Fig.1 PID control system

A block diagram of a PID controller in a feedback loop. r(t) is the desired process value or setpoint (SP), and y(t) is the measured process value (PV).

The dis­tin­guish­ing fea­ture of the PID con­troller is the abil­ity to use the three con­trol terms of pro­por­tional, in­te­gral and de­riv­a­tive in­flu­ence on the con­troller out­put to apply ac­cu­rate and op­ti­mal con­trol. The block di­a­gram on the right shows the prin­ci­ples of how these terms are gen­er­ated and ap­plied. It shows a PID con­troller, which con­tin­u­ously cal­cu­lates an error value e(t) as the dif­fer­ence be­tween a de­sired set­point SP = r(t) and a mea­sured process vari­able PV = y(t), and ap­plies a cor­rec­tion based on pro­por­tional, in­te­gral, and de­riv­a­tive terms. The con­troller at­tempts to min­i­mize the error over time by ad­just­ment of a con­trol variable u(t), such as the open­ing of a con­trol valve, to a new value de­ter­mined by a weighted sum of the con­trol terms.

In this model:

· Term P is proportional to the current value of the SP − PV error e(t). For example, if the error is large and positive, the control output will be proportionately large and positive, taking into account the gain factor "K". Using proportional control alone in a process with compensation such as temperature control, will result in an error between the setpoint and the actual process value, because it requires an error to generate the proportional response. If there is no error, there is no corrective response.

· Term I accounts for past values of the SP − PV error and integrates them over time to produce the I term. For example, if there is a residual SP − PV error after the application of proportional control, the integral term seeks to eliminate the residual error by adding a control effect due to the historic cumulative value of the error. When the error is eliminated, the integral term will cease to grow. This will result in the proportional effect diminishing as the error decreases, but this is compensated for by the growing integral effect.

· Term D is a best estimate of the future trend of the SP − PV error, based on its current rate of change. It is sometimes called "anticipatory control", as it is effectively seeking to reduce the effect of the SP − PV error by exerting a control influence generated by the rate of error change. The more rapid the change, the greater the controlling or dampening effect..

Tun­ing – The bal­ance of these ef­fects is achieved by "loop tun­ing" (see later) to pro­duce the op­ti­mal con­trol func­tion. The tun­ing con­stants are shown below as "K" and must be de­rived for each con­trol ap­pli­ca­tion, as they de­pend on the re­sponse char­ac­ter­is­tics of the com­plete loop ex­ter­nal to the con­troller. These are de­pen­dent on the be­hav­iour of the mea­sur­ing sen­sor, the final con­trol el­e­ment (such as a con­trol valve), any con­trol sig­nal de­lays and the process it­self. Ap­prox­i­mate val­ues of con­stants can usu­ally be ini­tially en­tered know­ing the type of ap­pli­ca­tion, but they are nor­mally re­fined, or tuned, by "bump­ing" the process in prac­tice by in­tro­duc­ing a set­point change and ob­serv­ing the sys­tem response.

Con­trol action – The math­e­mat­i­cal model and prac­ti­cal loop above both use a "di­rect" con­trol ac­tion for all the terms, which means an in­creas­ing pos­i­tive error re­sults in an in­creas­ing pos­i­tive con­trol out­put for the summed terms to apply cor­rec­tion. How­ever, the out­put is called "re­verse" act­ing if it is nec­es­sary to apply neg­a­tive cor­rec­tive ac­tion. For in­stance, if the valve in the flow loop was 100–0% valve open­ing for 0–100% con­trol out­put – mean­ing that the con­troller ac­tion has to be re­versed. Some process con­trol schemes and final con­trol el­e­ments re­quire this re­verse ac­tion. An ex­am­ple would be a valve for cool­ing water, where the fail-safe mode, in the case of loss of sig­nal, would be 100% open­ing of the valve; there­fore 0% con­troller out­put needs to cause 100% valve opening.

Mathematical form

The over­all con­trol func­tion can be ex­pressed math­e­mat­i­cally as

Selective use of control terms

Al­though a PID con­troller has three con­trol terms, some ap­pli­ca­tions use only one or two terms to pro­vide the ap­pro­pri­ate con­trol. This is achieved by set­ting the un­used pa­ra­me­ters to zero and is called a PI, PD, P or I con­troller in the ab­sence of the other con­trol ac­tions. PI con­trollers are fairly com­mon, since de­riv­a­tive ac­tion is sen­si­tive to mea­sure­ment noise, whereas the ab­sence of an in­te­gral term may pre­vent the sys­tem from reach­ing its tar­get value.

