2 Lumped parameter system are those for which the hysical characteristics are assumed to be concentrated in one or more,and thus independent of any special distribution For example springs are massless and electrical leads resistanceless 3 A stationary or time-invariant system is one whose parameters do not vary with time 4 A single-variable system is defined as one with only one output for one reference or command input(siso) A multivariable( MIMO)system has any number of inputs and outputs A continuous-variable system is one for which all the system variables are continuous functions of time 2022-2-3
2022-2-3 11 2 Lumped parameter system are those for which the physical characteristics are assumed to be concentrated in one or more “lumps” and thus independent of any special distribution .For example springs are massless and electrical leads resistanceless. 3 A stationary or time-invariant system is one whose parameters do not vary with time. 4 A single-variable system is defined as one with only one output for one reference or command input (SISO) 5 A multivariable (MIMO)system has any number of inputs and outputs. 6 A continuous-variable system is one for which all the system variables are continuous functions of time
2. Mathematical foundation 2022-2-3 12
2022-2-3 12 2.Mathematical Foundation
2.1 The transfer function concept From the mathematical standpoint algebraic and the dynamic behavior of a system In systems theory, the o differential or difference equations can be used to describe block diagram is often used to portray system of all types For linear systems, transfer functions and signal flow graphs are valuable tools for analysis as well as for design o If the input-output relationship of the linear system of Fig 1-2-1 is known, the characteristics of the system itself are also known The transfer function of a system is the ratio of the transformed output to the transformed input 2022-2-3 13
2022-2-3 13 2.1 The transfer function concept ¨ From the mathematical standpoint, algebraic and differential or difference equations can be used to describe the dynamic behavior of a system .In systems theory, the block diagram is often used to portray system of all types .For linear systems, transfer functions and signal flow graphs are valuable tools for analysis as well as for design ¨ If the input-output relationship of the linear system of Fig.1-2-1 is known, the characteristics of the system itself are also known. ¨ The transfer function of a system is the ratio of the transformed output to the transformed input
p output system p output TF(S) Finger 1-2-1 input-output relationships(a) general(b)transfer function TF(S) outputs) d inputs 2022-2-3 14
2022-2-3 14 system input output a TF(s) input output b ( ) ( ) ( ) ( ) ( ) r s c s inputs outputs TF s Finger 1-2-1 input-output relationships (a) general (b) transfer function (2-1)
Summarizing over the properties of a function we state 1. a transfer function is defined only for a linear system, and strictly only for time-invariant system 2. A transfer function between an input variable and output variable of a system is defined as the ratio of the Lap lace transform of the output to the input 3. All initial conditions of the system are assumed to zero 4. a transfer function is independent of input excitation 2022-2-3 15
2022-2-3 15 Summarizing over the properties of a function we state: 1.A transfer function is defined only for a linear system, and strictly, only for time-invariant system. 2.A transfer function between an input variable and output variable of a system is defined as the ratio of the Lap lace transform of the output to the input. 3.All initial conditions of the system are assumed to zero. 4.A transfer function is independent of input excitation