Excercise AS-5b

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Institute of Automatic Control and Robotics Faculty of Mechatronics

Automation Systems laboratory

Excercise AS-5b

"Single loop control system of air temperature in pipeline”

Autors : PhD. Eng. Danuta Holejko, PhD. Eng. Jakub Możaryn,

BSc. Eng. Michał Bezler.

Warsaw 2016

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AUTOMATION SYSTEMS

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Single loop control system of air temperature in pipeline

The aim of the exercise is to execute, study static and dynamic properties, and then assess the quality of single loop control system of air temperature in the pipeline. Quality will be rated based on the values of indices of transient response of a system caused by step change in the setpoint or disturbance. The aim of the research is to determine the effect of the type of control algorithm and on values of parameters (controller settings) on the quality of the system. Identification of controlled system carried out in laboratory excercise AS-4b enables the selection of parameters (settings) of PID controller implemented in the used SIMATIC S7-1200 PLC (Programmable Logic Controller). Analysis of obtained indices will allow the assessment of the accuracy of the compensation of the disturbances acting on the process and the precision of process value (PV) signal following the changing setpoint (SP).

1. DESCRIPTION OF THE PROCESS / LABORATORY STAND

Experiments aere conducted on laboratory stand presented in Fig. 1. Controlled process is a change of air temperature T in a pipe. Fig.1 presents installation diagram.

The flow of air is forced by the fan (S). Temperature control can be realized in the installation by regulationg the amount of heat generated by the heater (G) at a constant flow of air supplied by a fan (S) or by controlling the amount of air provided by the fan at a constant amount of heat supplied by the heater (G). Input signals are power of heater (YG) and speed of a fan drive (YW). All signals are standard current signals 4 - 20 mA and are generated by the control system with the PLC controller.

The disturbances are :



step change of the gap of the air outlet (by moving the position of the iris P closed / open which means changing the gap form 389 to 1661 mm²),



step change of the heating power of the heater G by connecting or disconnecting the additional resistance (switch position "0" or "1" - changes the resistance heater from 100  to 75 ),



step change of the fan drive speed realized by a step change in the signal YW supplied to the control system of the fan (S) in case when controlled variable is heater power (YG), or



step change of the heater power realized by a step change in the signal YG supplied to the control system of the heater (G) in case when controlled variable is fan drive speed (Yw),

Temperature measurement was performed using T / I resistance thermometer Pt100 (special low inertia) with linearization and standard output 4 - 20 mA. Range of the sensed temperature is 25 - 75 ⁰C.

Air flow rate measurement was performed by measuring the pressure drop p at the measurement orifice. Range of the differential pressure transmitter p / I with an output 4 - 20 mA is 0 - 50 mm H2O.

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„Single loop control system of air temperature in pipeline”

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3

44444 4-2

4-20 [mA]

4-20

[mA] 4-20

[mA]

PV

p/I T/I

P1 Y_G

Y_w

Figure 1. Installation scheme of the laboratory stand for designing the control system of the air temperature in the pipeline.

Symbols: P - iris for a step change of the gap of the air intake, S - fan drive with variable speed, G - electric heater, PV - current signal from the temperature sensor T / I, Q - current signal from the Venturi flowmeter, p/I - differential pressure sensor, P1 - "0-1"

switch to change the resistance of the heater, Yw - signal to change fan speed, YG - signal to change the power of the heater.

2. SELECTION OF THE CONTROLLERS SETTINGS

Continuous controllers used in inustry are universal devices. Their parameters (settings) can be changed (adjusted) within a wide range, so they can work properly with objects of different dynamics. Depending on the set requirements for control quality, following settings should be adjusted:

 k_p– magnitude of proportionalm part [unitless],

 Ti – time constant of derivative part [s]

 Td – time constant of integral part [s].

Abovementioned PID cotroller settings are ususally selected depending on requirements posed by the quality of controll according to different procedures (selection of settings).

Based on theoretical considerations, modelling research and experience from system expolitation there were developed many rules for PID parameters choice depending on the specific model of the controlled process, type and location of disturbances, adopted criterion of quality and control algorithm. The most widely accepted criterion of control quality is transient response characteristics of the control system.

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There are usually taken into consideratino following types of transient responses:

1. aperiodic transient response with overshoot 05% and minimal control time tr, that provides a minimum of integral index ^



e t dt

0 )

( , this is the criterion described as IAE (Integral of the Absolute value of Error).

