Introduction

          The automatic control of system (or machine) is a very accurate and effective means to perform desired function by the system in which the human operator is replaced by a device there by relieving the human operator from the job thus saving physical strength. The automatic control systems are also called as self-activated systems. 

          The centrifugal actuated ball governor which controls the throttle valve to maintain the constant speed of an engine is an example of an automatically controlled system.

The automatic control systems are very fast, produces uniform and quality products. It reduces the requirement of human operators thus minimizing wage bills.

Types of Automatic Control System

Types of Automatic Control System

The automatic control systems are classified into two types they are:

1) Open loop (or) Unmonitored system

2) Closed loop (or) monitored system 

1. Open-loop or unmonitored system: When the input to a system is independent of the output from the system, then the system is called an open-loop or unmonitored system. It is also called calibrated system. Most measuring instruments are open-loop control systems, as for the same input signal, the readings will depend upon things ambient temperature and pressure. Following are the examples of open-loop system:

• A simple Bourdon tube pressure gauge commonly used for measuring pressure.
• A simple carburattor in which the air-fuel ratio adjusted through venturi remains same irrespective of load conditions.
• In traffic lights system, the timing of lights is present irrespective of intensity of traffic.

2. Closed-loop or monitored system: When output of a system is measured and is continuously compared with the required value, then it is known as closed-loop or monitored system. In this system, the output is measured and through a feedback transducer, it is sent to an error detector which detects any error in the output from the required value thus adjusting the input in a way to get the required output. Following are the examples of a closed-loop system:

(a) In a traffic control system, if the flow of traffic is measured either by counting the number of vehicles by a person or by counting the impulses due to the vehicles passing over a pressure pad and then setting the time of signal lights.

(b) In a thermostatically controlled water heater, whenever the temperature of water heater rises above the required point, the thermostat senses it and switches the water heater off so as to bring the temperature down to the required point. Similarly, when the temperature falls below the required point, the thermostat switches on the water heater to raise the temperature of water to the required point.

Thermostatically controlled water heater

Block Diagrams

Block Diagrams

Fig. Block diagram of a single Carburettor.

          The block diagrams are used to study the automatic control system in simplified way. In this, the functioning of a system is explained by the inter connected blocks where each block represents a labelled rectangle and is thought of as a block box with a definite function. These blocks are connected to other blocks by lines with arrow marks in order to indicate the sequence of events that are taking place. It may also show how the system operates, what are its inputs and outputs at various stages, and how the energy, information, and/or materials flow through it. Above Fig., shows the diagram of a simple carburattor. The reduction of a control system to a block diagram greatly facilitates the analysis of the system performance or response.

Lag in Response

Lag in Response

          We know that response is the subsequent result of the system to the command. In any control system, there is a delay in response (output) due to some inherent cause and it becomes difficult to measure the input and output simultaneously. This delay in response is termed as lag in response. For example, in steam turbine, with the sudden decrease in load, the hydraulic relay moves in the direction to close the valve. But unless the piston valve ports are made with literally zero overlap, there would be some lag in operation, since the first movement of the piston valve would not be sufficient to open the ports. This lag increases the probability of unstable operation.

Damping

Damping

          When torque is applied in a system in a direction opposite to its motion, it is known as Damping. In case of coulomb damping, the opposition is constant and, thus there will be a constant difference between the input and the output under steady conditions. In the viscous damping provided by dashpot, the opposition is proportional to the relative velocity. As the relative velocity is zero in the steady state, the damping is also zero.

Transfer Function

Transfer Function

          The transfer function is a mathematical expression showing the relation between output and the input to  each unit or block of a control system. If the system has a single input and a single output, it can be represented by block diagram as shown in Fig., 

Transfer function is defined as the ratio of output over the input with all initial conditions equal to zero. Mathematically, 

Transfer function =  θ0 / θ_i

              Where      θ0 = Output signal of the block of a system, and 

                               θ_i  = Input signal to the block of a system.

Thus, the output from an element be obtained by multiplying the input signal with the transfer function.

Note : From the transfer function of the individual block, the equation of motion of system can be formulated.

Overall Transfer Function

Overall Transfer Function

          In the previous topic, we have discussed the transfer function of a block. In this we are going to know the Overall transfer function of a control system. A control system actually consists of several such blocks which are connected in series. The overall transfer function of the series is the product of the individual transfer functions. Consider a block diagram of any control system represented by the three blocks as shown in Fig., 

Fig. Overall transfer function.

          Thus, if  are individual transfer functions of three blocks in series, then th overall transfer function of the system is given as 

Where       K = Constant representing the overall amplification or gain, and 

                  G(D) = Some function of the operator D.

Note: The above equation only true if there is no interaction between the blocks, that is the output from one block is not affected by its connection to the subsequent blocks.

Open-Loop Transfer Function

Open-Loop Transfer Function

          The open loop transfer function is defined as the overall transfer function of the forward path elements. Consider an open loop control system consisting of several elements having individual transfer function such F₁(D), F₂(D), F₃ (D)  as shown on in Fig.,  

Fig. Open loop control system.

 Thus

                                    = F1 (D ) X F2 (D ) X F3 (D ) = KG (D)

The simplified block diagram of the open loop transfer function is shown in Fig.,

Fig. Simplified open loop control system.

Closed - Loop Transfer Function

Closed - Loop Transfer Function

          The closed - loop transfer function is defined as the overall transfer function of the entire control system. It is a mathematical expression (algorithm) describing the net result of the effects of a closed (feedback) loop. Consider a closed loop transfer function or feedback loop consisting of several elements as shown on Fig.,

Fig Closed-loop transfer function.

Now, for the forward path element, we know that

where      K G (D ) = F1 (D ) X F2 (D ) X F3 (D)

On rearranging, we get

               θo = K G ( D )θi − K G ( D)θo

or             [1 + K G ( D )] θo = K G ( D)θi

          The above expression shows the transfer function for the closed-loop control system. Thus the block diagram may be further simplified as shown in Fig., where the entire system is represented by a single block.

Fig. Simplified closed-loop system.

EXERCISES

EXERCISES

1. Define the following terms: 

         (a) Response    (b) Process control     (c) Process Controller

         (d) Regulator   (e) Transducer             (f) Feedback

2. Explain different types of Automatic Control Systems? Explain with an example. 

3. Discuss the importance of block diagrams in control systems. 

4. Draw the block diagrams for the following control systems: 

      (a) A simple carburettor, 

      (b) A thermostatically controlled electric furnace. 

5. What is a transfer function ? 

6. Derive Open - loop and closed - loop transfer functions?

Objective type questions

Automatic Control

Objective type questions

1. The device which is used to keep the variable at a constant desired value is called a  

(a) amplifier                   (b) regulator

(C) deviation sensor     (d) process controlled

2. A simple Bourdon tube pressure gauge is a

(a) closed-loop control system 

(b) manually operated system 

(c) open-loop control system

(d) none of the above 

3. The transfer function of a 4 to 1 reduction gear box is

(a) 2          (b) 1/4 

(c) 4          (d) 1/2

 4. The overall transfer function of three blocks connected in series is 

(a) {F1 ( D ) X F2 ( D)}/F3 ( D)          (b) {F1 ( D ) X F3( D)}/F2 (D)

(c)  F1 ( D ) X F2 ( D ) X F3( D)          (d)  1 / {F1 ( D ) X F2 ( D ) X F3 ( D)}