Experiment: Temperature Sensor Experiment

Objective:
1. To determine the characteristic of a thermo-resistance as position transducer of
temperature.
Apparatus:
● Digital multimeter
● Set of leads
Safety Precautions:
● Check the digital multimeter, leads, and thermo-resistance for visible damage or wear.
● Replace or repair faulty equipment to avoid hazards or inaccurate readings.
● Operate RTDs with low voltage (typically less than 10V) to prevent overheating and damage.
● Avoid high voltage to maintain accurate measurements and ensure safety.
● Avoid direct contact with the RTD or other heated components during experiments.
● Use heat-resistant gloves if adjustments are needed while the sensor is hot.
● Monitor temperature to ensure it stays within the recommended range.
● Avoid exposing the sensor to temperatures beyond its specified limits to prevent damage.
● Wear personal protective equipment (PPE), including lab coats, safety goggles, and closed-toe
shoes.
● Follow all safety guidelines to protect against potential risks.
● Work in a well-ventilated area when using heating elements.
● Maintain airflow to reduce heat buildup and minimize exposure to fumes

Theory:

Introduction to Transducers

Transducers are devices that convert one form of energy into another. In the context of
temperature measurement, temperature transducers specifically transform temperature variations
into electrical signals, such as voltage, current, or resistance changes. These signals are easy to
measure, record, and process, making temperature transducers essential in industries that require
precise temperature monitoring and control.

Types of Transducers

Transducers can be categorized into two primary types: input (sensing) transducers and output
(actuating) transducers. Input transducers detect and measure physical parameters, such as
temperature, pressure, or light intensity, converting these measurements into electrical signals.
Temperature transducers fall under this category as they sense temperature changes and transmit
them in the form of electrical signals. In contrast, output transducers take electrical signals as

0
input and generate a specific physical effect or output. For instance, speakers act as output
transducers, converting electrical signals into sound.

Transducers can also be classified based on the physical principle used for energy conversion.
Resistive transducers alter their electrical resistance in response to temperature changes, with
thermistors and Resistance Temperature Detectors (RTDs) as common examples. Voltage
transducers produce voltage signals proportional to temperature changes, with thermocouples
being the most widely used devices in this group. Current transducers, though less common,
generate a current output corresponding to temperature variations and are employed in
specialized applications.

Resistive Temperature Transducers (RTDs)

RTDs are among the most significant resistive temperature transducers. They operate on the
principle that a material’s electrical resistance changes predictably with temperature. Platinum is
the most commonly used material for RTDs due to its stability and reliability. These devices
provide highly accurate and consistent temperature measurements, making them indispensable in
applications requiring precise thermal control.

Operating Principle: The resistance of a thermo-resistance changes linearly with temperature

and follows the formula:
Rt=R0(1+αΔT)
Where:
● Rt: Resistance at temperature T
● R0: Resistance at a reference temperature (commonly 0°C)
● α: Temperature coefficient of resistance (specific to the metal)

When temperature increases, the kinetic energy of atoms in the metal lattice increases, causing
more collisions with electrons and increasing resistance. This is particularly reliable for
platinum, which has a high purity and stable response over a wide range of temperatures.

RTDs as Transducers

A transducer is a device that converts one form of energy into another. An RTD (Resistance
Temperature Detector) serves as a transducer by converting temperature (thermal energy) into an
electrical signal, either as voltage or resistance. When connected to an electrical circuit, the
RTD's resistance change can be measured and calibrated to accurately determine the
corresponding temperature.

Resistance-Temperature Relationship

1
RTDs operate on the principle that the electrical resistance of certain materials, such as platinum,
systematically increases with temperature. Most materials exhibit this behavior, but RTDs are
specifically designed to measure resistance changes within a linear range, ensuring high accuracy
and repeatability in temperature sensing.

Wiring Configuration

To enhance accuracy in detecting minute resistance changes, RTDs are often connected within a
Wheatstone bridge circuit. This configuration minimizes the effects of external factors, such as
lead resistance, and provides precise measurements of temperature variations.

Measurement Process

Once an RTD is installed, a steady current is supplied to it, and the resulting voltage is measured.
As the temperature changes, the RTD’s resistance changes accordingly, causing a corresponding
change in voltage. This voltage variation is directly proportional to the temperature change,
allowing accurate temperature monitoring.

