Category: CDS 101/110 Fall 2003

Identifiers: FN H0 H1 H2 H3 H4 H5 H6 H7 H8 L0.0 L1.1 L1.2 L10.1 L2.1 L2.2 L3.1 L3.2 L4.1 L4.2 L5.1 L5.2 L6.2 L8.1 L9.1 L9.2

Questions

• Will we get extra credit for the "Optional" homework questions?

• Homework #4 issues

• Will we get extra credit for the "Optional" homework questions?
  Submitted by: lars
  Submitted on: October 20, 2003
  Identifier: H0 , H3 , H4

  Yes, extra credit will be granted for proper completion of the optional questions, and partial credit will be granted at the discretion of the grading TA. Your total score, however, will not exceed the total possible score from the required homework problems.

  For example, if you get 32 out of a total possible 40 points from the required questions, and get 10 points from an optional question, your total score will be 40 out of 40.

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• Homework #4 issues
  Submitted by: mreiser
  Submitted on: October 22, 2003
  Identifier: H4

  On Problem #2 the inverted pendulum:

  1) There is a mistake in the figure, which shows theta defined as zero in the up position, this is inconsistent with the equations of motion which have theta = pi defined as up. Please use theta = pi as the equilibrium point you need to stabilize.

  2) Also in the problem statement, part (c) there is a correction for the non-zero equilibrium point listed as u = -K(x-x0), this should be x_e, the equilibrium point, and not x0, the initial condition. Since these simulations are initialized near the equilibrium point this does not actually prevent convergence, but it can be confusing.

  3) The closed loop simulation will give an error about unsolvable algebraic loops if the simulation is started far away from the equilibrium point, which is the default on the model (all ic's are 0). To set initial condition, specify an i.c. value for each of the 4 integrators (one for each state).

  If anyone has compatibility issues running the .mdl file on an older version of Simulink, please email me (mreiser@caltech), and I'll generate a model that is compatible with the older simulink.

  Problem #3 - discrete time system:

  You are supposed to solve for the general output of the system in part (c). Some of you have discovered that this equation was actually given in Lecture 2.2 (by D. MacMartin). For parts (a) & (b) do not use this equation , you should be able to answer these questions without using the general solutions. For part (c), please derive this formula.

  Note that in (b) the initial condition should be z_0, not x_0. To solve for the transient response due to z_0, make sure you have zero input (u = 0).

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