Complex Transfer Function

I have searched around a little and can not work out how to enter a transfer function in the following form to Matlab:

G(s) = 1 / ( s*(s+0.5 +- 2j) )

Note that in the brackets it is "s plus 0.5 plus/minus 2 j' which is complex. Any assistance is appreciated.

[Garba Elhassan]

Hello and Good day, I m working on a deadbeat controller with time delay in the plant. I was able to design a controller with the time delay into consideration.

my plant is :T_(d(z))=(0.26158 (z+11.81) (z+0.5335) (z+0.02728))/((z-1) (z^2- 0.2404z + 0.09597)) z^(-2) and

my controller is (0.2986z^4-0.07178z^3+0.02865z^2 )/(z^3+1.483z^2+0.5315z+0.01342)

the controller gives good response using the code.

The controller has more zeros than the poles.

now is the time to test in controller in Simulink, Transfer function block couldnot work, I try expressing the controller in partial fraction but two of the fraction has complex zeros and poles. I try using the block, expressing the controller using d-operators but I have z terms in the output equation.

I am realy confused on how to solve this issue.

your kind answers shall be highly appreciated.

Answer 1

[Fangjun Jiang]

Take a look at the example of

doc zpk

[John]

Yes I see a similar example. However, I am not sure if the two are the same:

(i) - (s+0.5 +- 2j)

(ii) - (s+0.5 + 2j)(s+0.5 + 2j)

Thus I am not sure how to enter it in if (i) and (ii) are not the same?

[Fangjun Jiang]

I don't understand your question. The point is to use zpk() to create the transfer function. For (i), it is zpk([],[-0.5+i,-0.5-i],1). For (ii), it is not a valid transfer function.