What is an LTI system?
An LTI (Linear, Time-Invariant) system, in a simplified
sense, will exhibit two behaviors:
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- Time Invariance - The system must behave the same in
any two trials in time if the inputs and starting conditions are
identical.
- Additive Superposition - If you excite a system with
input a and get output A, then excite it with b
and get B, then when you excite it with input (a
+ b), then you should get output (A + B).
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This is a simplistic
view of determining that a system is LTI, but it is very demanding. No
real system will adhere to these characteristics perfectly. Some examples
of non-LTI systems are systems with friction that varies with time or
temperature, clipping amplifiers, and robots that vary their mass moment
of inertia with position.
So how do you determine if your system is LTI (enough)?
Basically, if you are using permanent magnet motors (brushless or brushed)
with current amplifiers, you can probably assume that your system is LTI
if you can reproduce your test conditions. If you are not using that type
of system, you will need to consider if it satisfies the two criteria
above.
Since no system is perfectly LTI, realize that data you collect (and the
models you may generate from that data) will only be approximations of
the real system. The more your system differs from LTI, the more you should
look at your data with some suspicion and caution. You may want to increase
your stability margins as your system is less and less LTI.
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