[scilab-Users] z^(-1/2) half cycle delay in discrete time

[Dean Parsons]

David,

Thanks for your prompt response. Let me ask my question in a different way.

In MATLAB I can add a delay to the input of a continuous time system with the following code sequence:

time_delay = 0.5;
sys_continuous_time = ss(A,B,C,D);
set(sys_continuous_time,'InputDelay',time_delay*[1 1 1]);

In transfer funtion representation my sys_continuous_time = -1 - 1/s - 1/s^2
I believe the third line of code above multiples sys_continuous_time by [exp(-0.5*s)   exp(-0.5*s)   exp(-0.5*s)] which is equivalent to multiplying by [z^(-1/2)   z^(-1/2)   z^(-1/2)]

I know how to write Scilab code for the first 2 lines of code above. My question is: Is there a way in Scilab to do what the 3rd line of code above does?

If I try to create a term like exp(-0.5*s) or z^(-1/2) in Scilab in order to do this multiplication, I get the following error messages:


-->s=poly(0,"s");
 
-->a = exp(-0.5*s);
                !--error 246 
Function not defined for given argument type(s),


  check arguments or define function %p_exp for overloading.

-->z = poly(0,"z");
 
-->a = z^(-1/2);
             !--error 30 
Invalid exponent.


How can I add a half clock cycle of delay to the input of a continuous time system in Scilab? (I am modeling a sigma delta modulator which uses continuous time integrators as well as a sampling quantizer which has a half clock cycle of delay - all in the same loop. This is why it is necessary to have a mixture of continuous time & discrete time math in the same system.)


Dean Parsons

  ----- Original Message ----- 
  From: David PICARD 
  To: users at lists.scilab.org 
  Sent: Tuesday, May 10, 2011 2:42 AM
  Subject: Re: [scilab-Users] z^(-1/2) half cycle delay in discrete time


  z^-1 is the  value of the system 1 sampling period in the past. But as sampling is discrete, does it make sense to reference a value that is between 2 samples, but that does not exist in your model, since, by definition, it is not sampled ?


  Le 09/05/2011 19:27, Dean Parsons a écrit : 
    Hello,

    I want to add a half cycle delay to a discrete time transfer function by multiplying the transfer function by z^(-0.5). It seems Scilab doesn't allow non-integer exponents with the discrete time variable z:

    -->z=poly(0,"z");
     
    -->a = z^(-0.5);
                 !--error 30 
    Invalid exponent.

    Is there a work around for this? Is there another way to create the discrete time delay z^(-1/2)?

    Thank you for your help with this.

    Dean Parsons
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