2. oscillatory transient response with overshoot  20% and minimal control time tr, that provides a minimum of integral index ^



te t dt

0 )

( ; this is the criterion described as ITAE (Integral of the Time weighted Absolute Error),

3. transient response that provides a minimum of integral index ^



^

0

2( dtt) min

e , with

overshoot  45%; this is the criterion described as ISE (Integral of Square of the Error).

When selecting settings for static processes, the important parameter is the ratio of delay time to substitute first order lag time constant T0/Tz that characterizes susceptibility of the process to control action. When the ratio exceeds 0.3 the quality control with the best-chosen PID controller settings PID worsens significantly.

In the exercise there will be applied the following methods of tuning:

a) tabular method of tuning based on the experimental identification of the object (AS-4), b) The experimental method of Ziegler - Nichols.

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5 2.1. Tabular method of controller tuning

This method requires knowledge of the parameters of process mathematical model.

For the static model the parameters are kob, T0, Tz. If we do not have theoretical description of the model, then we use tables or nomograms that require the prior identification of the process, eg. using step response on the basis of which one can determine the required parameters of the model. Knowing these parameters the controller settings are defined to ensure the required quality of control, eg. requirement oscillatory or aperiodic nature of the transient response of the control system.

Tab. 1 summarizes the sample equations that define the set of regulators parameters for static processes. These formulas take into account the point of entry of disturbances. One set of parameters for provides a fixed set point control and as quickly as possible compensates the influence of disturbances, while the other should be chosen when the same system is to operate as a set point following system ensuring proper reproduction of the setpoint (SP) changes.

Table 1. A list of formulas for setting controllers for the process

1

0



 

zs T e sT kob ob s

G ( )

Type of the

response Type of the

controller kob kp T0 /Tz Ti / T0 Td / T0

Z(t)=1(t)

 = 0 % min tr

P 0.3 - -

PI 0.6 0.8 + 0.5 Tz /T0 -

PID 0.95 2.4 0.4

 = 20 % min tr

P 0.7 - -

PI 0.7 1 + 0.3 Tz /T0 -

PID 1.2 2.0 0.4

Change of the setpoint SP

 = 0 % min tr

P 0.3 - -

PI 0.35 1.17 Tz /T0 -

PID 0.6 Tz /T0 0.5

 = 20 % min tr

P 0.7 - -

PI 0.6 Tz /T0 -

PID 0.95 1.36 Tz /T0 0.64

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AUTOMATION SYSTEMS

6 2.2. Experimental Ziegler-Nichols method

The method of tuning controllers developed in 1942 by Ziegler and Nichols is one of the most commonly used and widespread methods of experimental tuning of the PID controllers. This method is used when the controller and other elements of the actual control system are already installed, their functioning is tested (in manual control mode), and one should only choose the controller parameters. The method of Ziegler - Nichols (abbreviated Z-N) can be encountered in two variants:

1) the controller settings are selected on the basis of the parameters of the closed control system moved to the border of stability (using excitation system),

2) the controller settings are selected based on parameters defined the characteristics of the transient response of the control object due to the step input signal change (static processes only).

In the exercise there will be applied Z-N method using excitation system. Within this method, the choice of the parameters is conducted based on the following steps:

 Step 1: In the manual mode (M) by changing control variable (CV), adjust the process variable (PV) to a state in which it is equal with the required setpoint (SP).

 Step 2: Set the controller to the proportional action (switch off integral and derivative actions), set the operation point control value of the controller equal to the setting obtained in the Step 1 and set the initial value of the controller gain k_p 0.

 Step 3: Switch the system to automatic control (A) and if the system maintains equilibrium, by changing SP produce an impulse with some amplitude and pulse duration depending on the expected dynamics of the process; observe or record the change in the controlled variable. It is recommended to use a pulse with amplitude of 10 % of the process value changes (PV) and pulse duration of about 10% of the estimated value of the time constant of the controlled process.

 Step 4: If the transient response is underdamped, set higher values of the proportional gain (Steps 1-3) until a system be on the border of stability (constant oscillations) - fig.

3c.

 Step 5: From the steady oscillations read 'critical' proportional gain pkrytk and oscillation period oscT .

 Step 6: Set the controller patameters according to the table of formulas developed by Ziegler-Nichols (Tab. 2).

During the experiments there should be monitored if the control signal CV does not reach the limit values. If this happens, reduce the SP pulse parameters.

The controller parameters are calculated on the basis of read values of pkrytk and oscT , using the formulas given in Tab. 2.

