A speed control for a gasoline engine is shown inFigure P9.5. Because of the restriction at the carburctorintake and the capacitance of the reduction inanifold,the lag 7, occurs and is equal to 1 second. The enginetime constant 7. is equal to J/b = 3 s. The speed mea-sureinent time constant is Tin = 0.4 s. (a) Determinethe necessary gain K if the steady-state speed error isrequired to be less than 10% of the speed reference set-ting. (b) With the gain determined from part (a), applythe Nyquist criterion to investigate the stability of thesystem,P9.5 Res) -ThrotleTorqueKY(s)SpeedFIGURE P9.5Engine speedcontrol.Tm + 1

The disparity between the input and output of a system in the limit as the time approaches infinity is known as steady-state error. The discrepancy between the desired value and the actual value of a system when it has reached a steady-state is known as a steady-state error.The Nyquist ISI criteria in communications outline the requirements that, when met by a communication channel (including transmitting and receiving filter responses), result in no inter symbol interference or ISI. This time-domain condition is related to an analogous frequency-domain condition by the Nyquist theorem.The Nyquist limit is the highest Doppler shift frequency that can be accurately recorded in color or pulsed wave ultrasonography without aliasing.a.) From the given figure figure τ1=1secτe=3secτm=0.4sec closed to open-loop transfer function Gs1+GsHs=1τ1s+1×1τes+11+1τ1s+1×Kτes+1×1τms+1Gs1+GsHs=Kτ1s+1τes+1τ1s+1τes+1τms+1+Kτ1s+1τes+1τms+1Gs1+GsHs=Kτms+1τ1s+1τes+1τms+1+Kput the values of τ1 ,τe, τmGs1+GsHs=K0.4s+1s+13s+10.4s+1orThe loop transfer function isLs=GcsGsHs =Ks+13s+10.4s+1 The steady-state error of the transfer function is ess=lims→0Esess=R1+K It is zero type transfer function because the number of poles is not present at origin. Here the required steady-state error is ess=0.1R0.1R=R1+K0.1=11+K1+K>10K>9 b.) K=9 The Nyquist plot is shown below. Need to determine that P=0 and N=0. Hence Z=0 so the system will be stable. Nyquist diagram for Ls=GcsGsHsLs=9s+13s+10.4s+1 the system is stable.