HW+_4+Solution

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1. Consider a measurement system than includes a transducer whose parameters are not known. In order to compensate for the transducer dynamics it is necessary to estimate the dynamic parameter(s) for this device. A step input to the transducer yields the following response. Determine the transducers system parameters. Then write the transfer function of this system. [Hint: The step response is similar to that of a first order system]. Since there is no overshoot in the step response, it is reasonable to assume that the system is of 1 st order. For a second order system we need to determine two parameters. 1) Time constant and 2) Static sensitivity. Since the response of the system is twice as much as the input at steady state (time > 4 sec), the static gain is 2. The time constant can be determined by locating 0.632*Step_value = 1.264 point on the response plot and determining the time. Therefore the time constant is given by, τ = 0.5 sec. The transfer function of the system is then given by:
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2. An accelerometer has the following step response. What is the system order of the
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