Another Example of First-Order System Cde(t)=q(t)dt 900=-6 R Θ+θ(t) de(t) =q0）= e。-(t) ⊙+0n dt R ⊙+0。 Rcd90+80）=9, C(kcal/C):thermal capacitance dt R(C/kcal/s):thermal resistance q (kcal/s):heat input 1 1 ⊙，(s) RCs+1 Ts+1
Another Example of First-Order System b ( )t Cd t q t dt () () • C (kcal/ oC): thermal capacitance • R ( oC/kcal/s): thermal resistance • q (kcal/s): heat input ( ) ( ) b t q t R () () ( ) b dt t C qt dt R ( ) ( ) b d t RC t dt b () 1 1 () 1 1 b s s RCs Ts
Transient Response of First-Order Systems Examples of first-order systems Ra R C + P RC- .=P b R R de。+e=ei d Vin =Rgia +Km@ T=Ki。=J.o+bw L Bdk。+x。=X K dt 0 KT 二 R(Jas+b)+KKm)
Transient Response of First-Order Systems • Examples of first-order systems + _ Vemf J a R a i a Vin b V Ri K in a a m T Ki J b Ta a () ) T in a a T m K V R Js b KK P i Po R C RC dpo dt po pi R C RC deo dt eo ei ei + - + - eo K B B K dxo dt x o xi xi xo
General Form of First-Order Systems C(s)_ T dc +c=u dt U(s) Ts+1 Ifu(t)is a step input of magnitude a'. (t≥0) a C(S)= 1 c04 ope=号 c(t)(-eir）a Ts+1s a Ta C(s)= a S Ts+1 0.632a 960.66 c0=a1-e不 261:P0 No steady-state error T 2T 3T 4T 577
General Form of First-Order Systems If u(t) is a step input of magnitude ‘a’. No steady-state error 1 ( ) 1 a C s Ts s (t 0) ( ) 1 a Ta C s s Ts 1 ( ) (1 )t T ct a e dc T cu dt () 1 () 1 C s U s Ts