1 / 31

Lecture #2

Lecture #2. Introduction to Systems. system. A system is an entity that manipulates one or more signals to accomplish a function, thereby yielding new signals. Example of system. System interconnection. System properties. Causality Linearity Time invariance Invertibility. Causality.

nuwa
Download Presentation

Lecture #2

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Lecture #2 Introduction to Systems signals & systems

  2. system A system is an entity that manipulates one or more signals to accomplish a function, thereby yielding new signals. signals & systems

  3. Example of system signals & systems

  4. System interconnection signals & systems

  5. System properties • Causality • Linearity • Time invariance • Invertibility signals & systems

  6. Causality A system is said to be causal if the present value of the output signal depends only on the present or past values of the input signal. signals & systems

  7. Causal and noncausal system Example: distinguish between causal and noncausal systems in the following: (1) Case I Noncausal system signals & systems

  8. (2) Case II Delay system causal system (3) Case III causal system At present past signals & systems

  9. (4) Case IV noncausal system At present future (5) Case V noncausal system signals & systems

  10. signals & systems

  11. Linearity A system is said to be linear in terms of the system input x(t) and the system output y(t) if it satisfies the following two properties of superposition and homogeneity. Superposition: Homogeneity: signals & systems

  12. Example 1.19 linear system signals & systems

  13. Example 1.20 Non linear system signals & systems

  14. Properties of linear system : (1) (2) signals & systems

  15. Time invariant system Time invariance A system is said to be time invariant if a time delay or time advance of the input signal leads to an identical time shift in the output signal. signals & systems

  16. Example 1.18 Time varying system signals & systems

  17. Invertibility A system is said to be Invertible if the input of the system can be recovered from the output. H Hinv signals & systems

  18. Example 1.15 Inverse system Example 1.16 signals & systems

  19. LINEAR TIME-INVARIANT (LTI) SYSTEMS: A basic fact: If we know the response of an LTI system to some inputs, we actually know the response to many inputs System identification signals & systems

  20. signals & systems

  21. example The system is governed by a linear ordinary differential equation (ODE) Linear time invariant system linearity signals & systems

  22. LTI System representations Continuous-time LTI system • Order-N Ordinary Differential equation • Transfer function (Laplace transform) • State equation (Finite order-1 differential equations) ) Discrete-time LTI system • Ordinary Difference equation • Transfer function (Z transform) • State equation (Finite order-1 difference equations) signals & systems

  23. Continuous-time LTI system Order-2 ordinary differential equation constants Linear system  initial rest Transfer function signals & systems

  24. signals & systems

  25. Homogenous solution Particular solution Natural response Forced response Zero-input response Zero-state response 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: + Transient response Steady state response signals & systems

  26. (1) Particular solution: Example: solve the following O.D.E signals & systems

  27. (2) Homogenous solution: have to satisfy I.C. signals & systems

  28. (3) zero-input response: consider the original differential equation with no input. zero-input response signals & systems

  29. (4) zero-state response: consider the original differential equation but set all I.C.=0. zero-state response signals & systems

  30. (5) Laplace Method: signals & systems

  31. Complex response Zero state response Zero input response Forced response (Particular solution) Natural response (Homogeneous solution) Steady state response Transient response signals & systems

More Related