Csl10 9 f15

ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION

Control Systems

First and second order system performance


Outline of the topic

• Open loop and closed loop system• Transient and Steady state response• First order system• Performance parameters of First order system• Second order system• Performance parameters of Second order

system


Transient and steady state response

• Closed loop or feedback control systems– Ability to adjust the transient and steady state

performance– Desired performance obtained by adjusting the

system performance

Speed at 60km/hrPress accelerator

Speed desired80km/hr

Difference


• Transient response - disappears with time• Steady state response – exists for along time

following an input signal initiation• To analyze and design a control system – Define and measure its performance– Design specifications • Time response indices for a specified input command• Desired steady state accuracy

Transient and steady state response


First order system -Example 1

Differential equation

𝑌 (𝑠)𝑈 (𝑠 )

= 1𝑚𝑠+𝑏

Taking Laplace transform

Transfer function

1𝑚𝑠+

-

Y(s)U(s)

𝑏

1𝑚𝑠+𝑏

U(s) Y(s)


First order system –Example2

Differential equation

Taking Laplace transform

𝑅𝐶𝑠𝑌 (𝑠 )+𝑌 (𝑠 )=𝑈 (𝑠)

Transfer function𝑌 (𝑠)𝑈 (𝑠 )

= 1𝑅𝐶𝑠+1

1𝑅𝐶𝑠+

-

Y(s)U(s)

1𝑅𝐶𝑠+1

U(s) Y(s)


• First order system – system with one pole• General for of first order system

First order system

𝐶 (𝑠)𝑅(𝑠)

= 1𝑠𝑇+1


First order system with unit step

• Unit step response • Output c• Steady state response • Transient response which decays to zero as t

infinity


First order system with unit step

• Steady state error – error after the transient response has decayed and leaves a continuous response

error signal = • As t approaches infinity, the exponential

becomes 0


First order system with step input - response

Slope is 1/T

Pole is -1/T

At t=T, c

T is called the Time constant, time taken to reach 63.2% of the final value

c(2T) =0.895 c(3T)=0.95c(4T)=0.982c(5T)=0.993For T>4T response remains within 2% of final value, this is settling time


First order system with unit ramp


First order system with unit impulse

Csl10 9 f15

Engineering

Transcript of Csl10 9 f15