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Suppose we have a proportional feedback and that the system is modelled by a block diagram i.e

enter image description here

where C is a constant. Do we think about this as a signal "moving" in time around this loop or is the time the same everywhere inside these blocks and for all signals?

How does one keep track of which t, say for y(t_j), corresponds to u(t_i)?

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  • \$\begingroup\$ Assuming continuous systems, some have pure time delay blocks, typically temperature control systems. Otherwise, systems are assumed to be lumped, so everything is considered to happen concurrently. Digital or hybrid systems sometimes exhibit delays due to the sampling process. \$\endgroup\$ – Chu Mar 29 '18 at 15:52
  • \$\begingroup\$ For the most part, you typically treat a feedback system as a system where everything happens simultaneously. Realistically, yes, there could be some delay in your system from one block to another. However, we characterize feedback systems with transfer functions and utilize the Laplace Domain, which is different from the Time Domain. You could keep track of behavior of the feedback system at time t if you go one step at a time in the block diagram. \$\endgroup\$ – KingDuken Mar 29 '18 at 15:56
  • \$\begingroup\$ I don't get what you mean, if you switch a voltage onto a resistor/capacitor circuit, the voltages and currents are transients and take time to settle to new values. The same happens in control systems. Motors do not change speed instantaneously - if you apply a step change to a block, the output will have some sort of transient unless it's a pure gain. \$\endgroup\$ – Chu Mar 29 '18 at 15:59
  • \$\begingroup\$ @user21312 if you delete your comments, the thread of the discussion becomes disjointed. \$\endgroup\$ – Chu Mar 29 '18 at 16:28
  • \$\begingroup\$ @Chu yea sorry I was tying to find a better formulation. \$\endgroup\$ – user21312 Mar 29 '18 at 16:39
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Unless time-dependency is specified, assume there isn't any.

Nothing in your diagram seems to mention time at all. You can therefore assume each block does whatever it does instantly.

Of course in the real world, there will always be some time delays. Part of knowing how to design good control systems is to know when these delays matter and when they don't.

In general, you want the dominant time constant to come from the plant, with the controller itself being faster.

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  • \$\begingroup\$ I think I got it now. If we think in terms of basic mechanics and u being some force then the y(t) depends on all the u(s) s<t and the u(t) affects the y(t) instantaneously affecting it to move in some fashion in t+d(where new contols are generated for each time in the small intervall) . Is that a good way to think about it? \$\endgroup\$ – user21312 Mar 30 '18 at 11:01

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