A composition sensor is used to continually monitor the contaminant level in a liquid stream. The dynamic behavior of the sensor can be described by a first-order transfer function with a time constant of 10s,

where C? is the actual contaminant concentration and C?_m is the measured value. Both are expressed as deviation variables (e.g., C = C ? C). The nominal concentration is C = 5 ppm. Both C and C_m have values of 5 ppm initially (i.e., the values at t = 0). An alarm sounds if the measured value exceeds the environmental limit of 7 ppm. Suppose that the contaminant concentration C gradually increases according to the expression, C(t) 5 + 0.2t, where! is expressed in seconds. After the actual contaminant concentration exceeds the environmental limit, what is the time interval, ?t, until the alarm sounds?

Transcribed Image Text:

C(s) 10s + I C'(s)