Control System (ECE411) Lectures 13 & 14

Time-Domain AnalysisAnalyzing Simple ControllersControl System (ECE411) Lectures 13 & Azimi, ProfessorDepartment of Electrical and Computer EngineeringColorado State UniversityFall AzimiControl SystemsTime-Domain AnalysisAnalyzing Simple ControllersSteady-State Error AnalysisRemark: For aunity feedback System (H(s) = 1):e(t) =r(t) c(t)E(s) =R(s) C(s) =R(s) R(s)M(s) =E(s) = [1 M(s)]R(s)whereM(s)is the closed loop transfer ,ess= lims 0sE(s) = lims 0s[1 M(s)]R(s)For a unit stepR(s) =1s, we getess= [1 M(0)]Note:The above results could sometimes be used for cases whenH(s)6= 1(tracking error).ExampleGiven a unity feedback System shown below with closed loop transfer functionM(s) =K(s2+2s+2)(s+a), AzimiControl SystemsTime-Domain AnalysisAnalyzing Simple ControllersSteady-State Error Analysis-Cont.

Transient Response of 2nd-Order Control System Consider a control system with closed-loop transfer function, M(s) = C(s) R(s) =!2 n s2 +2˘! n s+!2; M(0) = 1 Characteristic Equation : ˆ(s) = s2 +2˘! n s+!2 = 0 has the following roots, s 1;2 = ˘! n j! n p 1 ˘2 = j! These are depicted in the following gure. cos = ˘, tan = p 1 ˘2 ˘ M.R ...

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