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PART A1.Obtain the step response timed output data from an instrument, linear and time invariant open loop control system.Sol: Linear and time invariant (LTI) system of 2nd order is asT/F= C(S)/R(S)= WO2/S2 + 2ƐWnS +Wn2 ( C.L.T.F)T/F= C(S) / R(S) (O.L.T.F) =WO2/S2 + 2ƐWnSLet Wn=10 and Ɛ= 0.6then, O.L.T.F will beC(S)/R(S)= T/F = 102/S2 + 2 * 0.6 * 10=100/S2 +12SFor step response r(t)=1 or R(s)= 1/sso, C(S)= R(S)100/S2+12SC(S)=1/S * 100/S2 +12SC(S)= 100/S3 + 12S2Matlab codeclear all;clc;
syms sGn = ;Gd = [1 12 0];G = tf (Gn,Gd)step(G);grid on;graphStep ResponseTime (seconds)Amplitude051015202530350501001502002503002.Draw a block diagram of the measured system and describe its operation.
Sol: 1) Primary sensing element: which senses the quantity under measurement2)Plant: It is physical quantity or system whose tranfer function is used for calculation of system.3)Variable convension element: which modified suitably output of the primary sensing element.4)Variable manipulation element: manipulated signal preserving original nature5)Data transmission system: which transmit the signal.6)Data storage element: which stores the data.7)Data presenting system: present the measured physical quantity in human readable form to the observer.Primary sensing elementMeasuring quantityplantVariable manupution centreData transmission systemData storage elementData presentation system
Plant[G(s)]= Wn2/S2+2ƐWn(S)Here plant is physical system whose transfer functions can calculated using mathematical expression of it.Feedback path [H(s)]=1 ; Generally feedback path=1Wn2/s2+2єWnSG(s)c(s)R(s)
Input= C(s)Plant=physical systemError=e(t)C(s)=outputproportional= Kp e(t)H(s)=feedback pathIntegral= Ki ∫ e(T)dTDerivative= Kd de(T)/dt3.Model this system on Matlab or Simulink and test that the output's response to a step input accurately mimics your real system.Kp e(t)Kiƪe(T)dtKd de(T)/dtKiƪe(T)dtError e(t)PlantεC(s)C(s)OutputH(s)=1