.

1. Prepared By:
Kishan Beldiya (140040109002)
Jaydeep Chandra (140040109009)
5th Sem., EE. Engg. Dept.,
BHGCET, Rajkot
Internal Guide:
Prof. Nirav B Mehta
Electrical Dept.
BHGCET, Rajkot
Presentation on
Types Of Controller
Under the subject of
Control System Engineering

2. Types Of Controller
• On-Off Controller
• P Controller
• PI Controller
• PD Controller
• PID controller

3. On-Off Controller
• On-Off control is the simplest form of feedback
control and it has only two mode.
• A common example of on-off control is the
temperature control in a domestic heating system.

4. P Controller
• To Understand P Controller We Need a Model
Velocity
Gas paddle

5. P Controller
• The relationship between the error signal and
controller output
m(t)=Kpe(t)+m0
Here , m(t)=Controller output,
e(t)=error
Kp=Proportional gain constant
m0=Controller output at zero error

6.  Block-Diagram
Kp ωn²/s(s+2ξωn)
R(s) e(t) m(t)
b(t)
C(s)
-

7. Kpωn²
C(s) G(s) s(s+2ξωn)
R(s) 1 + G(s)H(s) 1 + Kpωn²
s(s+2ξωn)
Kpωn²
s²+2ξωns+Kp ωn²
= =
=
Using block diagram reduction

8. PI Controller
The integral action is given by,
mi(t) = ki ∫e(t)dt+ m(0)
Mathematical expression for P-I controller
m(t)=kpe(t) + ki∫e(t)dt + m(0)

9. Kp ωn²/s(s+2ξωn)
e(t)
c(s)
m(t)
-
Kp∫dtKi/s
+
+
R(s)
(Kp+ki/s)ωn²/s(s+2ξωn)
 Block Diagaram

10. We use Block Diagram Reduction Techniques
C(s) G(s)
R(s) 1 + G(s)H(s)
(Kp s + Ki)ωn²
s³ + 2ξs²ωn +Kp ωn²+Ki ωn²
=
=

11. P-D Controller
The derivation action is given by,
md(t)=Kd
𝑑
𝑑𝑡
e(t)
mathematical expression for P-D Controller is
m(t)=Kpe(t)+ Kd
𝑑
𝑑𝑡
e(t)+m0
Now take laplace,
M(s)=KpE(s) + Kd sE(s)+M0

12. Kp ωn²/s(s+2ξωn)
e(t)
c(s)
m(t)
-
Kd 𝑑/𝑑𝑡Kd s
+
+
R(s)
Kp + kd s
 Block Diagaram

13. • Hence the T.f is ,
C(s) G(s)
R(s) 1 + G(s)H(s)
=
= (Kp s + Ki)ωn²
s² + 2ωn(ξ+kdωn )+Kp ωn²
2
C(s)
R(s)

14. mathematical expression for P-I-D Controller
m(t)=Kpe(t)+ ki ∫e(t)dt+ Kd
𝑑
𝑑𝑡
e(t)+m0
Now take laplace
M(s)=KpE(s) +Ki Es +Kd sE(s)+M0
s
PID Controller

15. Kp
Kd s
Ki/s
ωn²/s(s+2ξωn)
R(s)
-
+
+
+
C(s)
Kp+ Kd s+ Ki/s
 Block-Diagram

16. Hence the T.f is ,
C(s) G(s)
R(s) 1 + G(s)H(s)
=
C(s) (Kds²+kps+ki) ωn²
R(s) 𝑆3 + (2ξωn+kdωn² ) s²+Kp ωn²s
=