E X P E R I M E N T 6

I N T R O D U C T I O N T O P I D C O N T R O L L E R

SUMMARY

The main objective of this laboratory is to get a basic understanding for how feedback

control can be used to modify the behavior of a dynamic system. In particular, we will

consider PID-control of a simple process consisting of two water tanks. The letters PID

here stand for Proportional, Integral and Derivative control, respectively. PID controllers

are by far the most common type of controllers used in industrial systems, mainly

because they are relatively simple and still often able to provide good performance. The

laboratory experiments will hopefully confirm this.

In addition to establish an understanding for the fundamental principles of feedback

control, the laboratory will provide some experience of manually tuning PID-controllers.

Based on the input supplied from the controller to the system, result will be obtained in

form of graph. This graph can be printed later from the computer. There are several

conditions that the students will do as to know what the result will be like.

Therefore, at the end of this experiment, student will understand on what will happen if

some parameters are varied.

OBJECTIVES

Learn the importance of the vital system characteristics in the assessment of control loop efficiency

Learn on how to evaluate the PID elements using the PCU computer controlled cycle

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THEORY

PID CONTROLLER

A proportional–integral–derivative controller (PID controller) is a generic control loop feedback

mechanism (controller) widely used in industrial control systems – a PID is the most commonly used

feedback controller. A PID controller calculates an "error" value as the difference between a

measured process variable and a desired set point. The controller attempts to minimize the error by

adjusting the process control inputs.

The PID controller calculation (algorithm) involves three separate constant parameters, and is

accordingly sometimes called three-term control: the proportional, the integral and derivative values,

denoted P, I, and D. Heuristically, these values can be interpreted in terms of time: P depends on

the present error, I on the accumulation of past errors, and D is a prediction of future errors, based on

current rate of change. The weighted sum of these three actions is used to adjust the process via a

control element such as the position of a control valve, or the power supplied to a heating element.

PROPORTIONAL CONTROL MODE

In this mode the output of the controller is proportional to the error between the set

point and the measured value. Proportional control may be expressed as either

proportional gain or proportional band. Mathematically,Mp =PG(SP-MV)+C = PG e(t) +CWhere, Mp = Controller OutputPG = Proportional GainSP = Set pointMV = measured valueC =Output with zero errore (t) = Error as a function of time.

The error band where the output is between 0% and 100% is called the proportional

band (PB), and given by PB = 100/PG. Thus, the higher the gain, the smaller the band.

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This control mode rarely produce adequate control, where there usually an offset.

INTEGRAL MODE

This mode of control is often used to remove proportional offsets errors. The integral

mode determines an output based on the history of error. It is calculated by finding the

net area under the error curve versus time and multiplying by a constant called the

integral action time (IAT) in seconds. The controller output equation is:

The integral Action time is defined as the time taken for the integral action to duplicate

the proportional action of the controller, if the error remains constant during this

period. It is used commonly to remove any steady state errors incurred when using a

proportional controller.

DERIVATIVE CONTROL MODE

Derivative control mode is often used to reduce the response time of the system; it is

based on the time rate of the change of error. The time taken for the proportional action to duplicate the instantaneous output of the derivative element is called derivative action time (DAT).

The controller output equation is:The derivative control mode is never used alone as there is no controller output corresponding to zero rate of change. So it is commonly used with Proportional controller (PD). However, it can also exaggerate high frequency noise in the system.

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Mi( t )= PGIAT∫e ( t )dt

Md=PG×DATde ( t )dt

SYSTEM RESPONSE

Figure 1 shows the typical system response of a control system. There are three types of

response for a second order system, which are over damped, under damped, and critical

damped response. The system response depends on the PID gains set in the experiment.

The characteristic of the response is shown in Figure 2

Figure 1 – Graph of controlled variable versus time

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Figure 2 – Graph of step input versus time

Some of the important system performance parameters are:

Peak overshoot: is often expressed as percent overshoot at the first peak

and given by (Peak value- input value)/input value * 100

Settling time: The time taken to settle within 2% of the final value

Rise time: The time taken for the system to respond to a fraction of the

final value on the initial part. Typically 5-95% or 10-90%.

Steady state error: Any error between the set point and the controlled

variable once the system has stabilized.

APPARATUS

THE SYSTEM RIG

The System Rig is the hardware for the process, which is to be controlled by the

microcomputer. The unit is based around a fluid flow process, where flow and

temperature may be controlled. This reflects a typical process control situation such as

in the food and drink manufacturing petrochemical industry.

Each feature on the System Rig has a manual or computer control option. Users may

select either of the modes allowing a comparison between human and computer control

operation to be made. This allows a rapid appreciation of the advantages and

disadvantages under both modes of control.

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DESCRIPTION

A - Mains switch G - Overflow pipe

B - Water pump switch H - Proportional valve

C - Bottom reservoir tank I - Water inlet port

D - Bypass valve J - Water drain port

E - Return valve K - Water pump

F - Water level tank L - Control panel

M - Level foot

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FEEDBACK

Feedback is an essential requirement for the control of any process. It consists of

various transducers measuring the conditions on the rig and feeding this information

back to the controlling microcomputer.

On the Process Control Unit the temperature at the sump, flow line and process tank

are measured using platinum resistance thermometers. The flow rate is measured by an

in-line flow meter. These analogue signals are fed back to the signal conditioners on the

Computer Control Module (CCM) from where they are sampled by the microcomputer

via an analogue to digital converter (ADC). LED meters are used to display the

temperatures and flow rate on the system rig. Indicators are provided for the cooler,

tank full sensor and drain/diviner solenoids, giving a status check when the Process

Control Unit is in operation.

