By William K. Roots (Auth.)
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14 shows semilogarithmic plots of A = 1/(1 + a2)1/2 φ = — arctan(a) These plots are called Bode diagrams after their originator. 14(a) is a semilogarithmic plot of the amplitude response (A) that has two asymptotes that intersect at A = 1 = 0 dB V = ωΤ = 1 This intersection is often called the break point (or corner), and the angular frequency ω = l/T (v = 1) is called the break frequency (or corner frequency). Before the break frequency, the horizontal asymptote is the straight line A = 1 = 0 dB.
T h e bulk of practical temperaturecontrol problems involve systems that are linear, or which can safely be assumed to be linear. 38 2. Λ Λ }J \J ^ UT FIG. 17. T h e superposition principle. T h e steady-state response of a linear process subjected to an input (a) is the sum of the steady-state responses to each com ponent of the input (b-d). 20) is the steady-state response of an exponential lag to the type of input of Eq. 19) once the transient caused by the complementary function has decayed.
5. Such an error is called a velocity error. It would be zero if the time constant were infinitely short (T = 0). Transient response (from the complementary function): Θ = QT txpi-t/T) 20 2. THERMAL-PROCESS RESPONSE Steady-State Error <^jj* k e (°F) Ό Transient Error at t = T ^ 20773 •■HThermometer Input Indicated Temperature Temperature /(sec) FIG. 5. Transient and steady-state errors of a thermometer, or any similar exponential-lag element, when the input (temperature) rises at a constant rate (a ramp-function input).
Fundamentals of Temperature Control by William K. Roots (Auth.)