Question 10.3.8: The drive system for one link of a robot arm is illustrated ......
The drive system for one link of a robot arm is illustrated in Figure 10.3.13. The equivalent inertia of the link and all the drive components felt at the motor shaft is I_e. Gravity produces an opposing torque that is proportional to sin θ but which we model as a constant torque T_d felt at the motor shaft (this is a good approximation if the change in θ is small). Neglect friction and damping in the system. Develop the block diagram of a proportional control system using an armature-controlled motor for this application. Assume that motor rotation angle θ_m is measured by a sensor and is related to the arm rotation angle θ by θ_m = Nθ, where N is the gear ratio.
As shown in Example 3.5.5, t the mechanical subsystem is described by
I_e \frac{d^2 \theta_m}{d t^2}=T-\frac{1}{N} T_d (1)
where the motor torque is T = K_T i_a. The system is like that shown in Figure 10.3.4. The block diagram can be obtained by modifying Figure 10.3.8 using equation (1) and collecting the various gains into one gain: K_P = K_{tach}K_1K_a. The resulting diagram is shown in Figure 10.3.14. Note that the system actually controls the motor rotation angle, so the arm angle command θ_r must be converted to the motor angle command θ_{mr}.
