FEEDBACK CONTROL SYSTEMS

ECM2105 - Control Engineering Dr Mustafa M Aziz (2013)________________________________________________________________________________5.1.2. Static velocity error constant K vThe steady-state error of a system with a unit-ramp (velocity) input is:esss= e( ∞)= lime(t) = limsE(s) = limt→∞s→0s→02s (1 + G(s))= lims→01sG(s)The static velocity error constant K v is defined by:K limsG(s) =v=s → 01essFor a type 0 system, K = limsG(s) 0 . For a type 1 system, K = limsG(s) C. For a type 2 or→ →higher system,K=v s 0= limsG(s)= ∞ .v s → 0=v s 05.1.3. Static acceleration error constant K aThe steady-state error of a system with a unit-parabolic (acceleration) input, r(t) = t 2 /2, is:s1= e( ∞)= lime(t) = limsE(s) = lim= limt→∞s→0s→03s (1 + G(s)) s→0s G(s)ess2The static acceleration error constant K a is defined by:2Ka= lims G(s) =s → 01ess22For a type 0 system, K = lims G(s) 0 . For a type 1 system, K = lims G(s) 0 . For a type 2→ →system,K=a s 02lims G(s) = Ca s 0a s 0=2= lims G(s)=s → 0.= . For a type 3 or higher system, K∞→Exercise: A unity feedback system has the following forward transfer function:1000(s + 8)G(s) =(s + 7)(s + 9)(a) Evaluate the system type, K po , K v , and K a .(b) Use your answers to (a) to find the steady-state errors for the unit-step, unit-ramp, and unitparabolicinputs.17