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a) b) c)

Figure 3. Changes of the process variable (PV) obtained during Ziegler – Nichols experiment Similar methods, based on experimental procedure, are implemented in modern microprocessor controllers or PLCs as the so-called autotuning.

Table 2. Settings of the PID controllers according to Ziegler – Nichols method Controller

algorithm

Z-N settings

kp Ti Td

P 0.5 k_pkryt - -

PI 0,45 kpkryt 0.85Tosc -

PID 0.6 kpkryt 0.5 Tosc 0.12 Tosc

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AUTOMATION SYSTEMS

8 3. EXPERIMENTS

Identification of the described process will be conducted in the control system presented in the scheme at Fig.2.

Identification of the process will be conducted on the basis of the measurement of the static characteristics in the full range of possible changes in the controlled variable and the time response of the process to introduced step input signal for a chosen operationg point selected from static characteristic. This will be therefore an experiment in which intentional influence on the process will take place through the control signal set by the operator.

Measurements of static and dynamic properties of the object will be carried out in a fixed set point open control system of air temperature in the pipe (in manual mode). Static and dynamic properties would be represented by the relationship between the controlled variable, which is the air temperature T processed to a measured signal PV and the control signal CV (YG) or between the controlled variable and the introduced disturbances. These compounds will be represented by the transfer function of a process Gob (s) and the transfer functions of disturbances GZ1 (s), GZ2 (s). These transfer functions will represent the dynamic properties od the system in the vicinity of the operating point of the process.

Figure 2. Electrical scheme of the control system of the air temperature in pipeline.

The laboratory stand include:

1. SIMATIC S7-1200 PLC (Programmable Logic Controller) with the analog inputs / outputs modul and power supply 24V,

2. HMI display with a color touch screen,

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3. desktop PC with TIA Portal software, 4. Industrial Ethernet network,

5. pipeline installation, 6. power supply.

Analog outputs of the controller are

speed S (AO1) and the power of the heater G (AO2) installed in the pipeline. To digital controller, through the AC adapter

the iris (DI1) and to change the resistance

program to control fan speed (%) and the power of the heater set the value of the control

extortions and system response.

3.1 Visualisation

During the exercise (SIMATIC HMI KPT600).

On the Home screen, select an object structure of a control system (

the object visualization pressing

„Single loop control system of air temperature in pipeline

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9 top PC with TIA Portal software,

Ethernet network, pipeline installation,

s of the controller are connected to the input signals controlling speed S (AO1) and the power of the heater G (AO2) installed in the pipeline. To

hrough the AC adapter, there are supplied signals indicating the position of the iris (DI1) and to change the resistance of the heater (DI2). The controller implements a program to control fan speed (%) and the power of the heater (%). Panel HMI enables

signal. The simulation on the computer monitor can record and system response.

During the exercise user communicates with the PLC via the operator On the Home screen, select an object tank (Zbiornik) and the

control system (Jednoobwodowy). After pressing the "Start" button, the object visualization pressing the buttom "Rurociąg" (Pipeline) (Fig.4)

Figure 4. Start screen (HMI KTP 600)

Single loop control system of air temperature in pipeline”

signals controlling fan speed S (AO1) and the power of the heater G (AO2) installed in the pipeline. To inputs of the supplied signals indicating the position of heater (DI2). The controller implements a . Panel HMI enables user to . The simulation on the computer monitor can record plots of

communicates with the PLC via the operator diplay and the single close-loop the "Start" button, user go to (Pipeline) (Fig.4).

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Once the configuration

general structure of the system under study (Fig.

Figure 5. Structure of the single feedback loop control system Icons under the controller block

Reverse, and Error Acknowledge controller screen (Fig. 6).

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Once the configuration is set, press button "Start" and go to the screen that shows the general structure of the system under study (Fig. 5).

Structure of the single feedback loop control system

controller block indicate the current operating mode (Auto / Manual, Normal / Acknowledge). After pressing controller block, one

Figure 6. Screen of the controller.

go to the screen that shows the

indicate the current operating mode (Auto / Manual, Normal / After pressing controller block, one can go to the

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Controller screen allows to change:

 Algorithm of a controller by typing the appropriate setting, or selecting a mode in the

"Type of control".

 Switching of the controller mode: Auto /

 Swiching the controller direction: Normal / Reverse.

 Tuning procedures.

 Reset of the controller parameters.

