Control system(INPUT- OUTPUT RElATION

                Introduction & Background
 >>Control system is the behavior of the system is    described by the differential equations. The differential equation may be ordinary differential equation or difference equation.
  
 >>The first significant control device was James Watt's fly-ball governor. It was invented in 1767. the working principle was to keep the speed of the engine constant by regulating the supply of the steam to the engine.
           
             What is open loop control system?

 

The control system  without feedback is called open loop control

system or non feedback control system. In open loop systems the

control action is independent on the desired output.

Examples: Automatic washing machine, Immersion rod, a field control D.C motor.

 

 Advantages of open loop control system

• Open loop control system are simple.
•  Open loop control system are economical.
•  Less maintenance is required and not difficult.
•  Proper calibration is not a problem.

     Disadvantages of open loop control system

•  Open loop control system are inaccurate.
•   These are not reliable.
•   These are slow.
•  Optimization is not possible     

       What is close loop control system? 

 Close loop control systems are known as feedback control system.

In close loop control system the control action is dependent on the

desired output. 

Example: Air conditioners provided with thermostat. 

 

  

 Advantages:  

• These systems are more reliable.
•   Close loop systems are faster.
•  A number of variable can be handled simultaneously. Optimization is possible 

      Disadvantages :

•  Close loop systems are expensive.
•  Maintenance is difficult.
•  Complicated installation 

                     What is transfer function?

Transfer function is defined as the ratio of Laplace transform of the

output to the Laplace  transform of input with all initial conditions

are zero.

Consider a open loop control system                                

   R(s) = Laplace  transform of input.             

   C(s)= Laplace transform of output.

   G(s)= Transfer function.

 

Transfer function G(s)=C(S)/R(S)

 Characteristics equation of a transfer function

Characteristics equation of a transfer function is 

 

POLES:  The poles of G(s) are Those values of ‘s’ which make G(s)

tend to infinity. Above transfer function having simple poles at

 s=0,s=-2,double poles at s= -4

ZEROS:The zeros of G(s) are Those values of ‘s’ which make G(s)

tend to Zero. Here the simple Zero at s= -3.

Graphical representation of POLES & ZEROS 

Poles are represented by ‘X’ & Zeros are represented by ‘O’.

Now the Pole-Zero plot of the previous transfer function is

 

           Time Response of Control system

Time domain representation of a control system is known as time

response . Time response of a control system is divided into two

parts. 

  1. Transient response        

   2.  Steady state response        

 

Time response of the 1st order system with unit step input 

 Some definitions of transient response of 2nd                                order system

 DELAY TIME: It is the time required for the response to reach 50% of  the final value in first time.

RISE TIME: It is the time required for the response to rise 10% to 90% of its final value for over-damped system and 0 to 100% for under damped system 

 PEAK TIME: It is the time required for the response to reach the first peak of the time response or first peak overshoot

MAXIMUM OVERSHOOT: It is the normalized difference between the peak of the time response and steady output.

 

SETTLING TIME: It is the time required for the response to reach and stay within the specified range   (2% to 5%) of the final value.

 

STEADY STATE ERROR:  It is the difference between actual

 output and desired output as time ‘t’ tends to infinity.