CHI-TSONG CHEN KAPITEL 2- Systems Kortfattade läsanvisningar Läs hela kapitlet utom 2.9 och 2.10.

En presentation över ämnet: "CHI-TSONG CHEN KAPITEL 2- Systems Kortfattade läsanvisningar Läs hela kapitlet utom 2.9 och 2.10."— Presentationens avskrift:

1 CHI-TSONG CHEN KAPITEL 2- Systems Kortfattade läsanvisningar Läs hela kapitlet utom 2.9 och 2.10

2 2.1. Introduktion  Detta är en inledning – du kan koncentrera dig på att förs¨å de kursiverade orden

3 2.2 CT Systems with and without memory  A system is called a memoryless system if its output y(t 0 ) depends only on the input u(t) applied at time t=t 0  A system is called a causal system if its current output depends on past and present inputs, but not on future inputs  Every physical system is causal

4 2.3 The concept of state  Antag att du studerar en kropp på ett plant underlag. Kroppen påverkas av en kraft u och kroppens tillstånd kan beskrivas av dess förflyttning (y) och hastighet (v) vid en viss tidpunkt  The set of y(t) and v(t) is called the state variable

5 Lumped system  If the number of state variables is finite the system is a lumped system

6 2.3.1. Zero input response  If u(t)=0 for t>0 zero-input response = natural response = unforced response  If x(t 0 )=0 zero state response = forced response  A system is initially relaxed if x(t 0 )=0 - input before t=0 has no effect

7 2.4 Linearity of memoryless systems  A memoryles system is linear if

8 2.4.1. Linearity of systems with memory  The response of such a system depends not only on the input but also on the initial state. Thus the additivity and homogeneity properties should also apply to the initial state

9 2.5 Time invariance and its implication  If the characteristics of a system do not change with time, the system is said to be time invariant.

10 2.6. Implication of linearity and time invariance – zero state responses  Responses of LTI systems can always be decopmposed into zero-input (natural) responses and zero-state (forced) responses

11 2.10 Discrete Time LTI-systems

12 2.11 Conclutions  Titta på figur 2.24