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# Lecture 13 ME 176 6 Steady State Error Re

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### Lecture 13 ME 176 6 Steady State Error Re

1. 1. ME 176 Control Systems Engineering Steady-State Errors Department of Mechanical Engineering
2. 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" Department of Mechanical Engineering
3. 3. Example: Sensitivity Calculate sensitivity of the closed-loop transfer function to changes in parameter a: Closed-loop transfer function: Department of Mechanical Engineering
4. 4. Example: Sensitivity Calculate sensitivity of the closed-loop transfer function to changes in parameter K and a, with ramp inputs: Department of Mechanical Engineering
5. 5. Review: Stability (Routh Table) Make the Routh table and tell how many roots are in the right, left, or jw -axis: Department of Mechanical Engineering
6. 6. Review: Stability (Routh-Hurwitz Criteria) Make the Routh table and tell how many roots are in the right, left, or jw -axis: Department of Mechanical Engineering
7. 7. Review: Stability (Routh Table) Find range of K to make system stable: Department of Mechanical Engineering
8. 8. Review: Stead-State Error Find steady-state error for the following inputs : 15u(t), 15tu(t), and 15t^2u(t): Department of Mechanical Engineering
9. 9. Review: Stead-State Error Evaluate system type, Kp, Kv, and Ka: Department of Mechanical Engineering
10. 10. Review: Stead-State Error Find value of K to yield 10% error in steady state: Department of Mechanical Engineering