The dynamic equation for a 1-DOF (P) joint-link pair actuated by a linear cylinder (not a DC motor) is given as: N = mä+bx+ kx where x is the link offset (d in lecture notes), m = 2 kg, b = 6 Nm/s, and k = 4 N/m (damping is due to the viscous friction acting on the (P) joint and k is due to the structural stiffness of the actuator and link). You are asked to design a PD controller for a set-point control problem where x, (see block diagram below) is the desired set point. Since the lowest structural resonance frequency is known to be at w, = 8 rad/s, determine the proportional (Kp) and derivative gains (Kd) of a PD controller that results in a critically damped resonance free system (hint: For a resonant free system, rule of thumb is w <»,/2). Robotics 2/4/202 Berke Gür Question 3 (cont.) (s)'x E(s) N (s) 1 X (s) K, +K„s ms² + bs + k Actuator & PD Controller Manipulator

The dynamic equation for a 1-DOF (P) joint-link pair actuated by a linear cylinder (not a DC motor) is given as: N = mä+bx+ kx where x is the link offset (d in lecture notes), m = 2 kg, b = 6 Nm/s, and k = 4 N/m (damping is due to the viscous friction acting on the (P) joint and k is due to the structural stiffness of the actuator and link). You are asked to design a PD controller for a set-point control problem where x, (see block diagram below) is the desired set point. Since the lowest structural resonance frequency is known to be at w, = 8 rad/s, determine the proportional (Kp) and derivative gains (Kd) of a PD controller that results in a critically damped resonance free system (hint: For a resonant free system, rule of thumb is w <»,/2). Robotics 2/4/202 Berke Gür Question 3 (cont.) (s)'x E(s) N (s) 1 X (s) K, +K„s ms² + bs + k Actuator & PD Controller Manipulator

Power System Analysis and Design (MindTap Course List)

6th Edition

ISBN:9781305632134

Author:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma

Publisher:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma

Chapter11: Transient Stability

Section: Chapter Questions

Problem 11.18P

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