(Solved): Prelab The open-loop system dynamics model for the NASA eight-axis Advanced Research Manipulator II ...

Prelab The open-loop system dynamics model for the NASA eight-axis Advanced Research Manipulator II (ARM II) electromechanical shoulder joint/link, actuated by an armature-controlled dc servomotor is shown in Figure P8.22. The ARM II shoulder joint constant parameters are $K_a=12,L=0.006\mathrm{H},R=1.4?$, $K_b=0.00867,n=200,K_m=4.375,J=J_m+J_L/n^2,D=D_m+D_L/n^2,J_L=1,D_L=0.5,J_m=$ 0.00844 , and $D_m=0.00013$ (Craig, 2005), (Nyzen, 1999), and (Williams, 1994). a. Obtain the equivalent open-loop transfer function, $G(s)=\frac{{?}_L(s)}{V_{ref}(s)}$. b. The loop is to be closed by cascading a controller, $G_c(s)=K_{D}s+K_P$, with $G(s)$ in the forward path forming an equivalent forward-transfer function, $G_e(s)=G_c(s)G(s)$. Parameters of $G_c(s)$ will be used to design a desired transient performance. The input to the closed-loop system is a voltage, $V_I(s)$, representing the desired angular displacement of the robotic joint with a ratio of 1 volt equals 1 radian. The output of the closed-loop system is the actual angular displacement of the joint, ${?}_L(s)$. An encoder in the feedback path, $K_e$, converts the actual joint displacement to a voltage with a ratio of 1 radian equals 1 volt. Draw the closed-loop system showing all transfer functions. c. Find the closed-loop transfer function. FIGURE P8.22 Open-loop model for ARM ll