In the right part of the screen

If the box "Error" is lit, the controller is in an i

error is temporary opening in the measurement circuit. In this case, just replace the damaged cable and reset the controller by pressing the "Reset"

Visualisation, in the

out on a PC using software TIA PORTAL. T Fig. 7.

Figure 7.

The start screen (Fig. 7)

pressing "Regulator główny" button, user will be send to the screen with monitoring of input and output variables (Fig.

„Single loop control system of air temperature in pipeline

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11 Controller screen allows to change:

Algorithm of a controller by typing the appropriate setting, or selecting a mode in the Switching of the controller mode: Auto / Manual.

Swiching the controller direction: Normal / Reverse.

Reset of the controller parameters.

In the right part of the screen are displays indicating the status of the controller.

"Error" is lit, the controller is in an inactive state. The most common cause of error is temporary opening in the measurement circuit. In this case, just replace the damaged cable and reset the controller by pressing the "Reset" button

the form of plots the changes of the input and output using software TIA PORTAL. The home screen of this visualisation

. Start screen in TIA Portal simulation (HMI KTP 1200).

(Fig. 7) contains information about the entered

"Regulator główny" button, user will be send to the screen with monitoring of (Fig. 8).

Single loop control system of air temperature in pipeline”

Algorithm of a controller by typing the appropriate setting, or selecting a mode in the

displays indicating the status of the controller.

nactive state. The most common cause of error is temporary opening in the measurement circuit. In this case, just replace the

button.

the input and output values, is carried of this visualisation is shown in

Start screen in TIA Portal simulation (HMI KTP 1200).

entered structure. When

"Regulator główny" button, user will be send to the screen with monitoring of the

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Figure 8.

Over plots there is a graph showing the active disturbances in the form of a bar chart:

 Red rolor - change of iris,

 Orange color - step change of the heater ressistance,

 Green color - "SP step function".

 Blue color - step change of the speed of the fan drive done using button „Zmiana obrotów”.

There are following buttons:

1. Start / Stop button allow user

2. The „Zwiększ przedział czasu” ( interval") buttons allow

15sec to 16min

3. The fields below the text Increasing the scope is

the scale the changes will be visible

4. . The "skok SP" ("SP step") button allows user together with the monitoring of it in the upper graph 5. The text next to the "Cofnij" (

activated the "Skok SP" ("

change the value of this field before resetting the value by pressing "Cofnij"

(""Undo") button.

6. The "Cofnij" ("Undo") button resets the button.

7. Button „Zmiana obrotów” allows to generate disturbances characterized by step change of the fand drive speed.

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Screen with monitoring of the input and output

change of iris,

step change of the heater ressistance,

"SP step function".

change of the speed of the fan drive done using button „Zmiana

There are following buttons:

Start / Stop button allow user to stop or resume monitoring of the input / output values.

„Zwiększ przedział czasu” ("Increase the time interval")

user to modify the currently displayed time interval ranging from The fields below the text „Oś” ("Axis") allow scaling of the Y

Increasing the scope is performed immediately. In the case of reducing the scope of the changes will be visible after some time.

("SP step") button allows user to generate the step function of together with the monitoring of it in the upper graph.

"Cofnij" ("Undo") button allows user to enter the

"Skok SP" ("SP step") button. After entering any of the values, do not change the value of this field before resetting the value by pressing "Cofnij"

button resets the step function activated by "skok

Button „Zmiana obrotów” allows to generate disturbances characterized by step change of the input and output variables

change of the speed of the fan drive done using button „Zmiana

the input / output values.

and ("Decrease time to modify the currently displayed time interval ranging from

"Axis") allow scaling of the Y-axis of the graph.

n the case of reducing the scope of the step function of a setpoint, to enter the value of the SP later After entering any of the values, do not change the value of this field before resetting the value by pressing "Cofnij"

step function activated by "skok SP" ("SP step") Button „Zmiana obrotów” allows to generate disturbances characterized by step change of

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To print the chart, the course of the changing values should be stopped by START / STOP button, the user should press the button on a computer keyboard PrtSc and then paste saved screen into graphical editor.

4. Course of the excercise

In the the exercise the controlled variable is the air temperatire T (represented by the process value - PV). Control signal CV (current, 4-20 mA) generated by the SIMATIC S7-1200 Siemens is a changing power of the heater. The disturbances are:



step change of the gap of the air outlet (by moving the position of the iris P closed / open which means changing the gap form 389 to 1661 mm²),



step change of the heating power of the heater G by connecting or disconnecting the additional resistance (switch position "0" or "1" - changes the resistance heater from 100  to 75 ),



step change of the fan drive speed realized by a step change in the signal YW supplied to the control system of the fan (S) in case when controlled variable is heater power (YG), Process properties were identified in out in the exercise AS-4b. The controller (PID) pameters should be selected according to the quality requirements in accordance with the tuning procedure.

