1 Lesson 2 Classification of the System response Linear system.

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Presentation transcript:

1 Lesson 2 Classification of the System response Linear system

2 System response: Output signals due to inputs and ICs. 1. The point of view of Mathematic: 2. The point of view of Engineer: 3. The point of view of control engineer: Homogenous solutionParticular solution ＋＋＋ Zero-state responseZero-input responseNatural responseForced response Transient responseSteady state response Linear system

3 Example: solve the following O.D.E (1) Particular solution: Linear system

4 (2) Homogenous solution: has to satisfy I.C. Linear system

5 (3) zero-input response: consider the original differential equation with no input. zero-input response Linear system

6 (4) zero-state response: consider the original differential equation but set all I.C.=0. zero-state response Linear system

7 (5) Laplace Method: Linear system

8 Complex response Zero state responseZero input response Forced response (Particular solution) Natural response (Homogeneous solution) Steady state responseTransient response Linear system