Question

A plant of order 50 is to track steps and sinusoids of frequency ω = 1 rad/sec. Write down the form of the pole placement controller which will guarantee stability and tracking. g

Answer 1

Answer:

The term for the pole placement controller is G/(s²  + 1) +GH

Explanation:

Solution

Given that:

A plant of order = 50

The sinusoids of frequency ω = 1 rad/sec.

Lt the transfer of equation of plant be represented as follows:

T/F = G/1+GH

= K/ans^50 + ans - 1^49 +........As +a₀

The pole placement order becomes:

Step 1:

Gc (s) =A/s

Now

The transfer function = GGc/1 +GG c H

=G/s + GHA

Step 2:

For sinusoidal controller w = = 1 rad/sec.

Gc (s) = w/s² + w²

= 1 + /s²  + 1

Thus

The transfer function = GGc/1 +GGcH

= G/(s²  + 1) +GH

the term for the pole placement controller is G/(s²  + 1) +GH