Due in class (at 10:00) on July 15
(Note: You can focus on internal stability only)- Determine acceptable closed-loop system eigenvalues to achieve the required behaviour in (a) and (b) below.a) Determine the eigenvalues for a second-order approximation to a first-order system with a time constant of 0.5 s. We can generate such an approximation by determining the position of the first order pole, then add an additional pole on the real-axis, 10 times further from the origin than the first order pole. Plot step responses for both systems using Matlab.
b) Determine the eigenvalues for a second-order system with 6% overshoot and a settling time of 4 s. Approximate this system with a third-order system and indicate the location of its additional eigenvalue (apply the rule of thumb that the third pole should be 10 times further to the left than the dominant second order pair). Plot step responses for both systems using Matlab.
- For the following (A, B) pair determine the state feedback gain vector K to set the eigenvalues of the closed-loop system dynamics matrix A – BK to -4 and -5:
Confirm that A – BK has the desired eigenvalues. - For the following (A, B) pair determine the state feedback gain vector K to set the eigenvalues of the closed-loop system dynamics matrix A – BK to -1 ± j. Note that A is not in CCF.
Confirm that A – BK has the desired eigenvalues.
