Some Important Topics In Control System

     What are the topics?

•        Open loop & Close loop control system.
• Transfer  Function.
• Elements or Components of Close loop system.
• Characteristics equation of a transfer function.
• Time response for 1st order system.
• Time response for 2nd order system.
• Transient response specification of 2nd order system.

Introduction & Background:

   Control system is the behaviour 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 flyball governer. 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.

       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:

1.         Open loop control system are simple
2.   Open loop control system are economical.
3.    Less maintenance is required and not difficult.
4.    Proper calibration is not a problem.

Disadvantages of open loop control system:

1.       Open loop control system are inaccurate.
2.        These are not reliable.
3.       These are slow.
4.       Optimization is not possible.

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 thermostate.

Advantages of close loop control system:

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

Disadvantages of close loop control system:

1.          Close loop systems are expensive.
2.           Maintenance is difficult.
3.           Complicated installation.

Transfer function:

      Transfer function is defined as the ratio of Laplas transfrom of the output to the Laplas transform of input with all initial conditions are zero.

       Consider a open loop control system                                

       R(s) = Laplas transform of input.

       C(s)= Laplas transform of output.

       G(s)= Transfer function.

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

Characteristics equation of a transfer function:

             

      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:
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 overdamped system and 0 to 100% for underdamped system.
       Rise time=

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

      peak time =

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

      Maximum overshoot=  

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.

      Settling time= 

STEADY STATE ERROR: It is the difference between actual output and desired output as time ‘t’ tends to infinity.

      Steady state error=