Temporal Response - State Transition Matrix - Part 2
In this video, we explore in-depth the temporal and transient response in linear time-invariant (LTI) systems using state variables. You'll learn how to solve for the transient response using the state transition matrix and how it relates to the transfer function. We cover key concepts such as free and forced response, and address input-output methodologies. We also explain the formulation and derivation of the state transition matrix, using approximations such as the infinite series for calculating exponentials. Ideal for students of control and automation.
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⏱ TIMESTAMPS ⏱
00:00 Transient Response Analysis in State Variables
02:08 Diagonal Form for Time Response
05:31 Frequency Response Method (Laplace)
09:28 Example in Laplace Transform
12:49 Cayley-Hamilton Theorem
21:36 Cayley-Hamilton Solution: Repeated Eigenvalues
23:08 Example using Cayley-Hamilton
27:52 Diagonal Form and Jordan Form
31:32 Example in Dorma: Diagonal Form and Jordan Form
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