Controlling the Position of a Robot Arm Link 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 Ie. Gravity produces an opposing torque that is proportional to sin θ but which we

Question

Controlling the Position of a Robot Arm Link

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 [latex]I_{e}[/latex]. Gravity produces an opposing torque that is proportional to [latex]\sin θ [/latex] but which we model as a constant torque [latex]T_{d}[/latex] 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 [latex]θ_{m}[/latex] is measured by a sensor and is related to the arm rotation angle θ by [latex]θ_{m} = N θ[/latex], where N is the gear ratio

Accepted Answer

The dynamics of the mechanical subsystem are described by
[latex]I_{e} \frac{d^{2} θ_{m}}{d t^{2}} = T − \frac{1}{N} T_{d} [/latex] (1)
where the motor torque is [latex]T = K_{T} i_{a}[/latex]. 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: [latex]K_{P} = K_{tach} K_{1} K_{a}[/latex]. 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 [latex]θ_{r}[/latex] must be converted to the motor angle command [latex]θ_{mr}[/latex].

Question 10.3.8: Controlling the Position of a Robot Arm Link The drive syste...

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