Poles

The questions below are due on Sunday February 24, 2019; 11:00:00 PM.

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Consider the following system, where K represents a constant.

Part 1

Determine the poles of this system when $K = \frac{3}{16}$. Enter these poles as a python list of (possibly complex) numbers, e.g., [1.2, 2.3+0.5j, 2.3-0.5j]. Don't forget the commas or the brackets.

List of poles:

Part 2

Determine the maximum value of $K$ for which the system is _stable_¹. Enter a single number.

Maximum stable value of K:

Part 3

Is it possible to adjust $K$ so that the dominant pole is 0.9? If yes, enter the value of $K$. If no, enter None.

Value of K or None:

Part 4

Is it possible to adjust $K$ so that the dominant pole is 0.1? If yes, enter the value of $K$. If no, enter None.

Value of K or None:

Part 5

What is the smallest possible magnitude of the dominant pole of this system?

Smallest possible dominant pole magnitude:

Footnotes

¹A system is considered to be stable if it does not diverge. (click to return to text)