Creating a recursive control system

Question

I am trying to design a digital control system of which output depends on the difference between 1 input signal 1 tick ago and the output 1 tick ago ,and 1 another input signal.

The output $y(n)$ = input $i(n)$ $\cdot$ $b(n)$ and $b(n)$ = input $d(n-1)$ $-$ $y(n-1)$ Here is what I have come up with so far:

I have made the time delay part.The inverse Z transform of $z^{-1}$ is $\delta(n-1)$ so I have created the time delay in both $D(s)$ and the feedback loop.However I need to somehow put I(s) in the overall system so that it does what I want but so far I have been unsuccesfull on doing so.How should I keep on?

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Here is what I have come up with:

Note:I have added a steady signal to the summer

Answer 1

First, recognize that your system, as given, is not linear time-invariant, because of the multiplication by $i(n)$. Depending on how you treat $i(n)$ and it's effects, your system is either nonlinear (if you take $i(n)$ as a regular old input) or time-varying (if you take $i(n)$ as a predefined signal, and make it part of the system's time dependence).

Either way, using $z$ notation on the signals is misleading. Even for non-linear systems, using $\frac 1 z$ inside a block to denote a unit delay is pretty common; that's what I do with the expectation that the reader will still understand it's not an LTI system. Here's what I would draw, using $\Sigma$ to denote a summing junction, and $\Pi$ to denote a product junction. It's pretty much the same except I've left out the $A$ term which you did not mention in your question.