LINEAR CONTROL SYSTEMS

1
LINEAR CONTROL SYSTEMS

• Ali Karimpour
• Assistant Professor
• Ferdowsi University of Mashhad

2
Lecture 18
Time domain design of control systems

• Topics to be covered include
• Effect of moving poles and zeros.
• Design of controller in time domain.
• Various controller configurations.
• Different kind of controllers.
• Controller realization.

3
Effect of moving poles.
????? ???? ?????
Consider following equation
Let b1 but a10, 9, 8, 3, 1
4
Effect of moving poles.
????? ???? ?????
Let a10
Let a10
5
Effect of moving poles.
????? ???? ?????
Let a9
-9
6
Effect of moving poles.
????? ???? ?????
Let a8
-8
7
Effect of moving poles.
????? ???? ?????
Let a3
-3
8
Effect of moving poles.
????? ???? ?????
Let a1
9
Effect of moving poles.
????? ???? ?????
a 1
a 3
a10
a 9
a 8
10
Various controller configurations.
????????? ?????? ??????
11
Various controller configurations.
????????? ?????? ??????
12
Various controller configurations.
????????? ?????? ??????
13
Various controller configurations.
????????? ?????? ??????
14
Various controller configurations.
????????? ?????? ??????
15
Various controller configurations.
????????? ?????? ??????
16
Series Compensation Structure
????? ???? ???

• In this Course consider the simple SISO control
  loop shown in the figure.

There is a lot of different controller!
17
In This course
Different kind of controllers
????? ??????
PID controllers.
Lead lag controllers
Different kind of controllers
In Graduate courses
H2 Controllers
H8 Controllers
..
Adaptive Controllers
Intelligent Controllers
NN Controllers
..
18
PID Controllers
?????? PID

• PID has become almost universally used in
  industrial control.
• These controllers have proven to be robust and
  extremely beneficial in the control of many
  important applications.
• PID stands for P (Proportional)
• I (Integral)
• D (Derivative)

19
Historical Note
????? ??????

• Early feedback control devices implicitly or
  explicitly used the ideas of proportional,
  integral and derivative action in their
  structures.
• However, it was probably not until Minorskys
  work on ship steering published in 1922, that
  rigorous theoretical consideration was given to
  PID control.
• This was the first mathematical treatment of the
  type of controller that is now used to control
  almost all industrial processes. (more that 95
  of closed-loop industrial processes.)
• Minorsky (1922) Directional stability of
  automatically steered bodies, J. Am. Soc.
  Naval Eng., 34, p.284.

20
PID Controllers
?????? PID

• The standard form PID are

Proportional only
Proportional plus Integral
Proportional plus derivative
Proportional, integral and derivative
21
Lead-lag Compensators
?????? ??? ??? ?? ???

• Closely related to PID control is the idea of
  lead-lag compensation. The transfer function of
  these compensators is of the form
• If alt1 , then this is a lag network. Or (zgtp) in
  other form.
• If agt1 this is a lead network. Or (zltp) in other
  form.

22
A phase Lag network
?? ???? ?? ???
So it is a Lag network
23
A phase Lead network
?? ???? ??? ???
So it is a Lead network