Lag-Lead Compensator
The lag-lead compensator is a mixture of a lag and a lead compensator, as the name suggests.
In a control system, the lag compensator creates an output that is phase-late. In a control system, the phase lead is used to produce the output by the lead compensator. As a result, the output of the lag-lead compensator has phase lead in one frequency area and phase lag in another.
It is made up of two capacitors, C1 and C2, and two resistors, R1 and R2.
Transfer function = H(s) = Vo(s) / Vi(s)
The lag compensator diagram’s output shows that the output is connected across the second branch and is represented as an RC circuit. It has a capacitor, C2, linked in series with one resistor, R2.
Vo(s) = R2 + 1/C2s
Let’s find the input.
It will be:- R2 + 1/C2s
The parallel combination :- R1 x 1/C1s/(R1 + 1/C1s)
The series combination of the combinations mentioned before will now be the comparable input, and it is provided by:
Vi(s) = R2 + 1/C2s + R1 (1/C1s)/(R1 + 1/C1s)
Now the TS will be H(s)
Transfer function H(s) = Vo(s)/Vi(s)
=( R2 + 1/C2s) / {(R2 + 1/C2s) (R1 + 1/C1s) + R1 x 1/C1s}/ ((R1 + 1/C1s)
= (R2 + 1/C2s) (R1 + 1/C1s) / R1R2C1C2s + (R1C1 + R2C2 + R1C2)s + 1
Let, AT1 = R1C1
BT2 = R2C2
T1T2 = R1R2C1C2,
if AB = 1
H(s) = Vo(s)/Vi(s) = (1 + AT1s) (1 + BT2s) / (1 + T1s) (1 + T2s)
Compensators
All of the topics covered in the Control System Tutorial, including the Introduction to Control Systems, Classification, Transfer Function, Signal Flow Graphs, Mason Gain Formula, Block Diagram, State Space Model, and more, are included in our tutorial.
The compensator is an extra part that is introduced to the control system’s structure throughout its redesign. It is included in order to make up for the system’s poor performance. A compensator can be mechanical, electrical, hydraulic, or any combination of these.
Table of Content
- What is a Compensator?
- Types of Compensator
- Gain Cross over point
- Phase Lead and Phase Lag
- Examples
- Advantages of Compensator
- Disadvantage of Compensator