The linear model of a robot arm system being driven by a DC motor, is shown in Fig. P 9.9 (a). The system variables and parameters are given below:

(a) Write equations describing dynamics of system with \(i_{a}(t)\) and \(\mathrm{T}_{\mathrm{L}}(t)\) as inputs and \(\theta_{m}(t)\) and \(\theta_{\mathrm{L}}(t)\) as outputs.
(b) Sketch signal flow graph choosing \(\mathrm{I}_{a}(s), \mathrm{T}_{\mathrm{L}}(s), \theta_{m}(s)\) and \(\theta_{\mathrm{L}}(s)\) as node variables.

Transcribed Image Text:

DC motor T = motor torque = K ia m K = torque constant ia = armature current of motor J = motor inertia m Bm m . m = motor friction coefficient = motor shaft displacement Robot arm J = arm inertia B = arm friction coefficient 0 arm displacement K = spring constant of shaft between the motor and arm B = friction coefficient of shaft between motor and arm T = disturbance torque on arm