Applicability

The use of the PID al­go­rithm does not guar­an­tee op­ti­mal con­trol of the sys­tem or its con­trol sta­bil­ity Sit­u­a­tions may occur where there are ex­ces­sive de­lays: the mea­sure­ment of the process value is de­layed, or the con­trol ac­tion does not apply quickly enough. In these cases lead–lag com­pen­sa­tion is re­quired to be effective. The re­sponse of the con­troller can be de­scribed in terms of its re­spon­sive­ness to an error, the de­gree to which the sys­tem over­shoots a set­point, and the de­gree of any sys­tem os­cil­la­tion. But the PID con­troller is broadly ap­plic­a­ble, since it re­lies only on the re­sponse of the mea­sured process vari­able, not on knowl­edge or a model of the un­der­ly­ing process.

Simulink Model

The model shown in following figure can be given by this equation:

Fig.2 Simulink Model of PID control system

Result:

Experiment:3

Develop assembly language program for arithmetic subtraction of two numbers using μP 8085 kit

APPARATUS REQUIRED: -

1 8085 Microprocessor programming kit, instruction coding sheet.

2. Power supply A.C (230V Mains)

3. ASCII key board

The program takes the content of memory location 2009, subtracts it with the content of memory location 200A & stores the result back at memory location 200B.

Steps:

1. Initialize HL Reg. pair with address where the first number is lying.

2. Store the number in accumulator.

3. Get the second number.

4. Subtract the second number from the first and store the result in 200B.

5. Go back to Monitor

Steps taken by Microprocessor in executing the program are:

· Let: (2009 H) = 05 H

· (200B H) = 03 H

· Result = 05 H - 03 H = 02 H

Flow of data during the execution can be given as under:

· (2009 H) >> A

· A àB

· (200A H) >> A

· A - B >> A

· A à(200B H)

Procedure to use the kit:

1. Switch on the power supply and connect ASCII key board to the 8085 kit.

2. Press “1”

3. Press “A”

4. Enter starting address (e.g. 2000)

5. Enter the mnemonics of the program

6. After entering the complete program press “Esc”

7. For entering the data in memory location press “M”

8. After entering the data press “G” following the starting address.

9. Press “.”

10. Then check the result in particular memory location as per step-7

11. To check the content of accumulator – A (or any other registers) press “R” followed by “A”

Conclusion:

The assembly language program for 8 bit addition of two numbers was executed successfully by using 8085 microprocessor kit. It gives the result as per mathematical operation done manually.

Table-1

Experiment: 9

Simulation for Implementation of AND and OR Gates using PLC

APPARATUS REQUIRED: -

1. PC with Internet connection

Pre-requisites:-

Basics of Digital Electronics and Boolean Algebra.

Theory:

Evolution of PLC:-

When the first electronic machine control was designed, relays were to control the machine logic.

Relay logic has its own limitations.

1.Less reliability

2.The delay involved in switching of contacts

3.Less flexibility and difficult troubleshooting due to hard wired connection

What is PLC?

A Programmable Logic Controller, PLC, or Programmable Controller is an electronic device used for Automation of industrial processes, such as control of machinery on factory assembly lines. A programmable controller is a digitally operating electronic apparatus which uses a programmable memory for the internal storage of instructions for implementing specific functions, such as logic, sequencing, timing, counting and arithmetic, to control various machines or processes through digital or analog input/output devices. Unlike general purpose computers, the PLC is designed for multiple inputs and output arrangements, extended temperature ranges, immunity to electrical noise, and resistance to vibrations and impacts.

Programs to control machine operation are typically stored in battery-backed or non volatile memory. A PLC is an example of a real time system since output results are produced in response to input conditions within a bounded time, otherwise unintended operation results.

Basic Components of PLC:-

1.CPU and Memory module

2.Power supply

3.Input and output module

4.Programming device

Fig.1 Block diagram of PLC

Digitization is a process where continuous analog signal is converted into a finite number of discrete states. These states are well separated so that noise does not create errors.

