The document discusses control systems engineering concepts including sensitivity, stability analysis using Routh tables and Routh-Hurwitz criteria, steady-state error, and calculating gains. It provides examples of calculating sensitivity to parameter changes, using Routh tables to determine system stability, finding steady-state error for different input signals, and selecting gain values for desired steady-state error. The document is from a mechanical engineering course on control systems.

1. ME 176
Control Systems Engineering
Steady-State Errors
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Mechanical Engineering

2. Definition: Sensitivity
"The degree to which changes in system parameters affect
system transfer functions, and hence performance."
A system with zero sensitivity is ideal.
Greater the sensitivity, the less desirable.
"The ratio of the fractional change in the function to the fractional change
in parameter as the fractional change of parameters approaches zero"
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3. Example: Sensitivity
Calculate sensitivity of the closed-loop transfer function to changes in parameter a:
Closed-loop transfer function:
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4. Example: Sensitivity
Calculate sensitivity of the closed-loop transfer function to changes in parameter K
and a, with ramp inputs:
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5. Review: Stability (Routh Table)
Make the Routh table and tell how many roots are in the right, left, or jw -axis:
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6. Review: Stability (Routh-Hurwitz Criteria)
Make the Routh table and tell how many roots are in the right, left, or jw -axis:
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7. Review: Stability (Routh Table)
Find range of K to make system stable:
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8. Review: Stead-State Error
Find steady-state error for the following inputs : 15u(t), 15tu(t), and 15t^2u(t):
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9. Review: Stead-State Error
Evaluate system type, Kp, Kv, and Ka:
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10. Review: Stead-State Error
Find value of K to yield 10% error in steady state:
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