Flashcards
Ch 8: Root Locus Techniques
Cards in this deck (17)
- 1What does a root locus represent?the paths of the closed-loop poles as the gain is varied
- 2What does the number of branches of the root locus equal?the number of closed-loop poles
- 3What is a root locus?The plot of a system's closed-loop poles as a function of gain.
- 4Describe two ways of obtaining the root locus?1) Finding the closed-loop TF, substituting a range of gains into the denominator, and factoring the denominator for each value of gain. 2) Search on the s-plane for points that yield 180 degrees when using the open-loop poles and zeros.
- 5Do the zeros of a system change with a change in gain?No
- 6Where are the zeros of the closed-loop transfer function?At the zeros of G(s) and the poles of H(s)
- 7What are two ways to find where the root locus crosses the imaginary axis?1) Apply Routh-Hurwitz to the closed-loop TF's denominator. 2) Search along the imaginary axis for 180 degrees.
- 8How can you tell from the root locus if a system is unstable?If any branch of the root locus is in the rhp, the system is unstable.
- 9How can you tell from the root locus if the settling time does not change over a region of gain?If the branch of the root locus is vertical, the settling time remains constant for that range of gain on the vertical section.
- 10How can you tell from the root locus that the natural frequency does not change over a region of gain?If the root locus is circular with origin at the center
- 11How would you determine whether or not a root locus plot crossed the real axis?Determine if there are any break-in or breakaway points
- 12Describe the conditions that must exist for all closed-loop poles and zeros in order to make a second-order approximation.1. Poles must be at least five times further from the imaginary axis than the dominant second order pair. 2) Zeros must be nearly canceled by higher order poles.
- 13What rules for plotting the root locus are the same whether the system is a positive- or a negative-feedback system?Number of branches, symmetry, starting and ending points
- 14Describe how the zeros of the open-loop system affect the root locus and the transient response.The zeros of the open loop system help determine the root locus. The root locus ends at the zeros. Thus, the zeros are the closed-loop poles for high gain.
- 15Closed-loop poles change with changes in _____.system gain
- 16(s+a) is a_____ and can be represented by a vector drawn from the zero of the function to the point s.complex number
- 17The root locus technique can be used to analyze and design the effect of _____ upon a system's transient response and stability.loop gain
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- Undergraduate Controls Flashcards on Ch 8: Root Locus Techniques, created by David Smith on 09/11/2015.
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- David Smith
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