Lead Compensator
In a control system, the phase lead is used to produce the output by the lead compensator. Lead in this context refers to ahead. This kind of action is a successor to it.
The transfer function is defined as the H(s) which is ratio of output voltage to input voltage.
H(s) = Vo(s) / Vi(s)
Here , Vo(s) = R2
The elements in series or parallel configuration (capacitor and resistors) will be the input. The capacitor C1 and resistor R1 are linked in parallel. The resistor R2 is further linked in series with the equivalent parallel combination.
=> R1(1/Cs)/ (R1 + 1/Cs)
The equivalent Vi (s) = R2 + R1(1/Cs)/ (R1 + 1/Cs)
now we know that transfer function H(s) = Vo(s) / Vi(s)
= R2 / [R2 + R1(1/Cs)/ (R1 + 1/Cs)]
= R2(R1Cs + 1) / [R1R2Cs + 1/(R1 + R2)]
= R2/(R1 + R2) (R1Cs + 1) / [R1R2Cs/(R1 + R2) + 1]
Here T = R1 C
A = R2 / (R1 + R2)
H(s) = Vo(s) / Vi(s)
= A (Ts + 1) / (TAs + 1)
Pole = -1/AT
Zero = – 1/T
Phase angle(θ) = sin-1(1 – A / 1 + A)
θ = 90 – 2tan-1(A)1/2
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
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