A HelpMate transport robot shown below is used to deliver goods in a hospital setting. The robot can deliver food, drugs, laboratory materials, and patients’ records. Given the simplified block diagram of the robot’s bearing angle control system,

a. Find the closed-loop transfer function.

b. Select a gain K so that the closed-loop system is stable and the dominant complex conjugates have a negative real part close to -1.

TRC Actual bearing Vehicle angle p(s) s(s +3) Desired Motor and controller Actual wheel position angle bearing Computer Desired Wels) + wheel position +, s(s +2)