First & second order of the control systems
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This document summarizes key concepts about first and second order control systems. It discusses: - The characteristics of a first order system, which has one pole and is defined by its DC gain (K) and time constant (T). - Examples of first order systems and how to determine their DC gain and time constant. - That a second order system can have different responses depending on its parameters, such as damped or undamped oscillations. - How to determine the undamped natural frequency and damping ratio of a second order system by comparing its transfer function to the general second order transfer function. The document then provides example problems for determining properties of first and second order systems. It concludes by
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P73
1) Control theory deals with analyzing and designing closed-loop control systems to achieve desired output behaviors.
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3) State-space representation involves expressing higher-order differential equations as a set of first-order equations and representing the system using matrix equations that can be analyzed and simulated on computers. This allows visualization and analysis of dynamic systems.
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time response
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2. First-order systems have exponential responses to unit step and ramp inputs. Their time constant T determines the response. Second-order systems can have underdamped, critically damped, or overdamped responses depending on the damping ratio ζ.
3. System specifications like rise time, settling time, and overshoot can be determined from the time response plots. The location of poles and zeros affects stability and transient response. A system is only stable if all poles are in the left half plane.
BEC- 26 control systems_unit-II
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3. Additionally, the TCSC is shown to reduce short circuit current during a fault on the line from 350A to 250A, demonstrating its ability to limit fault current.
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This document provides an overview of a control systems engineering course. It discusses key topics that will be covered, including modeling dynamic systems using differential equations, obtaining accurate plant models, designing controllers to meet performance specifications, handling uncertainties, and bridging the gap between linear control theory and real-world industrial problems. The course aims to address issues like robust stability, robust performance, nonlinearities, and designing controllers when plant models are difficult to stabilize.
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First & second order of the control systems
- 1. First & Second Order of the Control Systems Presented by Mr. C.S.Satheesh, M.E., Assistant Professor, Department of EEE, Muthayammal Engineering College (Autonomous), Namakkal (Dt), Rasipuram – 637408 MUTHAYAMMAL ENGINEERING COLLEGE (An Autonomous Institution) (Approved by AICTE, New Delhi, Accredited by NAAC, NBA & Affiliated to Anna University), Rasipuram - 637 408, Namakkal Dist., Tamil Nadu, India.
- 2. Order system
- 3. Introduction - First order system The first order system has only one pole. Where K is the D.C gain and T is the time constant of the system. Time constant is a measure of how quickly a 1st order system responds to a unit step input. D.C Gain of the system is ratio between the input signal and the steady state value of output. 1 Ts K s R s C ) ( ) (
- 4. First order system Examples: The first order system given below. 1 3 10 s s G ) ( 5 3 s s G ) ( 1 5 1 5 3 s / / • D.C gain is 10 and time constant is 3 seconds. • For the following system • D.C Gain of the system is 3/5 and time constant is 1/5 seconds.
- 10. Second Order System We have already discussed the transient response of 1st order systems. Compared to the simplicity of a first-order system, a second-order system exhibits a wide range of responses that must be analyzed and described. Whereas, changes in the parameters of a second-order system can change the form of the response. A second-order system can display characteristics much like a first-order system or, depending on component values, display damped or pure oscillations for its transient response. 10
- 17. Problem 1 4 2 4 ) ( ) ( 2 s s s R s C Determine the un-damped natural frequency and damping ratio of the following second order system. 4 2 n 2 2 2 2 n n n s s s R s C ) ( ) ( • Compare the numerator and denominator of the given transfer function with the general 2nd order transfer function. 2 n s s n 2 2 4 2 2 2 2 2 s s s s n n 5 0. 1 n 17
- 18. Problem 2
- 20. Problem 3
- 28. Static error constant for various type number of system
- 29. Steady state error for various types of input
- 36. Problem 4
- 37. Problem 5
- 53. References : A.Nagoorkani, Control Systems, RBA Publications. 4/5/2021 53
- 54. Thank You 54