Podcast
Questions and Answers
What are the coefficients that will minimize the ITAE performance criterion for a step input in the general closed-loop transfer function?
What are the coefficients that will minimize the ITAE performance criterion for a step input in the general closed-loop transfer function?
What is the closed-loop transfer function for the given system?
What is the closed-loop transfer function for the given system?
What is the natural frequency of the closed-loop system?
What is the natural frequency of the closed-loop system?
What is the damping ratio of the closed-loop system?
What is the damping ratio of the closed-loop system?
Signup and view all the answers
How do you calculate the percent overshoot (P.O.) of a second-order system?
How do you calculate the percent overshoot (P.O.) of a second-order system?
Signup and view all the answers
What is the closed-loop transfer function for the given system?
What is the closed-loop transfer function for the given system?
Signup and view all the answers
What is the percent overshoot (P.O.) of the second-order system?
What is the percent overshoot (P.O.) of the second-order system?
Signup and view all the answers
What are the coefficients that will minimize the ITAE performance criterion for a step input in the general closed-loop transfer function?
What are the coefficients that will minimize the ITAE performance criterion for a step input in the general closed-loop transfer function?
Signup and view all the answers
What is the natural frequency of the closed-loop system?
What is the natural frequency of the closed-loop system?
Signup and view all the answers
How do you calculate the damping ratio of the closed-loop system?
How do you calculate the damping ratio of the closed-loop system?
Signup and view all the answers
What is the percent overshoot (P.O.) of the second-order system?
What is the percent overshoot (P.O.) of the second-order system?
Signup and view all the answers
What is the natural frequency of the closed-loop system in radians per second?
What is the natural frequency of the closed-loop system in radians per second?
Signup and view all the answers
Study Notes
The Performance of Feedback Control Systems
- The steady-state error of a feedback control system is determined by the equation: E(s) = R(s) - Y(s) = [1 - T(s)]R(s)
- The system's transfer function, T(s), is given by: T(s) = K1G(s) / [1 + K1G(s)H(s)]
- The steady-state error, ess, is calculated as: ess = lim(s→0) E(s) = 1 / [1 + K1G(0)]
Performance Indices
- A performance index is a quantitative measure of a system's performance, chosen to emphasize important system specifications
- A system is considered optimal when its parameters are adjusted to reach an extremum value (usually a minimum) of the performance index
- The performance index must be a positive or zero value
Types of Performance Indices
- T ISE (Integral of the Square of the Error): ∫e²(t) dt from 0 to T
- T IAE (Integral of the Absolute Magnitude of the Error): ∫|e(t)| dt from 0 to T
- T ITAE (Integral of Time multiplied by Absolute Error): ∫t|e(t)| dt from 0 to T
Optimum Coefficients of T(s) Based on the ITAE Criterion
- For a step input, the optimum coefficients of T(s) are: s + ωn, s² + 1.4ωn s + ωn², s³ + 1.75ωn s² + 2
- To get ess = 0, a type 1 system is required for a step input, and a type 2 system is required for a ramp input
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Test your knowledge of feedback control systems and performance indices with this quiz. Explore topics such as steady-state error, performance measures, and system specifications.