4.1. Tabular method of controller tuning

Based on the results of the identification of the object carried out in the exercise AS-4 specify the parameters of the object identified with the tangent or secant methods (acc. to TA):

kob = ..., T0 = ..., Tz = ...

Using Table 1, calculate the settings of P/PI/PID controllers for transient response with overshoot 0% or 20% (as instructed by the TA) and write them into Table 3.

Table 3. Calculated parameters of controllers.

Controller  = 0 %  = 20 %

type [s] Tkp i [s] Td [s] k Tp i [s] Td [s]

P PI PID

4.2. Starting the instalation

Starting real plant control systems is usually carried out manually. The installed controller is switched by the operator to manual mode (MANUAL). Then the operator sets the controller algorithm, primary presets and planned for the installation setpoint SP, then, changing the control signal manual controls the process as long as the controlled variable PV reaches a permanent state established at a level corresponding to the desired setpoint SP. If all the devices included in the system are working properly and reached steady state is stable corresponding to a zero error, the operator switches the system from manual control to

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automatic control (AUTO). If the significant , abrupt changes are not observed and they are not beyond the certain limits of errors, then controller parameters shall be accepted as safe and start-up of the installation shall be considered completed.

In the controlled installation the operating point is the temperature 45± 2⁰C (PV ≈ 40± 4%), which corresponds to the control signal CV ≈ 50%.

To bring the system to the point of operation the following steps shall be performed:

Step 1: Set up the system according to the diagram (Fig. 2).

Step 2: Check the position of the switches P1 (fault VE1) and P2 (fault VE2), there shuld be no disturbance.

Step 3: Set controller into MANUAL mode: MAN.

Step 4: Set the panel CV (CV_man) = 50%.

Step 5: Wait until the level in the tank will stabilize.

Step 6: Set the setpoint SP = PV.

Step 7: Enter the controller settings.

Step 8: Set controller into AUTO mode: AUTO.

If, when changing the mode of the controller to the AUTO mode, there will be quite significant changes in the control signal CV and the resulting changes in PV, switch controller in MANUAL mode. Then set the safe control value CV and repeat the starting procedure after finding the cause of a malfunction of the system, eg. wrong controller settings.

4.3. The study of the P controller and settings according to tabular method.

4.3.1. Check the efectiveness to compensate the disturbance induced by change of the speed of the fan.

Laboratory procedure is as follows:

a) In the computer visualization choose observation of signals PV, CV, SP.

b) In the MAN mode, set CV_man = 50%, Yw=50%

c) After the stabilization of liquid level in tank, enter the SP = PV and set AUTO.

d) Change speed of the fan from 50% to 70%

e) Wait until the value of measured PV will stabilize - record minimum, maximum, and stable value of temperature.

f) At the computer visualization press Pause" ("Pauza") button to stop the trends.

g) Save on PC the plots of PV and SP with marked time, when disturbance occured.

h) Switch on the display of the control CV and save a plot of control signal.

i) Change speed of the fan from 70% to 50%.

j) Switch to MANUAL mode and set the CV_man = 50%.

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4.3.2. Check the efectiveness to compensate the disturbance induced by change of the heater ressistance.

d) Change the switch P1 position from 1 to 0,

i) Change the switch P1 position from 0 to 1,

4.3.3. Check the efectiveness to compensate the disturbance induced by change of the gap in the air intake.

d) open (horizontal position) the iris (P).

i) Close (vertical position) the iris (P).

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4.3.4. Check the efectiveness of the control system to follow the process value PV after set point value SP.

b) In the MAN mode, set CV_man = 50%.

d) in AUTO mode set ΔSP = +10%

e) Change the setpoint SP using the "Step SP" (Skok SP) button.

f) Wait until the value of measured PV will determine.

g) Press "Pause" (Pauza) button to stop the trends.

h) Save on PC the plots of PV and SP.

i) Switch on the display of the control CV and save a plot of control signal.

k) Reset the SP using button "Back" (Cofnij).

