The transfer function of a first order system is expressed as______________?
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Answer: A. 1/(Ts + 1)
Explanation
Linear first-order systems are mathematically modeled by a single-pole transfer function structure. The numerator represents the static process gain, while the denominator contains the time constant term. Setting time constant T to zero simplifies the expression to a pure proportional gain of unity. Transfer functions relate the Laplace transform of the output variable to the input variable. First-order models describe systems with one energy storage mechanism and a linear resistive path. Step responses of this standard transfer function follow a smooth exponential curve approaching stability.
Temperature sensors, liquid storage tanks, and simple electronic filters are modeled using this transfer function. Control system designers use first-order transfer functions to simulate plant behavior before hardware installation. Understanding this baseline equation is fundamental for studying advanced multi-loop industrial control systems. Option B represents pure integral action rather than a standard first-order dynamic lag system. Option C introduces a derivative numerator term that alters the system into a lead-lag configuration. Option D is incorrect because the standard first-order transfer function is explicitly given in option A.
- Subject
- Engineering
- Category
- Chemical Engineering
- Topic
- —
- Difficulty
- medium
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