Controller for plant transfer function.

Thread Starter

Saviour Muscat

Joined Sep 19, 2014
151
Hello,
Hope this thread finds you in good health,

Currently I'm doing a task given for homework and I'm little bit stuck. The task is to design a controller to minimize the effect of the two pairs of dominant poles by using pole-zero cancellation technique. The plant transfer function(G) is as follows:
(0.02 (s+1e05))
G=-------------------------------------------------------------------
((s+1000) (s^2 + 0.03371s + 0.1662) (s^2 + 0.0864s + 12.03))

I did an attempt for the controller(C) see below, I placed two pairs of complex zeros at the numerator(C) to cancel out the two pairs of complex poles found in the denominator of (G), further I placed at the denominator at (C): an integrator(to cancel out the steady state error) and complex pole to achieve the design specs( 2 seconds settling time and 5% overshoot).

C=(s^2 + 0.03371s + 0.1662) (s^2 + 0.0864s + 12.03)
---------------------------------------------------------
(s)(s^2+As+B)

My difficulty is it permissible to apply controller (C) with (G)? Or suggest any modifications of controller (C) that is compatible with (G), please.

(s^2 + 0.03371s + 0.1662) (s^2 + 0.0864s + 12.03) (0.02 (s+1e05))
--------------------------------------------------------- ----- --------------------------------------------------------------
(s)(s^2+As+B) ((s+1000) (s^2 + 0.03371s + 0.1662) (s^2 + 0.0864s + 12.03))

Thank you
SM
 

Thread Starter

Saviour Muscat

Joined Sep 19, 2014
151
Hello, sorry again
I already did controller C on root locus given by Matlab. as stated in the previous message and I got it within the specification.
My concern is one, can I apply controller C (numerator Order 4 and denominator order 3) to the plant transfer function G (numerator order 1 and denominator order 5 please?
1606657735787.png1606657766364.png
Thankyou
Saviour
 
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