The resulting digital signal has following advantages:

1. storage over arbitrary periods of time.

2. flawless retrieval and reproduction of the stored information

3. flawless transmission of the information

Some information is essentially digital. Hence it is natural to process and manipulate such information using purely digital techniques. Examples are numbers and words.

The drawback to digitization is that a single analog signal (e.g. a voltage which is a function of time, like a stereo signal) needs many discrete states, or bits, in order to give a satisfactory reproduction.

Logic

What can a digital circuit do?

The simplest task we can think of is a combinational type of logic decision. For example, we can design a digital electronic circuit to make an instant decision based on some information. Here we emphasize “instant” in the decision making process. That means, the process has no time delay.

X = It is a sunny day? Yes

Y = Is it Sunday or holiday? Yes

Action Z = Go for shopping

The rule is Z = X and Y. The circuit is a simple AND gate .

Each manufacturer of PLC systems has own style of writing the instructions. Different PLCs has different instruction sets but even some common basic instructions are shared by all the PLCs. All manufacturers give different software packages for programming PLCs. Ladder is most commonly used programming language. Prior to PLCs, relay logic was used in industry. Ladders were developed to mimic or imitate relay logic.

Relay Logic / Instructions

A relay is simple magnetic device which acts as a control switch.

When the switch is on, current will flow through the coil on iron piece. This iron core acts a electromagnet and due to the magnetic field upper contact gets attracted towards lower one and circuit gets completed, allowing current to flow from load.

Ladder_Programming

Ladder diagram is popular language of programming the PLCs. Ladder diagram shows the sequence of the logic execution which is presented diagrammatically. In ladder diagram, There are two vertical lines generally called as Phase (positive) or neutral. Rungs which show current flow in horizontal direction are the sequence in which the logic executes. The Analogous to relay, ladder has two main symbols which are contacts and output coil. Generally each rung has inputs (contacts) on left hand side and outputs (coil) on the right hand side. These contacts and coils are called as bits of the relays. Each input and output are individual bit in I/O files. An instruction in ladder instructs PLCs how to respond to the bits in I/O files which are stored in the memory. Input contacts are the condition area, the conditions must be fulfilled to change the status of the output coils.

Fig.4 Ladder Programming

Ladder programming for OR gate:

To represent OR gate using PLC, two switches are connected in parallel to give supply to the load/lamp. When both switches are off the output remains low. If any one or both the switches are ON, output becomes high.

Fig. 5 Simulation of OR gate using PLC

Ladder programming for AND gate:

To represent AND gate using PLC, two series connected switches are used to give supply to the load/lamp. When both switches are ON the output becomes high. If any one or both the switches are OFF, output becomes low.

Fig. 6 Simulation of AND gate using PLC

Conclusion:

The performance of AND and OR gates ladder program made in virtual lab gives output as per the truth table of respective gate. Before running the simulation it is required to compile the program.

After running the simulation, to check the output (for various condition of input), it is required change the logic states of inputs A and B.

Source: http://vlabs.iitb.ac.in/vlab/

APPARATUS REQUIRED: -

1. PC with Internet connection

Theory:

Evolution of PLC:-

When the first electronic machine control was designed, relays were to control the machine logic.

Relay logic has its own limitations.

1.Less reliability

2.The delay involved in switching of contacts

3.Less flexibility and difficult troubleshooting due to hard wired connection

What is PLC?

A Programmable Logic Controller, PLC, or Programmable Controller is an electronic device used for Automation of industrial processes, such as control of machinery on factory assembly lines. A programmable controller is a digitally operating electronic apparatus which uses a programmable memory for the internal storage of instructions for implementing specific functions, such as logic, sequencing, timing, counting and arithmetic, to control various machines or processes through digital or analog input/output devices. Unlike general purpose computers, the PLC is designed for multiple inputs and output arrangements, extended temperature ranges, immunity to electrical noise, and resistance to vibrations and impacts.

Programs to control machine operation are typically stored in battery-backed or non volatile memory. A PLC is an example of a real time system since output results are produced in response to input conditions within a bounded time, otherwise unintended operation results.

Basic Components of PLC:-

1.CPU and Memory module

2.Power supply

3.Input and output module

4.Programming device