Homework 7, due March 9, 2011.

[goodwine]

Reading: all of Chapter 7, Chapter 8, sections 1-3.

Exercises: 7.12, 7.13, 7.17, 7.20, 8.3 (numbers 8 and 11 only).

Note: there is a typo in 7.12. I'm pretty sure the "5x5" matrix should be "10x10".

[ceramics]

For problem 7.12, since it is a five mass problem, don't we need 10 eigenvalues for the place() command?

[goodwine]

For problem 7.12, since it is a five mass problem, don't we need 10 eigenvalues for the place() command?

Yes. Just select more consistent with the given ones.

[Adam W.]

Professor, using

Code: Select all

place(A,B,P)

apparently only functions for A(nxn) and B(n) with n = 15 (returning an error past that):

Code: Select all

  ??? Error using ==> place at 172
The "place" command could not place the poles at the specified locations. Probable causes include:
* (A,B) is nearly uncontrollable
* The specified locations are too close to each other. 

[/color]
while

Code: Select all

acker(A,B,P)

is said to break down in accuracy past an order of 10, although it can actually compute the values without returning an error statement.

Should we, then, resort to a five-mass system as originally stated?

[goodwine]

Professor, using

Code: Select all

place(A,B,P)

apparently only functions for A(nxn) and B(n) with n = 15 (returning an error past that):

Code: Select all

  ??? Error using ==> place at 172
The "place" command could not place the poles at the specified locations. Probable causes include:
* (A,B) is nearly uncontrollable
* The specified locations are too close to each other. 

[/color]
while

Code: Select all

acker(A,B,P)

is said to break down in accuracy past an order of 10, although it can actually compute the values without returning an error statement.

Should we, then, resort to a five-mass system as originally stated?

Yes, 5 masses is ok.

[sprender]

If you have it, can you post the code that implemented the lqr command? Thanks.

[goodwine]

If you have it, can you post the code that implemented the lqr command? Thanks.

I'll get them posted tomorrow morning.

[goodwine]

If you have it, can you post the code that implemented the lqr command? Thanks.

I'll get them posted tomorrow morning.

Done!

[whawes]

For problem 7.12, do we include the forcing function sin(omega*t) with the stabilizing force?

i.e.,

Code: Select all

 w = 0.25;
    f = sin(w*t);
    xdot = A*x + [0;(f+k1*x(1)+k2*x(2)+k3*x(3)+k4*x(4)+k5*x(5)+k6*x(6)+k7*x(7)+k8*x(8)+k9*x(9)+k10*x(10));0;0;0;0;0;0;0;0];

[goodwine]

For problem 7.12, do we include the forcing function sin(omega*t) with the stabilizing force?

i.e.,

Code: Select all

 w = 0.25;
    f = sin(w*t);
    xdot = A*x + [0;(f+k1*x(1)+k2*x(2)+k3*x(3)+k4*x(4)+k5*x(5)+k6*x(6)+k7*x(7)+k8*x(8)+k9*x(9)+k10*x(10));0;0;0;0;0;0;0;0];

The design of the controller is only to stabilize the system, so the literal answer is no. It would be interesting to see if the controller reduces the effect of the applied force on the motion of the system, however.

[sprender]

For the second part of problem 17 (with damping), can we use a computer to solve for the eigenvalues and just report the normalized vectors in our answer?

[goodwine]

For the second part of problem 17 (with damping), can we use a computer to solve for the eigenvalues and just report the normalized vectors in our answer?

You only need to solve the case with damping numerically. You are to use the undamped cases as a guide since the damping is so light.

[vsteger]

Where do the initial conditions fit in the place() function inputs, if anywhere?

[goodwine]

Where do the initial conditions fit in the place() function inputs, if anywhere?

The place function specifies the eigenvalues, so it has nothing to do with initial conditions.