Module 2 Transfer Function and Block Diagram Algebra (4 hours)
Module 2 Transfer Function and Block Diagram Algebra (4 hours)
2. I Modeling of physical systems Model of system the relationship between variables in system Differential Equation(mathematic model) (parameter model) Block Diagram and Transfer Function(parameter model) Response Curve(non parameter model)
2.1 Modeling of physical systems Model of system – the relationship between variables in system • Differential Equation (mathematic model) (parameter model) • Block Diagram and Transfer Function (parameter model) • Response Curve (non parameter model)
2. 1. 1 Why do we must study the model of control system? An accurate mathematic model that describes a system completely must be determined in order to analyze and control a dynamic system
2.1.1 Why do we must study the model of control system? ________ An accurate mathematic model that describes a system completely must be determined in order to analyze and control a dynamic system
2. 1.2 The Steps of Analyzing and Studying a dynamic System Define the system and its components Formulate the mathematic model and list the necessary assumptions Write the differential equations describing the model Solve the equations for the desired output variables Examine the solutions and the assumptions necessary, reanalyze or redesign n the system
2.1.2 The Steps of Analyzing and Studying a Dynamic System • Define the system and its components. • Formulate the mathematic model and list the necessary assumptions. • Write the differential equations describing the model. • Solve the equations for the desired output variables. • Examine the solutions and the assumptions. • If necessary, reanalyze or redesign the system
2.1.3 The Block Diagram Model which consists of block, arrow Differencing junction and pickoff point Differencing junction Forward path Input Error CONTROLLER Control PLANT Sign Measured output TRANSDUCER Pickoff point Feedback path Fig. 1. 3 Generalized feedback control system
2.1.3 The Block Diagram Model – which consists of block, arrow, Differencing junction and pickoff point. Pickoff point
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,t0 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
