• Skip to main content
  • Skip to primary sidebar
  • Basic Electronics
  • Digital Electronics
  • Electronics Instrumentation
  • ADC
  • Comparisons

Electronics Coach

All About Electronics

Lag Compensator

Definition: A lag compensator is a circuit that is designed to generate a steady-state sinusoidal signal having a phase lag to the applied input sinusoidal signal. This can also be stated in a way that it is a circuit that is when provided with a sinusoidal input produces a sinusoidal output signal whose phase lags the applied input.

It is sometimes referred as a lag network.

We know that compensators are used in the control system in order to have the desired output. Basically, the desired output through a control system is achieved when the system properly controls the ongoing process inside it.

However, for this purpose also, the system specifications must be proper.

When certain parameters of the system are changed then this sometimes leads to variations in the system specifications, and this causes malfunctioning of the control system. This is the reason the control system must be resigned.

So, redesigning a control system to produces accurate results by adding an external physical device is known as compensation. And the physical device added to the system is known as a compensator.

This addition of the external device introduces poles and zeros in the transfer function of the system. This varies the performance parameter of the system.

Phase Lag Compensator

We have already discussed in our previous article that a phase lead network generates an output with a leading phase than that of the supplied input.

The phase lag compensator performs just reverse operation as that of the lead compensator. It introduces a phase lag in the steady-state output when the input signal is provided to it.

A lag compensator has zero and dominating pole. A dominating pole is the pole present nearest to the origin in comparison to all the other poles in the s-plane. And the poles and zeros must be present on the negative real axis.

The figure below represents the phase lag network:lag compensator

First, we will apply KVL in the above circuit. Suppose i(t) is the current flowing through the loop. Thus, for loop 1,lag compensator eq1

We know to determine the response of the system; its transfer function must be determined.

The transfer function is given as the ratio of output to input in the frequency domain.

So, further we will take the Laplace transform of the above equation,lag compensator eq2

Now considering loop 2,lag compensator eq3

Again considering the Laplace transform:lag compensator eq4

Furtherlag compensator eq5

On substituting the above value of I(s) in Laplace equation of input loop, we will get,lag compensator eq6

On simplifyinglag compensator eq7

Furtherlag compensator eq8

The general expression is given as:lag compensator eq9

Hence, on comparisonlag compensator eq10

Hence, this shows that the zero of the lag compensator will be present at s = -1/T and pole will be at s = -1/βT.

Since β is greater than 1, thus pole of the transfer function is more dominating than the zero. The figure below represents the pole-zero plot of the lag compensator:

pole zero plot of lag network

Generally, β is considered as 10. This is the reason when lag compensator is serially connected to the control system; then a negative phase angle is introduced.

Lag Angle

We have discussed the transfer function of the lag compensator. Now proceeding towards determining the maximum lag angle offered by the compensator at a certain frequency.

Sincelag compensator eq11

Furtherlag compensator eq12

Substituting s = jω

lag compensator eq13

Therefore, the magnitude will be given as:lag compensator eq14

So, the phase angle will be:lag compensator eq15

The phase angle of the lag compensator shows similarity with the lead compensator, which is given as:lag compensator eq16

where the only difference is β>1

Now we will determine the particular frequency at which phase angle ɸ is maximum,

lag compensator eq17Thuslag compensator eq18

Furtherlag compensator eq19

So, we will get,lag compensator eq20

Furthermore,lag compensator eq21

Thus, it is clear that at this particular frequency, phase lag will be maximal.

Here ωm is the geometric mean of two corner frequencies,lag compensator eq22

Advantages of Lag Compensator

  1. A phase lag network offers high gain at low frequency. Thus, it performs the function of a low pass filter.
  2. The introduction of this network increases the steady-state performance of the system.
  3. The lag network offers a reduction in bandwidth and this provides longer rise time and settling time and so the transient response.

Disadvantages of Lag Compensator

  1. In lag compensator, the attenuation offered by it shifts the gain crossover frequency to a lower point, thereby decreasing the bandwidth.
  2. Though the system response is longer due to decreased bandwidth; however, the response is quite slow.
  3. A control system with a lag network shows more sensitivity towards variation in the parameters than a system with a lead network.
  4. Like in lead compensator, in lag compensator also, due to the addition of external network, some attenuation is introduced. So, the overall gain must be increased to handle the attenuation. But this will increase the requirement of more elements and so the cost and space requirement.
  5. A lad compensator somewhat acts as a proportional plus integral controller hence adversely affects the stability of the system.

It is to be noted in case of lag compensator that, it operates in a way to provide attenuation to high-frequency range. Thus in lag compensation, phase lag angle is of no justifiable use.

Related Terms:

  1. Bode Plot
  2. Transfer Function of Control System
  3. Bode Plot Construction with Example
  4. Lead Compensator
  5. Lag Lead Compensator

Reader Interactions

Leave a Reply Cancel reply

Your email address will not be published. Required fields are marked *

Primary Sidebar

Most Searched Terms

  • Difference Between Half Wave and Full Wave Rectifier
  • Sample and Hold Circuit
  • Full Wave Rectifier
  • Difference between LED and LASER
  • Characteristics of JFET
  • Varactor Diode
  • 3 Phase Rectifier
  • Number System
  • Difference Between Clipper and Clamper
  • Analogous Systems

Trending Terms

  • Difference Between LED and OLED
  • AC Servomotor
  • Pulse Code Modulation (PCM)
  • Difference Between Multiplexer (MUX) and Demultiplexer (DEMUX)
  • Peak Detector
  • Time Division Multiplexing (TDM)
  • Difference between RC and RL Circuit
  • Differential Amplifier

New Additions

  • Resonant Converters
  • AC Voltage Controllers
  • Static Circuit Breakers
  • Synchronous Motor Drives
  • DC Drives

Categories

  • Analog & Digital Communication
  • Basic Electronics
  • Comparisons
  • Control Systems
  • Digital Electronics
  • Electronics Instrumentation
  • Optical Fiber System
  • Power Electronics

Copyright © 2025 · Electronics Coach · Contact Us · About Us · Privacy