Chapter 1 basic components of control system

This presentation is on basic of control engineering subject which is offered to 5th sem Mechanical Engineering Department in Gujarat Technological University.

1. 1. BASIC CONCEPTS OF CONTROL SYSTEM DR V.R . GODHANIA COLLEGE OF ENGINEEFRING AND TECHNOLOGY, PORBANDAR PREPARED BY - HARISH ODEDARA DEPARTMENT OF MECHANICAL ENGINEERING SEM – 5

2. Introduction In modern era, control system plays a vital role in human life. The question is arises that: What is a control system? To answer the question, a system or mechanism which directs the input to other system and regulates their output. For example, in the domestic purpose, we need to control the temperature and humidity of homes, offices and buildings for comfortable living. Another example for transportation we need to control the automobile vehicle an airplane to go from one place to another place accurately and safely.

3. A system is a combination of components that act together to perform a specific goal . The basic part of control system can be described by: Input or objective of control Control action or control system Response or output Basic control system

4. Requirements of a Good Control System Accuracy : Accuracy is the measurement tolerance of the instrument and defines the limits of the errors made when the instrument is used in normal operating conditions. Accuracy can be improved by using feedback elements. To increase the accuracy of any control system error detector should be present in the control system . Sensitivity: The parameters of a control system are always changing with the change in surrounding conditions, internal disturbance or any other parameters. This change can be expressed in terms of sensitivity. Any control system should be insensitive to such parameters but sensitive to input signals only.

5. Noise: An undesired input signal is known as noise. A good control system should be able to reduce the noise effect for better performance . Stability: It is an important characteristic of the control system. For the bounded input signal, the output must be bounded and if the input is zero then output must be zero then such a control system is said to be a stable system . Bandwidth: An operating frequency range decides the bandwidth of the control system. Bandwidth should be as large as possible for the frequency response of good control system . Speed : It is the time taken by the control system to achieve its stable output. A good control system possesses high speed. The transient period for such system is very small . Oscillation : A small numbers of oscillation or constant oscillation of output tend to indicate the system to be stable.

6. Terminology Plant : A plant may be a piece of equipment, perhaps just a set of machine parts functioning together, the purpose of which is to perform a particular operation. We shall call any physical object to be controlled (such as a mechanical device, a heating furnace, a chemical reactor, or a spacecraft) a plant. Process: A process is any operation to be controlled. Processes can be chemical, economic, biological, etc. System: A system is a combination of components that act together and perform a certain objective. Disturbances: A disturbance is a signal that tends to adversely affect the value of the output of a system. If a disturbance is generated within the system, it is called internal, while an external disturbance is generated outside the system and is an input.

7. Feedback Control: feedback control is an operation in which the difference between the output of the system and the reference input by comparing these using the difference as a means of control. . Controlled Variable: The controlled variable is the quantity or condition that is measured and controlled. Manipulated Variable or Control Signal: The manipulated variable or control signal is the quantity or condition that is varied by the controller so as to affect the value of the controlled variable. Normally , the controlled variable is the output of the system . Control: Control means measuring the value of the controlled variable of the system and applying the control signal to the system to correct or limit deviation of the measured value from a desired value.

8. Block diagram of basic control system Room temperature control system Proportional control On-off control Room temperature control system Block diagram of room temperature control system

9. Aircraft elevator control Elevator control system for a high-speed jet Block diagram of elevator control system

10. Computer Numerically Controlled (CNC) machine tool Computer Numerically Controlled (CNC) machine tool Block diagram of (CNC) machine tool

11. Classifications of control systems Open loop control systems Those systems in which the output has no effect on the control action are called open-loop control systems . In other words, in an open loop control system the output is neither measured nor feedback for comparison with the input . The practical examples are washing machine, light switches, gas ovens, automatic coffee server, electric lift, traffic signals, theater lamp dimmer, etc.

