Category: CDS 110 Winter 2004

Identifiers: H10 H11 H14 H9 L1.1 L11.1

Questions

• Does the CDS110b FAQ site work?

• What is the definition of "argmin" ?

• Do we have to do problem 1-e and 1-f analytically?

• What should we plot for HW9, part 1 (f)?

• State space relation for the integrator in Pb 2(d)

• What is the input for HW9, part 1 (f)?

• Joint probability density function of independent continuous random varibles

• Errata for the Spectral Factorization handout

• Errata for HW 14 on C(s)

• Does the CDS110b FAQ site work?
  Submitted by: waydo
  Submitted on: January 6, 2004
  Identifier: L1.1

  It sure does!

  [Back to Top]

• What is the definition of "argmin" ?
  Submitted by: waydo
  Submitted on: January 6, 2004
  Identifier: L11.1

  The argmin of a function is the argument that minimizes it (similar for argmax). For example, if you are minimizing a function f(x) over x, min_x f(x) is the minimum value and argmin_x f(x) is the value of x at which f(x) is minimized. In other words, min_x f(x) = f( argmin_x f(x) )

  [Back to Top]

• Do we have to do problem 1-e and 1-f analytically?
  Submitted by: waydo
  Submitted on: January 8, 2004
  Identifier: H9

  No. You can pick a value for m (say m=1) and do parts (e) and (f) numerically using MATLAB.

  [Back to Top]

• What should we plot for HW9, part 1 (f)?
  Submitted by: waydo
  Submitted on: January 9, 2004
  Identifier: H9

  The "transient response" you should plot is the step response. You can pick some values of q1 and q2 from part (e) that give you interesting plots (you should pick plots that differ significantly from one another if you can). A plot of z only (not zdot) is fine for this part as well.

  [Back to Top]

• State space relation for the integrator in Pb 2(d)
  Submitted by: atiwari
  Submitted on: January 11, 2004
  Identifier: H9

  The state space relation for the integrator should be read as
  dx_i/dt = r - y

  [Back to Top]

• What is the input for HW9, part 1 (f)?
  Submitted by: waydo
  Submitted on: January 12, 2004
  Identifier: H9

  Now that we have a closed-loop controller, we want to give it reference positions to track, so a step input is r = [1,0]' and the control signal will then be u = K(r-y).

  [Back to Top]

• Joint probability density function of independent continuous random varibles
  Submitted by: atiwari
  Submitted on: January 19, 2004
  Identifier: H10

  Let X and Y be two mutually independent continuous random variables, with probability density functions p₁(x) and p₂(y) respectively.
  Then the joint probability density function of X and Y is given by:
  p(x,y) = p₁(x)p₂(y)

  [Back to Top]

• Errata for the Spectral Factorization handout
  Submitted by: waydo
  Submitted on: January 25, 2004
  Identifier: H11

  Both the description in Friedland _and_ the spectral factorization handout have some typos. The handout is basically correct except that the result should have z_i = sqrt( - α_i ) p_i = sqrt( - β_i ) Sorry for the confusion. A corrected handout should be posted soon.

  [Back to Top]

• Errata for HW 14 on C(s)
  Submitted by: macmardg
  Submitted on: February 20, 2004
  Identifier: H14

  Note that the formula for C(s) in the 3rd problem is incorrect in the original (the pdf on the web has been updated). The correct formula is C(s)=(J/r)k^2alphafrac{s+k/alpha}{s+kalpha}

  [Back to Top]