For the system of Problem P10.30, use a phase-lag compensator and attempt to achieve a phase margin of approximately 50°. Determine the actual overshoot and peak time for the compensated system.

Problem P10.30

An automated guided vehicle (AGV) can be considered as an automated mobile conveyor designed to transport materials. Most AGVs require some type of guide path. The steering stability of the guidance control system has not been fully solved. The slight "snaking" of the AGV about the track generally has been acceptable, although it indicates instability of the steering guidance control system [9].

Most AGVs have a specification of maximum speed of about 1 m/s, although in practice they are usually operated at half that speed. In a fully automated manufacturing environment, there should be few personnel in the production area; therefore, the AGV should be able to be run at full speed. As the speed of the AGV increases, so does the difficulty in designing stable and smooth tracking controls.

A steering system for an AGV is shown in Figure P10.30, where τ₁ = 40 ms and τ₂ = 1 ms. We require that the velocity constant K_v be 100 so that the steady state error for a ramp input will be 1 % of the slope of the ramp. Neglect τ₂ and design a lead compensator so that the phase margin is

Attempt to obtain the two limiting cases for phase margin, and compare your results for the two designs by determining the actual percent overshoot and settling time for a step input.