A very interesting and useful velocity control system has been designed for a wheelchair control system. We want to enable people paralyzed from the neck down to drive themselves in motorized wheelchairs. A proposed system utilizing velocity sensors mounted in a headgear is shown in Figure P6.8.The headgear sensor provides an output proportional to the magnitude of the head movement. There is a sensor mounted at 90° intervals so that forward, left, right, or reverse can be commanded. Typical values for the time constants are Ñ‚1 = 0.5 s, Ñ‚3 = 1 s, and Ñ‚4 = 1/4 s.
(a) Determine the limiting gain K = K1K2K3 for a stable system.
(b) When the gain K is set equal to one-third of the limiting value, determine whether the settling time (to within 2% of the final value of the system) is less than 4 s.
(c) Determine the value of gain that results in a system with a settling time of 4 s. Also, obtain the value of the roots of the characteristic equation when the settling time is equal to 4 s.
Figure P6.8
Wheelchair control system.

Sensor Wheelchair dynamics Amplifier Head in hat nod K1 velocity Velocity )(+1)