Compensators definition and s-plane representation is explained

1. compensators
 Types of compensators
 S-Plane representation of compensator
 Comparision of Compensators
Prepared By
Mr.K.Jawahar, M.E.,
Assistant Professor
Department of EEE
Compensators
Kongunadunadu College of Engineering and Technology Depar tment of EEE

2. Compensator
• The control system are designed to perform specific tasks. The
requirement of a control system are usually specified as
performance specifications.
• The specifications related to accuracy, relative stability and speed
of the response.
The design problem may be stated as follows:
• When a set of specifications are given for a system, then a
suitable compensator should be designed so that the overall
system will meet the given specification.
• The compensation schemes used for feedback control system is
either series compensation or parallel feedback compensation.
Compensators
Kongunadunadu College of Engineering and Technology Depar tment of EEE

3. The choice between series and parallel compensation depends on:
1. Nature of signals in the system
2. Power levels at various points
3. Components available
4. Designer’s experience
5. Economic considerations and so on.
The different types of electrical or electronics compensators used
are
 Lag compensator
 Lead compensator
 Lag-lead compensator
Compensators
Kongunadunadu College of Engineering and Technology Depar tment of EEE

4. In control systems, compensation is required in the following
situations,
• When the system is absolutely unstable, then compensation is
required to stabilize the system and also to meet the desired
performance.
• When the system is stable, compensation is provided to obtain
the desired performance.
 The systems with type number 2 and above are usually absolutely
unstable systems. Hence for systems with type number 2 and
above, lead compensation is required, because the lead
compensator increases the margin of stability.
 In the systems with type number 1 or 0, stability is achieved by
adjusting the gain. In such cases any of the three compensators
may be used to obtain the desired performance.
Compensators
Kongunadunadu College of Engineering and Technology Depar tment of EEE

5. S-plane representation of LAG compensator:
• The lag compensator has a pole at s=-1/ßT and a zero at s=-1/T.
• Here ß>1, so the zero is located to the left of the pole on the
negative real axis.
where T >0 and ß >1
S-plane representation of LEAD compensator:
• The lead compensator has a zero at s=-1/T and a pole at s=-1/αT.
• Here α<1, so the zero is closer to the origin than the pole.
where T >0 and α <1
Compensators
Kongunadunadu College of Engineering and Technology Depar tment of EEE

6. S-plane representation of LAG-LEAD compensator:
• The lag selection has one real pole and one real zero with pole to
the right of zero.
• The lead selection also has one real pole and one real zero but the
zero is to the right of the pole.
Where ß > 1 and 0<α<1
Compensators
Kongunadunadu College of Engineering and Technology Depar tment of EEE

7. Realization of lag compensator using electrical network:
Compensators
Kongunadunadu College of Engineering and Technology Depar tment of EEE

8. Compensators
Kongunadunadu College of Engineering and Technology Depar tment of EEE

9. Realization of lead compensator using electrical network:
Compensators
Kongunadunadu College of Engineering and Technology Depar tment of EEE

10. Compensators
Kongunadunadu College of Engineering and Technology Depar tment of EEE

11. S.
No
Lag Compensator LeadCompensator Lag-Leadcompensator
1 A compensator having the
characteristics of a lag
network is called lag
compensator.
A compensator having the
characteristics of a lead
network is called lead
compensator.
A compensator having the
characteristics of a lag-lead
network is called lag-lead
compensator.
2 If a sinusoidal signal is
applied, then in steady state
the output will have a phase
lag with respect to the input.
If a sinusoidal signal is
applied, then in steady state
the output will have a phase
lead with respect to the
input.
If a sinusoidal signal is
applied, then in steady state
both phase lag and lead
occurs in the output, but in
different frequency region.
3 Lag compensation results in
a large improvement in
steady state performance but
results in slower response
due to reduced bandwidth.
The lead compensation
increases the bandwidth,
which improves the speed of
the response and also
reduces the amount of
overshoot.
A lag-lead compensation
combines the advantages of
lag and lead
compensations.
Compensators
Kongunadunadu College of Engineering and Technology Depar tment of EEE

12. Reference:
• A.Nagoor Kani, “ Control Systems”, RBA Publications, June
2012.
Compensators
Kongunadunadu College of Engineering and Technology Depar tment of EEE