** LAG circuit** is an important circuit that can be added to control systems in order to increase accuracy and make response faster.

### What effect does the LAG circuit have on the system?

When added to the system, the ** LAG circuit** provides a convenient way to move a certain pole to the right. Therefore; increasing the accuracy and making the response faster. I have talked in a previous summary about the effects of pole locations on the stability of the system. You can read that summary

**here**.

### Drawbacks of adding a LAG circuit to the system

Even though moving poles to the right increases the accuracy and makes the response faster, it makes the system less stable.

### Where do we add the LAG circuit?

** LAG circuit** is always added in the low power section just before the system. This is because if the

**was added in the high power section, high power resistances and capacitors will be needed when designing the**

*LAG circuit***.**

*LAG circuit*### Diagram of LAG circuit

### Deducing the Transfer Function (TF) of LAG circuit (4 steps)

- Change the
from*LAG circuit*to*t-domain*(*Laplace domain*) according to the following:*S-domain*

Therefore; thebecomes:*LAG circuit* - Find the Input Resistance

### Example

Design a suitable circuit to remove the old pole (S+4) in the following control system by replacing it with a new pole (S+2). Sketch the circuit indicating whether it is LEAD OR LAG, and derive its ** Transfer Function** TF. Finally, find the values of R1, R2, and C?

It is clear from the designed circuit that a = 4 > b = 2. Therefore; the designed circuit is a ** LAG Circuit**. Also notice how the
pole (-4) was replaced by the pole (-2)

Finding the values of R1, R2, and C

**Note:** If the resulting values of R1 and C are illogic or don't exist on the market, we assume another value for R2 and repeat calculations. Therefore; it is highly recommended that you do all the calculations in an EXCEL spreadsheet.

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