# Design of a lead controller system

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### Control system

Generally, we define the system as a group of elements combined together to perform a specific role. A control system is defined as a group of devices that manages and directs the behaviors of a certain system to achieve an output. Simply put, it is a system used to control another system. They have been used in automating nearly every task.  Most of the aspects of our lives are affected by a control system. A perfect analogy is the home heating system controlled by a thermostat.

### Compensation in control systems.

Compensation is normally employed to fix metrics outside the operating unit. In a control system, they are necessary for the following reasons.

1. To ensure that we obtain the desired objective of the system.
2. They make an unstable system stable
3. Compensating networks change the performance specifications of a system.
4. They increase a system’s steady-state accuracy.

### Types of control systems.

In general, compensators can be classified into three sub-parts-

• lag compensators and

Its main function is to increase the function’s speed.  A lead compensator’s function is:

For this function to hold, the following features must be satisfied.

1. The absolute value of p should be greater than the absolute value of z.
2. The location of the pole and zero should be adjacent to the plane’s axis and on the real axis.

The values of the intersection will be negative. However, the number of zeros and the poles will remain constant, but they will have a large negative number. The net result is that the lead compensator would move the function more to the left which is a requirement for the system’s stability.

### Lag compensator.

Below is the transfer function for a lag compensator:

Tlag(s) =

As can be noted, there is a lot of similarities between this one and the previous compensator function. The characteristics of a lag compensator functions are shown below.

1. The absolute value of z should be greater than the absolute value of p.
2. The location of the pole and zero should be adjacent to the plane’s axis and on the real axis.

Lag compensator’s undesirable characteristic is that it moves of moving the function to the right of the plane. A solution to this effect is to ensure that the poles and zeros are close together, which will not have a big impact on stability.

When added to a system, the lag compensator results in an intersection with a negative number of smaller magnitude. Like the lead compensator, the magnitude of the zeros and the poles remains constant. The difference between lag compensators and lead compensators is that when they are applied to a function, lag compensators results into a smaller pole size