2.004 | Spring 2003 | Undergraduate

Modeling Dynamics and Control II


Day # Lectures Topics
1-3 Brief Review of 2.003 Uniaxial motion, fixed-axis rotation; first and second order systems; natural and forced response; transfer functions, zeroes, poles; elementary control: open-loop, closed-loop; closing the loop alters the natural and forced response characteristics; stability and instability.
4-5 Impulse Response Collisions; conservation of momentum; conservation of energy; coefficient of restitution; bouncing ball in the presence of air drag.
6-9 Plane-motion Kinematics of Rigid Bodies Combined translation and rotation of rigid body; angular velocity; generalized coordinates; common constraints. Kinetic energy of rigid body.
10-15 Plane-motion Dynamics of Rigid Bodies Linear and angular momentum principles for systems including rigid bodies; derivingequations of motion using momentum principles; conservation of energy; linearization in the neighbourhood of equilibrium, stability and instability; rolling cylinder inside rollinghoop; inverted pendulum on cart.
16-18 Vibrations of Two-Degree-of-Freedom Systems Natural modes and the eigenvalue problem; free and forced response to harmonic excitation; damping effects; Bode plots.
19-24 Control of Systems with Rigid Bodies Actuators, sensors; P, D, I feedback-loop strategies; root-locus design; application to inverted pendulum on cart, automatic self-balancing scale; frequency-domain design methods, gain margin, phase margin.