Module 8 System Type Steady-State Error and Muriple control (3 hours) Definition of the system type The kind of input of system How to identify steady-state error quickly How to eliminate steady-state error
Module 8 System Type: Steady-State Error and Muriple Control (3 hours) • Definition of the system type • The kind of input of system • How to identify steady-state error quickly • How to eliminate steady-state error
Definition of error. 8.1 Consider the following block diagram R(s)→)G(s) H(s) The true error is defined as the difference between the input and the output, while the actuating error is the input to the system g E(S=R(S-C(S)(ture error) E,(S=R(S-H(s)C(S(actuating error) For unit feedback systems(H=1), the two errors coincide
8.1
8.1.1 Why we should consider the actuating error Ea(P125) The true error e=r-c is not AE C G observable. since the output has to be measured by H(s) HC=CLH before its value is known EG I+Gh p/ observable, since C=HC car The actuating error ea=R-C e measure d. For the study convenience, we R now make a important 1+G assumption: H=l, that E= ea
8.1.1 Why we should consider the actuating error Ea (P125) • The true error E=R-C is not observable, since the output has to be measured by H(s) before its value is known. • The actuating error Ea =R-C’ is observable, since C’=HC can be measured. • For the study convenience, we now make a important assumption : H=1, that E= Ea R Ea C HC =C' G H R G GH C E + = = 1 1 R + G = 1 1
8.1.2 Errors of non-unity and unity feedback 只 E G Non-unity feedback sys HECH E=R-HC =H(,R-C) H HE R=RIGE E E |1 C GH Unity feedback system
8.1.2 Errors of non-unity and unity feedback R Ea C HC =C' G H R C H 1 GH ' 1 R R H = E' Non-unity feedback sys. Unity feedback system Ea = R − HC ) 1 ( R C H = H − = HE' Ea H E 1 ' =
8.2 The steady-state error ess (e(oo)) E(S=R(s)C(S) R(s) 1+G(S) e(oo)=lim SE(s)=lm SR(S) 1+G(s) e(oo)is determined by two factors r(t and G(s)
8.2 The steady-state error ess ( ) e() ( ) 1 ( ) 1 ( ) ( ) ( ) R s G s E s R s C s + = − = 1 ( ) 1 ( ) lim ( ) lim ( ) 0 0 G s e sE s sR s s s + = = → → e() is determined by two factors: r(t) and G(s)