Performing Error Analysis: Control Systems 2.5

The world doesn't always work out the way we plan, sometimes. At times like that, we need to do some error analysis. In this control systems tutorial, we can learn how to perform error analysis and what those results mean. In a control system, we are mostly concerned with the error that exists when the system appears to be settled. For this, we need to know the final value to which a system settles when it is excited by a certain input, either a step, ramp, or parabolic input. Formally, the final value of the system is that value which is obtained as time approaches infinity. Let's look through the different types of systems there are and how we can generalize the response of a system by its type and output.
This video tutorial is based on the amazing written tutorial that Kushal put together and we highly recommend you go check it out. He provides more in-depth information and takes a more rigorously mathematical approach. His tutorial is found here:
www.circuitbread.com/tutorial...
Table of Contents:
0:00 Introduction
0:43 What is the error in a control system?
2:12 Poles and zeroes in error analysis
3:22 Different input functions
3:53 Review of what we need
4:35 Error Equations
9:52 What we can learn from these equations
10:37 Summary
11:43 Have you seen everything that CircuitBread.com offers?
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[@wakeupthisisntreal8168]

The quality of these videos are always outstanding! Deserves way more views. Thank you for helping students like me learn these tough concepts with so much clarity!

[@CircuitBread]

Thanks for the kind words, glad it helps. 😎

[@GeoffryGifari]

So each of Kₛ , Kᵥ, and Kₐ can contribute to final steady state error? Can they all be finite for one system?
And since the relation is position-velocity-acceleration, are Kₛ , Kᵥ, and Kₐ independent or can they be derived from each other?

[@CircuitBread]

Thanks for the questions! Yes, they can all contribute to the final steady state error, but they cannot all be finite for one system. Well, technically, 0 is a finite number, so depends on your definition. But it makes sense if you think about it - if you have a steady state acceleration error, then you're not going to have a steady state (or finite) position or velocity error as they both will be changing continuously. And if you have a steady state position error, then you can't have a non-zero acceleration or velocity error, because then you wouldn't have reached a steady state in position.
And while the three static error coefficients are mathematically related, I'm not sure if there is a way to derive one from another. I'm also not sure if there is a reason you would ever need to do that. I'll have to think about this one more and let you know if anything comes to mind.

[@GeoffryGifari]

@@CircuitBread oh yeah that makes sense

[@GeoffryGifari]

@@CircuitBread I figure "steady-state" is the key word here