Introduction of control system || Types of control systems || Types of feedback || Transfer function || Effect of feedback || Mathematical model

CONTROL SYSTEM:
             A system which consist of number of components connected together to perform a specific function, in which the output  is controlled by input.

TYPES OF SYSTEM:
[1] Open loop system 
         

Advantage:

1] simple and economical

2] easier to construct

3] stable

Disadvantage:

1] inaccurate

2] changes in the output are not corrected automatically

[2] Close loop system 

Advantage:

1] accurate

2] less disturbed by noise

Disadvantage:

1] complex and costier

2] feedback reduces the overall gain of the system

3] stability is a main problem 

TYPES OF CONTROL SYSTEM:

1] Linear system

2] Non linear system

3] Time variant system

4] Time invariant system

5] Linear time variant system

6] Linear time invariant system

TYPES OF FEEDBACK:

1] positive feedback 

C(s)=[R(s)+C(s)H]G

       =GR(s)+GC(s)H

C(s)[1-GH]=GR(s)

then now,

TF= C(s)/R(s) = G/1-GH

2] negative feedback 

C(s)=[R(s)-C(s)H]G

       =GR(s)-GC(s)H

C(s)[1+GH]=GR(s)

then now,

TF= C(s)/R(s) = G/1+GH

TRANSFER FUNCTION:

              Transfer function of a control system is the ratio of laplace transform of output to laplace transform of input.

i.e.

Transfer function = LP of output / LP of input  |with  zero 

C(s)=[R(s)-C(s)H]G

       =GR(s)-GC(s)H

C(s)[1+GH]=GR(s)

then now,

TF= C(s)/R(s) = G/1+GH

EFFECTS OF FEEDBACK:

a] Gain 

we know that,

TF= G/1+GH           - (1)

 if GH ↑ then TF ↓

b] Sensitivity

we know that,

S= % change in T/ % change in G

c] Stability

MATHEMATICAL MODEL:

1] Differential equation model

2] Transfer function model

3] State space model