4.4. The study of the PI controller and settings according to tabular method.

Using the procedure described in section 4.3. choose the parameters of the PI controller based on Table 3, then repeat the study based on experiments from sections 4.3.1- 4.3.4. The study can proceed after checking whether:

a) the system is in operating point (CV = 50% PV≈60%) (properly carried start- up of installation).

b) entered (via the HMI visualization) settings are entered properly for the PI controller

4.5. The study of the PID controller and settings according to tabular method.

Using the procedure described in section 4.3. choose the parameters of the PID controller based on Table 3, then repeat the study based on experiments from sections 4.3.1- 4.3.4. The study can proceed after checking whether:

c) the system is in operating point (CV = 50% PV≈60%) (properly carried start-up of installation).

d) entered (via the HMI visualization) settings are entered properly for the PID controller

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17 4.6. Experimental Ziegler-Nichols method

Tuning based on Ziegler - Nichols method is carried out according to the following procedure:

1. Perform start-up procedure in manual mode (MAN) (acc. 4.2), set the CV = 50% and wait until a PV stabilizes.

2. The controller working with the process must be set to the P algorithm and a specific initial value of the proportional gain, eg. kp = 6, should be set, while all other regulator actions swithced off: Ti 99999,9,Td 0.

3. Manually set SP = PV.

4. In the computer visualization choose observation of PV and SP values.

5. Set the controller to AUTO.

6. Enter the impulse to change the setpoint, for example:. SP = 2-3% of the pulse duration timp (Fig. 3) sufficient to cause noticeable changes of PV. CV signal during the test should not reach the limit values - in the opposite situation, the test must be repeated.

7. Evaluate the changes of PV and compare it with the course of signal from Fig.

3.

8. If the course of PV corresponds to Fig. 7c, save the PV plot in the computer and go to p.11.

9. If the course PV corresponds to Fig. 7a, the switch controller mode "MAN", set the CV = 50%, increase the gain kp, wait for PV to stabilize, adjust the SP to SP = PV and repeat steps p. 5 - 7.

10. If the course PV corresponds rys.7b, the switch controller mode "MAN", set the CV = 50%, reduce the gain kp, wait for PV to stabilize, adjust the SP to SP

= PV and repeat steps p. 5 - 7.

11. Set the controller mode "MAN", set the CV = 50%.

12. Note the current value kkryt = kp that caused steady oscillations, then read the oscillation period Tosc and calculate the controller settings P / PI / PID according to Tab. 2.

Note: Any change of controller settings can be made only in MANUAL mode.

Table 4. The results of the experiment and of the controller settings according to the Z-N method.

Results of Z-N experiment Controller settings

kp Ti Td

kkryt Tosc P

PI PID

4.7. The study of the P, PI, PID controller and settings according to Ziegler- Nichols method

Using the settings gathered in Tab. repeat the study based on experiments from sections 4.3, 4.4, 4.5. The study can proceed after checking whether:

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c) the system is in operating point (CV = 50% PV≈60%) (properly carried start-up of installation).

d) entered (via the HMI visualization) settings are entered properly for the P, PI, PID controller

5. REPORT

The report shall contain the following elements: description of the exercises, diagrams, registered plots with data processing, graphs made on the basis of measurements, etc.

Following questions should be answered:

1) Draw the block diagrams of the considered control system.

2) Draw the expected changes of process value PV and control value CV - induced by disturbance Yw when using P control algorithm and controller in Normal mode.

3) Attach and describe the results of the Ziegler - Nichols experiment.

4) Compare transient responses of control system and evaluate its static and dynamic.

qquality. The quality should ne assessed on the basis of the readouts from the plots the following indices: e1 , e2 , est , em , tr ,  (overshoot). The results should be gathered in table (proposed by a person who creates a report).

5) Compare the results obtained for the controller settings by tabular method and by the Ziegler - Nichols method.

6) Calculate the steady state errors based on the transfer fuction of the process and the transfer function of the controler and compare them with the values obtained from the experiments.

7) Calculate, based using the transfer fuctions of procees and controller values of kpkryt and Tosc and compare them with the values obtained from Z-N experiment.

8) Answer the question: How from the plot of transient response caused by step change of the setpoint SP read the set value of the controllers' proportional gain kp?

6. BIBLIOGRAPHY

1.Kościelny W.J.: Materiały pomocnicze do nauczania podstaw automatyki dla studiów wieczorowych, WPW, 1997, 2001.

2. Węgrzyn S.: Podstawy automatyki. PWN 1980 3. Żelazny M.: Podstawy automatyki . PWN, 1976