2 chapter 2 review dynamics

SYSTEM DYNAMICS & CONTROL CHAPTER REVIEW DYNAMICS LAGRANGE’S METHOD Dr Vo Tuong Quan HCMUT - 2011 Lagrange’s Method Lagrange’s method: Calculate the kinetic energy of system (K or T) K  mv Calculate the rotation kinetic energy of system (K or T) K Rot  I Calculate the potential energy of the system (P or V or U) P  mgh  Lagrange equation: L = K – P Then: Calculate the equation (Called Lagrange’s Equation)  2011 – Vo Tuong Quan d  L  L  0   dt  q  q Lagrange’s Method Mass Spring system K  mx 2 P  kx 2  L  K  P  mx  kx 2  2011 – Vo Tuong Quan d x  m  kx  dt Lagrange’s Method Multi degree of freedom system  2011 – Vo Tuong Quan Lagrange’s Method Simple pendulum  We need to transform the coordinate  2011 – Vo Tuong Quan Lagrange’s Method Simple pendulum  2011 – Vo Tuong Quan Lagrange’s Method Double pendulum  2011 – Vo Tuong Quan Lagrange’s Method Double pendulum  2011 – Vo Tuong Quan Lagrange’s Method Double pendulum  2011 – Vo Tuong Quan Lagrange’s Method Double pendulum 10  2011 – Vo Tuong Quan Lagrange’s Method Using Lagrange’s method to calculate the dynamic equation of two-link elbow planar arm 11  2011 – Vo Tuong Quan Lagrange’s Method 12  2011 – Vo Tuong Quan Lagrange’s Method 13  2011 – Vo Tuong Quan Lagrange’s Method 14  2011 – Vo Tuong Quan Lagrange’s Method 15  2011 – Vo Tuong Quan Lagrange’s Method 16  2011 – Vo Tuong Quan Lagrange’s Method Modeling and designing a PID controller for an Inverted pendulum (M) mass of the cart (m) mass of the pendulum (b) coefficient of friction for cart (l) length to pendulum center of mass (I) mass moment of inertia of the pendulum (F) force applied to the cart (x) cart position coordinate () pendulum angle from vertical (down) Source: http://ctms.engin.umich.edu/CTMS/index.php?example=InvertedPendulum§ion=SystemModeling 17  2011 – Vo Tuong Quan Lagrange’s Method 18  2011 – Vo Tuong Quan ... arm 11  20 11 – Vo Tuong Quan Lagrange’s Method 12  20 11 – Vo Tuong Quan Lagrange’s Method 13  20 11 – Vo Tuong Quan Lagrange’s Method 14  20 11 – Vo Tuong Quan Lagrange’s Method 15  20 11 – Vo... (Called Lagrange’s Equation)  20 11 – Vo Tuong Quan d  L  L  0   dt  q  q Lagrange’s Method Mass Spring system K  mx 2 P  kx 2  L  K  P  mx  kx 2  20 11 – Vo Tuong Quan d x  m... pendulum  20 11 – Vo Tuong Quan Lagrange’s Method Double pendulum  20 11 – Vo Tuong Quan Lagrange’s Method Double pendulum  20 11 – Vo Tuong Quan Lagrange’s Method Double pendulum 10  20 11 – Vo