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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

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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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 (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 <w,/2). = 6 Nm/s, and k 4 N/m Robotics 2/4/202 Berke Gür Question 3 (cont.) (8)’X E(s) N (s) 1 X (s) K,+K„s ms“ + bs + k Actuator & PD Controller Manipulator
Transcribed Image Text: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 (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 <w,/2). = 6 Nm/s, and k 4 N/m Robotics 2/4/202 Berke Gür Question 3 (cont.) (8)’X E(s) N (s) 1 X (s) K,+K„s ms“ + bs + k Actuator & PD Controller Manipulator
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