Performance of second order system
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This presentation discusses the performance of a second-order system. It covers standard test input signals used to analyze systems, such as steps, ramps, and sinusoids. The response and performance indices of an underdamped second-order system are examined, including oscillatory behavior and effects on rise time and overshoot. Adding a third pole or zero can further impact the system response by changing the dominant system poles.
( 1
sGLtg
System impulse response:
t
sRsGLdrtgty )]()([)()()( 1
System response is the convolution integral of g(t) and r(t):](https://image.slidesharecdn.com/performanceofsecondordersystem-160425050439/85/Performance-of-second-order-system-6-320.jpg)
Performance of second order system
- 1. PRESENTATION ON PERFORMANCE OF A SECOND- ORDER SYSTEM
- 2. Main content Test input signals Performance of a second-order system Effects of a third pole and a zero on system response Steady-state error analysis
- 3. Introduction Transient response Steady-state response Design specifications How to get compromise? A distinct advantage of feedback control system is the ability to adjust the transient and steady-state response
- 4. Test input signals Step input Ramp input Parabolic input Sinusoidal input Unit impulse input The standard test input signals commonly used are:
- 5. Representation of test signals Step: Ramp: Parabolic: sinusoidal: 22 3 2 2 sin 1 0 2 1 1 0, 1 0),(1 s A tA s tt s tt s tt Input time domain frequency domain
- 6. Unit impulse response otherwise t t ,0 22 , 1 )( Unit impulse: )]([)( 1 sGLtg System impulse response: t sRsGLdrtgty )]()([)()()( 1 System response is the convolution integral of g(t) and r(t):
- 7. Standard test signal The standard test signals are of the general form: n ttr )( And its Laplace transform is: 1 ! )( n s n sR
- 8. Performance indices Time delay t d Rise time t r Peak time t p Settling time t s Percent overshoot % Transient Performance: Steady-state Performance: Steady-state error
- 9. Response and performance of a second-order system Model of 2nd-order system Roots of characteristic equation (Poles) 22 2 2)( )( )( sssR sY sT 12 2,1 nns The response depends on and n
- 10. Unit step response of 2nd- order system If ,2 positive real-part roots, unstable If ,2 negative real-part roots, underdamped If ,2 equal negative real roots, critically damped If ,2 distinct negative real roots, overdamped If ,2 complex conjugate roots, undamped 0 10 1 1 0
- 11. Case 1: underdamped Oscillatory response No steady-state error
- 12. Case 2: critically damped Mono-incremental response No Oscillation No steady-state error
- 13. Case 3: overdamped Mono-incremental response slower than critically damped No Oscillation No steady-state error
- 14. Performance evaluation ( underdamped condition) Performance indices evaluation 1 Time delay 2 Rise time 3 Peak time 4 Percent overshoot 5 Settling time
- 15. Effects of a third pole and a zero on 2nd-order system response Effect of a third pole Effect of a third zero Dominant poles
- 16. References 1. Modern Control System by Richarc C. Drof and Robert H. Bishop,11th Edition Person Int. 2. Modern Control Engineering by Katsuhiko Ogata, 4th Edition, Prentice Hall of India. 3. Automatic Control Systems by Benjamin C.Kuo, 8th Edition, Farid Golnaraghi, John Wiley & Sons. 4. Control Systems Engineering by Nagrath and Gopal New Age Publication 5. Feedback and Control Systems by Joseph J Distefano 2nd Edition TMH