Q1. Consider the following nonlinear dynamic model of a single-link flexible manipulator: lĝ1 + MgL sin qı + k(q1 – 92) = 0 Jä2 – k(q1 – 92) = u, where q1, 92 are angular positions, I,J > 0 are moments of inertia, k > 0 is a spring constant, M is the total mass, L is a distance, g is the gravitational constant, and u is a torque input. a) Choose state variables for this system and write down the nonlinear state equations. b) Choose I = k = L = 1, g = 9.81, J 0.5, and M = -. Find the equilibrium points of this 9.81 system and linearize the system about the equilibrium points. c) Analyze stability of the system. Give complete reasoning.

Q1. Consider the following nonlinear dynamic model of a single-link flexible manipulator: lĝ1 + MgL sin qı + k(q1 – 92) = 0 Jä2 – k(q1 – 92) = u, where q1, 92 are angular positions, I,J > 0 are moments of inertia, k > 0 is a spring constant, M is the total mass, L is a distance, g is the gravitational constant, and u is a torque input. a) Choose state variables for this system and write down the nonlinear state equations. b) Choose I = k = L = 1, g = 9.81, J 0.5, and M = -. Find the equilibrium points of this 9.81 system and linearize the system about the equilibrium points. c) Analyze stability of the system. Give complete reasoning.

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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