mmme2046 notes on control 2 lecture

uni/mmme/2046_dynamics_and_control/stability.md

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+---
+author: Akbar Rahman
+date: \today
+title: MMME2046 // Stability
+tags: []
+uuid: 2b0062f7-cc8a-4e52-8e12-1eb731e056af
+lecture_slides: ./lecture_slides/Control 2 2022.pdf
+---
+
+# Introduction to Transient and Steady-State Responses
+
+![](./images/vimscrot-2023-02-06T17:03:18,594676084+00:00.png)
+
+A stable system settles.
+An unstable system has increasing amplitude in its fluctuations.
+
+The steady-state error is how accurate a system will be once settled.
+
+If we subject control systems to standard input we can compare and tune their performance.
+
+Consider three inputs:
+
+i. step input
+ii. ramp input (linear change with time)
+iii. harmonic input (considered in vibration)
+
+These inputs are useful because they
+
+- are easily to apply in practice
+- approximate to operating conditions in control systems
+
+
+![](./images/vimscrot-2023-02-06T17:10:11,891784480+00:00.png)
+
+# Practical Measurement of Transient Response
+
+![](./images/vimscrot-2023-02-06T17:10:48,755879402+00:00.png)
+
+a. maximum overshoot
+b. number of oscillations
+c. rise time
+d. settling time
+e. steady state error