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I am discretizing the PID equation so we have this equation

enter image description here

Now if we separate the integral term we get

enter image description here

Applying backward euler method

enter image description here

Now as we already have a differentiation , by applying backward euler method enter image description here

and the end equation is something like this

enter image description here

I just want to ask if I did something mathematically wrong or did I miss a step ?

P.S I am new to this forum so I just added my solution I solved in a word file

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  • $\begingroup$ Rather than using images please learn Mathjax; then you can label your formulae making it much easier for people to comment on what you have done. $\endgroup$
    – James Arathoon
    Commented Jul 4, 2018 at 12:18
  • $\begingroup$ @JamesArathoon I am sorry for the rush , I am new to math stack exchange actually so had never used it before , I will try to improve it $\endgroup$
    – Novice_Developer
    Commented Jul 4, 2018 at 12:20
  • $\begingroup$ How do you define $e(t)$? and is there a typo on the 3rd formula line down with the extra $dt$? $\endgroup$
    – James Arathoon
    Commented Jul 4, 2018 at 12:20
  • $\begingroup$ @JamesArathoon $e(t)$ is basically the current error which is defined as error = setpoint - Processvalue which is the input to our PID controller $\endgroup$
    – Novice_Developer
    Commented Jul 4, 2018 at 12:24
  • $\begingroup$ @JamesArathoon you are right $dt$ is a typo $\endgroup$
    – Novice_Developer
    Commented Jul 4, 2018 at 12:25

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