force in the cable lifting a load will be as desired. The...

A pulley with a torque drive is shown in Figure 1.25. The goal is to maintain the prescribed profile of the torque of the pulley so that the force in the cable lifting a load will be as desired. The motor torque control loop is shown in Figure 1.26. The plant dynamics, i.e., the transfer function from torque to the angle, is out of the feedback loop since the torque sensor is measuring the pulley torque directly at the motor.

Figure 1.25

Figure 1.26

The torque sensor gain coefficient is 0.1 V/Nm. The controller transfer function is C(s)=0.8(s+15)/(s+100). The actuator (a motor with an appropriate driver) is a voltage-controlled torque source with a transfer function of 30 Nm/V. The disturbance torque due to the motor imperfections is 0.1 Nm. a. Find the loop transfer function and the input–output transfer function. Plot Bode diagrams for the loop transfer function and for the input–output transfer function. Plot an L-plane Nyquist diagram. Check whether the diagram enters the area surrounded by the 6 dB line on the Nichols chart. Plot the torque time response for the 0.01 V step command. Plot the torque time response to the disturbance torque as a step function. b. Assuming that the pulley radius is 0.1 m and the load mass is 2 kg, i.e., the plant moment of inertia is 0.02 kg × m2, i.e., the plant is a double integrator and its transfer function is 50/s2, plot the position time history in response to a step torque command (assume that at zero time the load is on the ground). c. Create a Simulink model. Include in the driver model a saturation with threshold 2 kW. Plot output responses to command steps of different amplitude. Explain the results. d. Using Simulink, plot the position time history in response to the following command: 1 V for the duration of 2 s, 0 V for the duration of the next 2 s, and −1 V for the duration of the next 2 s. e. Make a schematic drawing of torque control in a drilling rig. f. Make a schematic drawing of torque control in a lathe, for keeping constant the force applied to the cutting tool (there could be several possible kinematic schemes).