Question Solved1 Answer Problem Two A measuring system has a natural frequency of 0.5 rad/s, a damping ratio of 0.5, and a static sensitivity of 0.5 m/V. 2.A: Using MATLAB, plot the step response of the system where the step amplitude is 2 V and the step occurs at t = 0 sec. Assume that the initials conditions equal zero. In your MATLAB code, construct the time array such that the system reaches steady-state within the plotted timeframe. The deliverable is your MATLAB code and the plot it generates. 2.B: From the plot, estimate the system's 90% rise time and +10% settling time. 2A and B refer to the step response of an SOS (Lecture 7) 2C-G refer to the frequency response of an SOS (Lecture 8) 2.C: Plot the measurement system's magnitude ratio, Mw), vs input signal frequency, w. 2.D: Plot the measurement system's phase (in radians), (w), vs input signal frequency, w. Use "atan2" rather than "atan" when computing the phase. For parts C and D, use "semilogx" to use a logarithmic scale for the x-axis and plot input frequencies ranging from 0 to 10 rad/s. The deliverable is your MATLAB code and the plot it generates. 2.E: What is the system's transmission band? The transmission band, aka "passband," of a sensor (FOS or SOS) is the range of frequencies such that 0.707 < Mw) < 1.41 2.F: What is the system's resonance band? The resonance band of a sensor is the range of frequencies such that Mw) > 1.41 2. What is the system's filter band? The filter band of a sensor (FOS or SOS) is the range of frequencies such that Mw) < 0.707
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Transcribed Image Text: Problem Two A measuring system has a natural frequency of 0.5 rad/s, a damping ratio of 0.5, and a static sensitivity of 0.5 m/V. 2.A: Using MATLAB, plot the step response of the system where the step amplitude is 2 V and the step occurs at t = 0 sec. Assume that the initials conditions equal zero. In your MATLAB code, construct the time array such that the system reaches steady-state within the plotted timeframe. The deliverable is your MATLAB code and the plot it generates. 2.B: From the plot, estimate the system's 90% rise time and +10% settling time. 2A and B refer to the step response of an SOS (Lecture 7) 2C-G refer to the frequency response of an SOS (Lecture 8) 2.C: Plot the measurement system's magnitude ratio, Mw), vs input signal frequency, w. 2.D: Plot the measurement system's phase (in radians), (w), vs input signal frequency, w. Use "atan2" rather than "atan" when computing the phase. For parts C and D, use "semilogx" to use a logarithmic scale for the x-axis and plot input frequencies ranging from 0 to 10 rad/s. The deliverable is your MATLAB code and the plot it generates. 2.E: What is the system's transmission band? The transmission band, aka "passband," of a sensor (FOS or SOS) is the range of frequencies such that 0.707 < Mw) < 1.41 2.F: What is the system's resonance band? The resonance band of a sensor is the range of frequencies such that Mw) > 1.41 2. What is the system's filter band? The filter band of a sensor (FOS or SOS) is the range of frequencies such that Mw) < 0.707
More Transcribed Image Text: Problem Two A measuring system has a natural frequency of 0.5 rad/s, a damping ratio of 0.5, and a static sensitivity of 0.5 m/V. 2.A: Using MATLAB, plot the step response of the system where the step amplitude is 2 V and the step occurs at t = 0 sec. Assume that the initials conditions equal zero. In your MATLAB code, construct the time array such that the system reaches steady-state within the plotted timeframe. The deliverable is your MATLAB code and the plot it generates. 2.B: From the plot, estimate the system's 90% rise time and +10% settling time. 2A and B refer to the step response of an SOS (Lecture 7) 2C-G refer to the frequency response of an SOS (Lecture 8) 2.C: Plot the measurement system's magnitude ratio, Mw), vs input signal frequency, w. 2.D: Plot the measurement system's phase (in radians), (w), vs input signal frequency, w. Use "atan2" rather than "atan" when computing the phase. For parts C and D, use "semilogx" to use a logarithmic scale for the x-axis and plot input frequencies ranging from 0 to 10 rad/s. The deliverable is your MATLAB code and the plot it generates. 2.E: What is the system's transmission band? The transmission band, aka "passband," of a sensor (FOS or SOS) is the range of frequencies such that 0.707 < Mw) < 1.41 2.F: What is the system's resonance band? The resonance band of a sensor is the range of frequencies such that Mw) > 1.41 2. What is the system's filter band? The filter band of a sensor (FOS or SOS) is the range of frequencies such that Mw) < 0.707
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Given, damping ratio epsi=0.52.A)omega_(n)=0.5rad//s" ringing forequency "{:[omega_(d)=omega_(u)sqrt(1-epsi^(alpha))],[=0.433" rad ls "],[(0//p)/(I//p)=(0.5 xxomega_(u)^(alpha))/(s^(alpha)+alpha epsiomega_(u)9+omega_(u)^(alpha))],[=(0.5 xx(0.5)^(2))/(s^(alpha)+alpha xx0.5 xx0.55+(0.5)^(2))],[=(0.12 s)/(s^(2)+0.5 s+0.25)]:}:. Steody state value =0.5{:[" Now, "quadt_(r)=(pi-tan^(-1)(sqrt(1-epsi x) ... See the full answer