A thermocouple is immersed in a liquid to monitor its temperature fluctuations. Assume the thermocouple acts as a first-order system. The temperature fluctuations (in degrees Celsius) vary in time as T(t) = 50 + 25 cos(4t). The output of the thermocouple transducer system (in V) is linearly proportional to temperature and has a static sensitivity of 2 mV/°C. A step-input calibration of the system reveals that its rise time is 4.6 s. Using MatLAB answer the following: Determine the system's (a) time constant (in seconds), (b) output E(t) (in millivolts), (c) time lag (in seconds) at ω = 0.2 rad/s, (d) solve the response of this first-order system analytically to get temperature distribution equation, (e) solve this first-order system again with MATLAB (ode45) and plot the results along with input forcing function in one figure.
A thermocouple is immersed in a liquid to monitor its temperature fluctuations. Assume the thermocouple acts as a first-order system. The temperature fluctuations (in degrees Celsius) vary in time as T(t) = 50 + 25 cos(4t). The output of the thermocouple transducer system (in V) is linearly proportional to temperature and has a static sensitivity of 2 mV/°C. A step-input calibration of the system reveals that its rise time is 4.6 s.
Using MatLAB answer the following: Determine the system's (a) time constant (in seconds), (b) output E(t) (in millivolts), (c) time lag (in seconds) at ω = 0.2 rad/s, (d) solve the response of this first-order system analytically to get temperature distribution equation, (e) solve this first-order system again with MATLAB (ode45) and plot the results along with input forcing function in one figure.
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