Introduction of Control System

     CONTROL SYSTEM  

*What is a system?

---A system is a collection of an element which can take input and processed it to give the output.

#Block diagram of System:

*Its drawbacks:

---System has no control on its input which may cause damage to the system.

Due to this region, we need a control system.

*Control system:

---Control system is a system in which the input is controlled as per required.

#Block diagram of the control system:

*Types of control system:-

---There are two types of control system.

1. Open loop control system.

2. Closed loop control system.

1. Open loop control system:

--- Open loop control system is a type of control system in which the output is dependent on the input of the system. But the controlling action of the system is not dependent on the output of the system.

* Block diagram of the open loop control system:

---Block diagram of the open loop control system is given as:

*Example of the open loop control system:

---System Engine.

---Motor vehicle.

*Advantages:

---The advantages of the open loop system are as follows:

1. Simple construction.

2. Economical.

3. Easy to maintain.

4. Stable.

*Drawbacks of the open loop control system:

---Drawbacks of the open loop control system is that in open loop control system it is not possible to automatic control the output of the system, therefore, it is inaccurate.

This type of drawback can be removed by the closed loop control system.

2. Closed loop control system:

---Closed loop control system is a control system in which the controlling action is dependent upon the output or the change in the output of the system.

#Block diagram of the closed loop control system.

---The block diagram of the closed loop control system is given as:

Feedback of the system is the circuit consists of the inductor, resistor, and capacitor.

*Example of the closed loop control system:

1. Refrigerator.

2. Air conditioner.

3. Automatic electric iron. 

*Advantages of the closed loop control systems.

1. It is more accurate than open loop control system.

2. It has the noise reduction ability.

*Disadvantages of the closed loop control system:

1. Complex construction.

2. It is less stable.

3. It has less gain as compared to the open loop control system.

@Transfer function:

--- Transfer function of the control system is given as the ratio of the output to the input in its Laplace domain with zero (or no) initial condition.

It is given as:

*Transfer function of an open system is given as:

IF,

Input=R(s).

Output=C(s).

Transfer function=G(s).

Then,

Or it is also given as

 * Transfer function of a closed loop system:

---It is done for both the negative and positive feedback closed-loop system.

*Transfer function of a closed loop system (For the negative feedback):

---The block diagram for the transfer function of a closed loop control system for the negative feedback are as follow:

In this block diagram, the input is R(s), an output is C(s), error is E(s) and I(s) is the 
output of the feedback.

From the block diagram:

E(s) = R(s) - I(s)………………………………..(i)

And I(s) is given as,

I(s) = C(s) * H(s)…………………………….(ii)

And from the definition of the transfer function,

C(s) = G(s) * E(s)…………………………..(iii)

Put the value of E(s) from eq.(i) to the eq. of the transfer function[eq.(iii)].

We get,

C(s) = G(s)[R(s) – I(s)]

C(s) = G(s) * R(s) – G(s)*I(s).

C(s) + G(s) * I(s) = G(s) * R(s).

From eq (ii),

C(s) + G(s)*C(s)*H(s) = G(s) * R(s).

 

Is the required transfer function for a closed loop system(For a negative feedback). 

*Transfer function of a closed loop control system(For positive feedback).

---The block diagram for the transfer function of a closed loop control system (for positive feedback) are as follows:

In this case,

E(s) = R(s) + I(s).

Therefore, the transfer function is given as,

*Procedure for the calculation of the transfer function:

----The procedure for the calculation of the transfer function is given as follows.

(i). Write the differential equation of the given system.

(ii). Convert the differential equation into its Laplace domain.

(iii). Calculate the ratio of the output upon input in its Laplace domain.

*Reason for using the Laplace transform in the transfer function:

---By using the Laplace transform it became possible to convert both the input and the output in the same form which is required for the mathematical calculation of the transfer function.

EXAMPLE:

Where,

x(t) = Input of the system.

y(t) = Output of the system.

Transform it into the Laplace domain.

Then we get,

Is the required transfer function.