12. In any open-loop control system the output is not compared with the reference input . Open-loop control can be used, in practice, only if the relationship between the input and output is known and if there are neither internal nor external disturbances Advantages They are simple in construction and design. They are economic. Easy for maintenance. Not much problems of stability. Convenient to use when output is difficult to measure Disadvantages Inaccurate and unreliable because accuracy is dependent on calibration. Error in results due to parameter variations, internal disturbances. To maintain quality and accuracy, recalibration of controller is necessary in regular time interval.

13. 2. Closed loop control systems A system that maintains a prescribed relationship between the output and the reference input by comparing them and using the difference as a means of control is called a closed loop control systems . Sometimes , we may use the output of the control system to adjust the input signal. This is called feedback . Feedback control systems are often referred to as closed-loop control systems .

14. The practical examples are air conditioner, automatic electric iron, missile launched and auto tracked by radar, servo voltage stabilizer, sun-seeker solar system, water level controller, etc. The term closed-loop control always implies the use of feedback control action in order to reduce system error. Advantages: Accuracy is very high as errors are corrected. It senses changes in output due to parametric changes, internal disturbances, etc. and corrects them. Reduced effect of non- linearties . High bandwidth means large operating frequency range. Facilitates and supports automation. Disadvantages: Complicated in design and costlier maintenance. This system is generally higher in cost and power. Stability is a major problem in this system.

15. Comparison between open loop and closed loop control systems Open loop system Closed loop system No feedback and elements of feedback. Feedback and elements of feedback exists. No error detector. Error detector is present. Inaccurate. Accurate. Highly sensitive to parameter changes. Less sensitive to parameter changes. Small bandwidth. Large bandwidth. No issue of stability. Issue of stability. Lower in cost and power. Higher in cost and power. Examples: washing machine, light switches, gas ovens, automatic coffee server, electric lift, traffic signals, theater lamp dimmer, etc. Examples: air conditioner, automatic electric iron, missile launched and auto tracked by radar, servo voltage stabilizer, sun-seeker solar system, water level controller, etc.

16. Concept of superposition for linear systems Before understanding concept of superposition for linear systems, we have to understand concept of linearity. Linearity: Basically, a mathematical equation is said to be linear if the following properties hold homogeneity additivity Homogeneity requires that if the input (excitation) of a system (equation) is multiplied by a constant, then the output should be obtained by multiplying by the same constant to obtain the correct solution. Does homogeneity hold for the following equation? y = 4x If x = 1, y = 4. If we double x to x = 2 and substitute this value into above equation, we get y = 8.

17. Now for homogenity to hold, scaling should hold for y. That is, y has a value of 4 when x = 1. If we increase x by a factor of 2, when we should be able to multiply y by the same factor and get the same answer and when we substitute into the right side of the equation for x = 2. Additivity property is equivalent to the statement that the response of a system to a sum of inputs is the same as the responses of the system when each input is applied separately and the individual responses summed (added together). This can be explained by considering the following illustrations. Given, y = 4x Let x = x1, then y 1 = 4x 1 Let x = x 2 , then y 2 = 4x 2 Then y = y 1 + y 2 = 4x 1 + 4x 2 …. Eq 1.1 Also , we note, y = f(x 1 + x 2 ) = 4(x 1 + x 2 ) = 4x 1 + 4x 2 …. Eq 1.2 Since Equations (1.1) and (1.2) are identical, the additivity property holds.

18. Concept of Superposition The mathematical model of a system is linear if it obeys principle of superposition. The concept of superposition implies that if y 1 = f( x 1 ) and y 2 = f( x 2 ) then f( x 1 + x 2 ) = y 1 +y 2 . This is called the Superposition principle . What does that mean? It means that if we know that our system responds to a certain input ( x 1 ) with a certain output ( y 1 ), and we also know that it responds to another input ( x 2 ) with some other output ( y 2 ), then it response to the sum of these inputs should be the sum of the two outputs. Usually your inputs, and consequently your output vary over time (or over space), so a better way to write the above is: if y 1 (t) = f( x 1 (t)) and y 2 (t) = f( x 2 (t)) then f( x 1 (t)+ x 2 (t)) = y 1 (t)+ y 2 (t) Which is exactly what we wrote above, but with x replaced by x (t), and y replaced by y (t).