A process features an open loop transfer function K[({(s + 1) (s + 4)}/{(s + 2) (s + 3)})]. On its root locus diagram, poles will reside at ___________________?
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Answer: C. -2, -3
Explanation
Open loop poles are determined by setting the denominator of the transfer function to zero. Solving the equation yields poles specifically located at negative two and negative three on the axis. These poles represent the values of the Laplace variable that make the denominator completely vanish. The root locus method graphically displays closed loop pole locations as system gain varies continuously. Transfer functions mathematically model linear time invariant control systems using the Laplace domain variable. Denominator roots dictate the natural transient behavior and inherent stability characteristics of dynamical systems.
Control engineers utilize root locus diagrams to design robust feedback controllers for industrial chemical processes. Analyzing pole locations helps prevent unwanted system oscillations during transient load changes in plants. Proper placement of poles ensures that the controlled variable settles quickly to its desired target value. Positive values like one and four represent unstable right half plane pole locations in feedback systems. Options showing positive integers correspond to unstable configurations rather than stable open loop system poles. Incorrect pole locations would lead to divergent responses instead of standard stable transient decay profiles.
- Subject
- Engineering
- Category
- Chemical Engineering
- Topic
- —
- Difficulty
- medium
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