The AVR system block diagram is shown in Figure 1. The system's parameters are shown in...

  

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The AVR system block diagram is shown in Figure 1. The system's parameters are shown in Table 1. Vref (8) V₂(5) Amplifier gain K 0 KA Parameters Amplifier Exciter Generator Sensor KA 1+ TAS Amplifier Table 1: Nomenclatures Gain K₂ = 1 K = 1 KR = 1 Va(5) KE 1+ TES Exciter Peak time Ka 1+ TAS Time constant T₁ = 0.2 7=0.3 T = 1.0 TR = 0.05 VF(5) Ka 1+ Tas Generator Sensor Figure 1: A simplified automatic voltage regulator block diagram a) Use Routh-Hurwitz criteria to find the range of Amplifier gain K for control system stability. b) Find the critical value for K (denotes as K) and the frequency of oscillation we at KA- Note that we is the frequency of oscillation at marginally stable condition (before the system become unstable). c) Confirm the value of K and win (b) by plotting the locus of the system. Use MATLAB command rlocus (Hint: when plotting a root locus, the initial K, should be set to unity, i.e. K₂ = 1). d) Use MATLAB command to observe the transient behavior of the AVR in Figure 1. Tabulate the result as in Table 2. Table 2: Translent performance with multifarious amplifier gain Rise time Settling time Peak amplitude V₂(5) % Overshoot Steady- state error The AVR system block diagram is shown in Figure 1. The system's parameters are shown in Table 1. Vref (8) V₂(5) Amplifier gain K 0 KA Parameters Amplifier Exciter Generator Sensor KA 1+ TAS Amplifier Table 1: Nomenclatures Gain K₂ = 1 K = 1 KR = 1 Va(5) KE 1+ TES Exciter Peak time Ka 1+ TAS Time constant T₁ = 0.2 7=0.3 T = 1.0 TR = 0.05 VF(5) Ka 1+ Tas Generator Sensor Figure 1: A simplified automatic voltage regulator block diagram a) Use Routh-Hurwitz criteria to find the range of Amplifier gain K for control system stability. b) Find the critical value for K (denotes as K) and the frequency of oscillation we at KA- Note that we is the frequency of oscillation at marginally stable condition (before the system become unstable). c) Confirm the value of K and win (b) by plotting the locus of the system. Use MATLAB command rlocus (Hint: when plotting a root locus, the initial K, should be set to unity, i.e. K₂ = 1). d) Use MATLAB command to observe the transient behavior of the AVR in Figure 1. Tabulate the result as in Table 2. Table 2: Translent performance with multifarious amplifier gain Rise time Settling time Peak amplitude V₂(5) % Overshoot Steady- state error