0.8 Phase-lead compensation of a rotational rigid-body system

Phase-lead compensation of a rotational rigid-body system

Objectives

• Use frequency domain techniques to design a phase-lead compensator for a rigid, rotational disk.

Pre-lab

• Derive the equations of motion for the 1DOF rotational system that you will control in this lab. The plant configuration is shown below. The disk will be loaded with four $0.5kg$ brass weights placed at a distance $9.0cm$ from the center of rotation.

• Design and simulate a phase-lead compensator that satisfies the following performance specifications:
  • Zero steady-state error to a step input.
  • Gain margin $\ge 15\hspace{0.17em}db$
  • Phase Margin $\ge 45^o$

Lab procedure

• Configure the plant for this experiment.
• Code your phase-lead compensator into the control loop VI.
• Perform a 3000 count step input, and save the plot.
• Perform a ramp input with a velocity of 1000 counts/second and a dwell time of 3 seconds. Save the plot.

Post-lab

• What was the system's steady-state error to the ramp input? What would you expect it to be for a parabolic input?
• Explain how gain margin and phase margin relate to a system's stability.