The 6DOF Robot's base uses a direct drive (i.e. no gearbox) motor for which its dynamics can be linearised and are descr

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The 6dof Robot S Base Uses A Direct Drive I E No Gearbox Motor For Which Its Dynamics Can Be Linearised And Are Descr 1 (164.77 KiB) Viewed 29 times

The 6DOF Robot's base uses a direct drive (i.e. no gearbox) motor for which its dynamics can be linearised and are described by the following linear time-invariant ordinary differential equations: Where and Im L A = dw (t) dt di(t) dt de (t) dt = = Km i(t) Kw(t) - Ks0(t)... (1) u(t) - Ri(t) - KEW(t) w(t). i(t) is the motor's armature current in amps (A), Im is the robot's base moment of inertia of 0.01 kgm², Km is the motor torque constant of 0.1 Nm/A, K is the viscous friction constant of 0.05 N/m/s, K is the first link stiffness of zero N/radian in this case, R is the motor's electrical resistance of 202, KE is the motor's back EMF constant of 0.01 V/m/s, L is the motor's armature electrical inductance of 0.001H. i) Show that the differential equations of the open-loop system for the inner-loop angular velocity controller (i.e. where THE OUTPUT SIGNAL y(t) = w(t)) can be expressed as the following continuous time state and output equations: x(t) = A x(t) + Bu(t) and y(t) = Cx(t) where u(t) is the motor input vector, x(t) = [ w(t), i(t), 0(t)] ¹ is the system state vector and y(t) is the system output vector for the inner-loop controller and and C = [100] -5 10 0 -10 -2000 0 0 1 - [1000] Y(s) U(s) B = ii) Using the state and output equations derived in (i), show that the open-loop transfer function of the system is given by: 10000 s² + 2005s + 10100 iii) Again using the state and output equations from (i), derive the system's poles and zeros and state the order and relative degree of the system.