a block diagram represents the flow of information and the function performed by each component in the system Arrows are used to show the direction of the flow of information The block represents the the function or dynamic characteristics of the component and is represented by a transfer function The complete block diagram shows how the functional components are connected and the mathematic equations that determine the response of each component
• A block diagram represents the flow of information and the function performed by each component in the system. • Arrows are used to show the direction of the flow of information. • The block represents the the function or dynamic characteristics of the component and is represented by a transfer function. • The complete block diagram shows how the functional components are connected and the mathematic equations that determine the response of each component
2.2 Laplace Transform(Review) Properties of Laplace transform F(s)=f(e-stdt A. Conditions for the existence of F(s) (1)f(1)=0,t<0 (2)f(t)is integrable for any intergal tE la, bl (3)there are constants M>0 and So>0, for which f(s Meso, for any t B Linearity p(af(t)+bg(0))=a(f(t))+bi(g(t)
2.2 Laplace Transform (Review)
C. Delay theorem ef(t-r=e-F(s) D. Shifting theorem ele -atf(=F(+a) E. Transform of derivatives (()=s"F(s)-snf(0)-s"2r(0)-…-f0-)(0 F. Final value theorem lim f(t=lim SF(S) t→ →0 G. The relationship between time G. L aF(as and frequency
aF(as) a t G L f = . G. The relationship between time and frequency
2.3 System Model and Transfer functions (Transfer function: Laplace transform of the input-output relation of a system) 7 SP1. Electric Circuit u=Ri+l-+u Sⅴstem R C Uo LC a2+h出n L=1 U1(s) LCs+ rcs+1
2.3 System Model and Transfer Functions (Transfer function: Laplace transform of the input-output relation of a system) SP1. Electric Circuit System R L C Ui Uo i o i o o u u dt du RC dt d u LC + + = 2 2 1 1 2 LCs + RCs + U (s) i U (s) O = = + + i dt C u u dt di u R i L o i o 1
SP2 Mechanic Movement(Translation) System with Spring-MaSs-Damper 总 k friction b y Displacement b dt Mass orce
SP2. Mechanic Movement (Translation) System with Spring – Mass – Damper Displacement Mass kydt dy b