For this project, we will use the specific robot joint control system shown in Figure $4.$

Figure $4.$ Example of robot joint control system

a$)$ Provide a detailed description of the feedback system

b$)$ Give detailed equations of the motor actuating the robot joint; provide the electrical equations and the mechanical equations of the motor and justify the block diagram of the motor subsystem.

c$)$ In the block diagram of Figure $4,$ replace the compensator with a gain K and generate the root locus of the uncompensated system.

d$)$ Develop design performance requirements for this control system application. Explain and justify your design requirements.

e$)$ Design a PD controller to achieve your design requirements specified in $($d$).$