FLOW MEASUREMENT

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Example of flow meter

The flow rate of the fluid is measured by means of a flow meter of the impeller type.

The fluid flows through the meter rotating the impeller, which has six blades. Mounted

either side of the impeller is an infra red transmitter and receiver producing an infra red

beam which is broken by the rotating impeller. Six pulses are therefore produced for

one revolution of the rotor, thus producing a frequency output 'which is proportional to

the flow rate.

The approximate full-scale frequency is 570Hz (pulses/sec) which is converted to a

voltage by the signal conditioning circuit. This voltage is used to drive the flowrate LED

display on the rig and also converted into a digital word by the Data Acquisition circuit.

Figure 5 – process flow on the flow measurement system

PUMP

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Example of centrifugal pump

The pump used is a centrifugal type. It is not a positive displacement type and thus its output

is not necessarily linearly proportional to speed, though variation in speed will, of course, vary

the output flow rate.

Activating Voltage : 12V D.C

Maximum Continuous Current: 6 Amps

PROCEDURE

SOFTWARE OPERATION

a) Turn on both the computer system and the process control unit.

b) Once you get into Windows click start, program, shut down, go to DOS mode.

c) Type cd\pcu4 Enter. Then type pcu

d) Once you’re in the program this to familiarize yourself try these commands:

F1 (to on/off), Yes, F1-F9 (to toggle and control each unit), then try out other commands

too.

SECTION 1 : ASSESSMENT OF SYSTEM PERFORMANCE

a) By operating the Process Control Unit using computer controlled, the vital

characteristics can be easily demonstrated by varying the tuning of PID controller.

b) Click F2 (flow control), Yes (for control using PID), F2 (computer control)

c) Set the “Set point” to 1.0 instead of 1.6 and “Time length” to 50 seconds instead of 100

seconds.

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d) Set the PID controller using the given values and your own values. Print out your results

and observe the graphs. Label the graphs.

DATA, OBSERVATIONS AND RESULTS

Controller Setting Peak

Overshoot

(liter/min)

Setting

Time

(s)

Rise

Time

(s)

Steady

state

error

Under

damped/

over

damped/

CriticalProportional

GainIntegral Derivative

R1 1 0.1 1 6.5 - - -Over

damped

R2 3.5 0.01 0 7.8 40 25.9 –

6.8

Under

damped

R3 7 0.05 0.5 6.75 40 105.5 –

6.8

Critical

R4 14 0.025 0.5 7.5 30 10 4.8 –

6.7

Critical

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R5 6 0.5 0.1 5.5 10 31.0 –

3.4Critical

Table 1 – Result obtained in this experiment

DISCUSSION

1- In this experiment, there are 5 graphs that were drawn. Namely R1, R2, R3, R4, and R5.

All these graphs have different value of proportional gain, integral time and

derivative time. For details about it, it can be explained here:

a- Graph R1

- It is in overdamped response. This is because, the system does not reach the

set point through in 50 seconds. Plus, the graph also does not stop oscillating

with a steady state value.

b- Graph R2

- This graph is in underdamped response. The reason behind this is because, it

requires short time to reach the set point. Peak overshoot occurs

furthermore it takes longer time to reach the steady state because of high

oscillation occurs on high underdamped system.

c- Graph R3, R4, R5

- These three graphs are in critically damped response. This happens because

the time in all these 3 graphs takes to reach steady state is fast due to the fact 11

that they have linear oscillation. In ideal cases, there should be no oscillation

at steady state value.

2- For case 1 – Based on the graph, the proportional gain, P is changing for every 20

seconds and it becomes the only manipulated variable. It means, for every increase

in gain, the response will also changes. On the graph, it can be seen that the most

stable gain is at 7.2

3- For case 2 – Based on this case 2 graph, we can simplify that the flow rate is

increasing and closely match the steady state value. On the graph, at 30 seconds, the

pass value is opened, the flow rate drop significantly and gradually increasing again

until it reaches 1.3 lpm and becomes stable at 40 seconds of time until the end of

process (maintained at 1.3 lpm).

4- For case 3 – Based on this case 3 graph, the fixed value on the proportional gain is

used as a reference point which is 7.2. The procedure conducted in this case 3 is the

same as in case 1. Based on the graph, the optimum value at the integral time is 0.05

as the graph must stable within that interval. After that, it can be seen that the flow

rate becomes stable showing that the optimum values at I and P are already

determined.

5- For case 4 – In this case, it is actually almost the same as with case 2 but the only

thing different is, the value of P and I are fixed using the value that have been

determined earlier. Those values are (P=7.2, I=0.05). Therefore, when the

experiment is conducted, the flow rate amount almost reaches the steady state and

becomes constant. After 30 seconds, disturbances was introduces again.

6- For case 5 – Based on the graph obtained in this case, the value increases from 200

and becomes stable at first 20 seconds time. After that, the graph started to fluctuate

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until the end of the experiment. The optimum value achieved for D is 0 and the final

value for others are P=7.2, I=0.05 and D=3.

7- For case 6 – From the graph obtained, it shows the same result as what have been

achieved in case 4. Some disturbances were introduced into the system. The flow

rate drops and becomes stable again and maintained its stability until the end of the

experiment.

CONCLUSION

At the end of this experiment, we managed to understand the importance at the vital

system characteristics in this experiment of control loop efficiency and we have

successfully learnt on how to evaluate the PID Control Circuit using the computer

control flow cycle. We can conclude that the optimum PID controller can be

determined through test and experiment. Therefore, we can say that we have fulfilled

the objective of this experiment.

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