## What are compensation techniques?

The compensation techniques are the methods that are employed in the electrical control systems to enhance the performance of the system. The performance are generally affected by the factors like lag in the compensating devices, slow response of the system of the components like sensors used in the control system. The basic compensation technique involves lag compensation, lead compensation or the combination of the both.

## Principle of compensation techniques

During run-time, the compensators improve performance (i.e., dynamic and steady-state states) characteristics. The method of compensation changes depending on the plant. The compensator could be a device or network; that is electrical, mechanical, hydraulic, pneumatic, or any other type. An electric network serves as a compensator in most control systems or circuits. Lead, lag, and velocity-feedback (tachometer) compensators are among the different compensators used.

## Network of compensation techniques

The compensating network adds more poles/zeros to the original system, causing the transfer function to change. The sinusoidal angle of a network's sinusoidal output is a function of the total input frequency if it has a phase lead (or lag) compared to the input frequency. Both phase lag and phase lead are present in the output of the lag-lead network, but in separate frequency regions, i.e., phase lead is present in the high-frequency zone while phase lag is present in the low-frequency region.

The following diagram depicts the compensation techniques or methods that have been employed for the feedback control system/circuit.

It is used to enhance the circuit's transient state characteristics, i.e., the speed content with which the system acknowledges.

In this case, zero has the upper hand over a pole. As a result, adding a lead compensator into a circuit transfer function has the effect of adding a zero.

## Lag compensator

It is used to improve the system's steady-state response characteristics, i.e., to eliminate the system's steady-state error.

In this case, dominant pole compensation has the upper hand over zero. As a result, adding a lag compensator with the system/circuit transfer function has the effect of adding a pole.

It is utilized to improve the system's transient and steady-state properties.

One capacitor is parallel with the resistor, and the other is in series with the other resistor. Its frequency response compensation shows simultaneously lead and lag compensator features. A lag-lead compensator is emloyed if one wants the effect of both lag and lead compensators simultaneously.

## Comparison between lead and lag compensators

### Phase lead compensator

• It boosts transient phase response time.
• It improves the system's dynamic reaction.
• There was no discernible reduction in steady-state inaccuracy.
• It shortens the time it would take to rise.
• It expands the available bandwidth.
• It improves the margin of stability, making the system more stable.
• The output signal's high-frequency noise increases or the SNR falls.
• It can't be used when the uncompensated system's phase angle quickly grows near the crossover frequency.

### Phase lag compensator

• It improves steady-state performance and slows down the system's dynamic reaction.
• It lowers steady-state error.
• It lengthens the time it takes to ascend.
• It reduces the available bandwidth.
• It decreases the margin of stability, making the system less stable.
• The output signal's high-frequency noise diminishes or the SNR rises.
• It cannot be used if the phase angle of the uncompensated system in the low-frequency band is insufficient to give the required phase margin.

## Uses of compensators

These are used in various industrial controllers. An automatic control system/circuit employs a control action to keep its output within acceptable bounds. An error detector detects any departure in the output from the reference input. The discovered error is used as an actuation signal for controlling action via a controller.

The following are the six different types of controllers:

• Proportional (P) Controller
• Integral (I) Controller
• Derivative (D) Controller
• Proportional Integral (P-I) Controller
• Proportional derivative (P-D) Controller
• Proportional Integral Derivative (P-I-D) Controller

## Application of lag and lead compensators

The loop gain crossover frequency compensation techniques are shifted to higher values by the lead compensator, allowing the appropriate phase margin to be maintained. As a result, it works well when the uncompensated system's slope at the gain cross-over frequency is modest.

The lag compensator reduces the gain crossover frequency to a lower value that allows for the necessary phase margin. As a result, it works well when the uncompensated system's slope around the gain cross-over frequency seems high.

## Common Mistakes

Remember that the geometric mean of the two corner frequencies is where the biggest phase lead or lag occurs. The peculiar characteristics of both lead and lag compensators can be separately observed.

## Context and Applications

In each of the expert exams for undergraduate and graduate publications, this topic is huge and is mainly used for

• Bachelor of Technology in Electrical and Electronic Engineering
• Bachelor of Science in Physics
• Master of Science in Physics
• Root locus techniques of the low-power circuit system
• Frequency domain analysis of control system
• Time-domain analysis of control system
• Industrial controllers of an op-amp
• Mendeley

## Practice Problems

Q1. Which of the following is not a valid justification for choosing feedback compensation over cascaded compensation?

(a)There is no need for amplification because the transfer of energy is from a greater to a lower level.

(b) There are no suitable compensatory devices

(c) Increases rigidity in the face of load perturbations

(d) It is cost-effective

Correct option: (d)

Explanation: In most circumstances, cascade compensation is quite satisfactory and cost-effective.

Q2. In terms of filtering properties, what is the lead and lag compensator?

(a) high and low pass

(b) low and high pass

(c) both high pass

(d) both low pass

Correct option: (a)

Explanation: A lead compensator is analogous to a high pass filter. A lag compensator works in the same way as a low pass filter.

Q3. What effect does phase-lag compensation have on servo open-loop system performance?

(a) The velocity constant is escalated with specified relative stability.

(b) The velocity constant is reduced for given relative stability.

(c) The system's bandwidth is raised.

(d) The oscillate time is shortened.

Correct option: (a)

Explanation: An integrator is phase lag compensation. The steady-state error is reduced. The steady-state error is conversely proportional to the velocity constant. As a result, the velocity constant is raised.

Q4. Compensation for phase leads resulted in

(a) a rise in overshoot.

(b) a reduction in the closed-loop system's bandwidth.

(c) a decrease in the profit margin.

(d) The rise time of the closed-loop system is reduced.

Explanation: Compensation for phase lead increases Bandwidth, which reduces settling time and hence improves the velocity of the time response.

Q5. When a PD controller is employed to adjust a system, what advantages does the compensated system have over the uncompensated system?

(a) Increased type number

(b) Reduced damping

(c) Increased noise amplification

(d) Increased transient overshoot

Explanation: The compensated system have the advantage over the uncompensated system that it has increased value of the noise compensation in the PD controller.

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### Compensation Techniques in Transmission Line

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