Signal Conditioning

After obtaining the voltage signal, signal conditioning is performed to amplify and adjust it to a
measurable level. This process ensures that the output is accurate and suitable for further
processing or display in temperature monitoring systems.

Procedure:
● Press the main switch (ON).
● Insert one terminal of a digital multimeter (Ohmmeter) in bush No. 1 and the other one in
bush No. 2 of the resistor TESTER.
● Regulate the trimmer TESTER to read the value of 100 Ohms (resistance of the PT100 at
0°C).
● Use the multimeter as a Voltmeter, set in de, and move one terminal in bush No.3 and the
other one in the earth bush.
● Connect, through leads, bushes No. 1 and 2 (0°C) of TESTER to bush No. 1 and 2 of
TEMPERATURE SENSOR INTERFACE.
● Regulate the trimmer OFFSET to read DV on the voltmeter.
● Remove the leads from bushes No. 1 and 2 of TESTER and insert in the saine bushes the
terminals of the multimeter.
● Use the multimeter as an Ohmmeter and regulate the trimmer TESTER to read the value
of 138.5 Ohms (resistance of the PT100 at 100°C).
● Use the multimeter as a Voltmeter and move one terminal to bush No. 11 and the other
one to the earth bush.
● Connect bushes No. 1 and 2 (100°C) of FESTER to bushes No 1 and 2 of
TEMPERATURE SENSOR INTERFACE.

2
 ● Regulate the trimmer GAIN to read on the multimeter the value of 10V: you have now
calibrated the temperature sensor establishing IV per 10°C.
● Remove the leads from bushes No. 1 and 2 of TESTER and connect them to bushes No. 1
and 2 of the temperature sensors as figure 2.1.
● Connect bush No. 11 of the HEATER DRIVER to bush No. 11 and bush No. 12 to bush
No. 12 as figure 2.2.
● Connect the bush of SET POINT No bush No. of the HEATER DRIVER.
● Check if the level of the water is 8cm.
● Regulate the voltage on SET POINT at /10V: the heating element will start the operate.
● Insert one terminal of the voltmeter, set in de, in bush No. 3 of the temperature interface
and the other one in the earth bush.
● Read on the voltmeter the voltage values corresponding to the different values of
temperature shown on the thermometer.
● Write down the voltage value for each temperature values listed in the Table.
● Turn OFF the main switch.
● Remove all the connections.
● Draw the graph of the voltage as a function of the temperature.
● Analyze the results.

Circuit Figure:

Table:

Temperature (℃) Voltage (mV)

36 3.5
37 3.5
38 3.7
39 3.8
40 3.9
41 3.9
42 4
43 4.1 3
44 4.2
45 4.2
Graph:

Voltage Vs Temperature
4.3
4.2
4.1
4
3.9
3.8
3.7
3.6
3.5
3.4
36 37 38 39 40 41 42 43 44 45 46

Voltage Vs Temperature

Analysis:
In this experiment, a plot of voltage versus temperature will illustrate how the voltage output
varies with temperature as a result of resistance changes in the thermo-resistance. The exact
shape of this graph will depend on the circuit configuration used, such as a Wheatstone bridge or
a voltage divider.
Expected Behavior

If a stable power source is applied, the voltage is anticipated to increase in a linear manner with
rising temperature.

Interpretation of Results

This linear trend confirms that the thermo-resistance is performing correctly as a temperature
transducer. The graph's slope represents the sensor's sensitivity, indicating how much the voltage
changes for every unit increase in temperature.

By examining this graph, the sensor’s accuracy and linearity can be assessed. A consistent linear
response is essential for ensuring dependable temperature measurements in real-world
applications.

Conclusion:
Based on the "Temperature vs. Voltage" graph, the experiment confirms a linear relationship
between temperature and voltage for the thermo-resistance (RTD) sensor. The equation
y=0.0673x+1.4255 represents the linear fit, indicating a steady increase in voltage with

4
temperature. If x = 42 than y = 4.2521. This consistency demonstrates that the RTD effectively
translates temperature changes into proportional voltage changes, validating its reliability as a
temperature sensor. The strong linearity also suggests high accuracy, making RTDs suitable for
precise temperature measurement applications.

Experiment: Closed Loop Proportional Control - PC of the Temperature

Objective:
● To verify the effects of the gain of the loop on the dynamic response of the system
● To draw the dynamic response curve of the system
List of equipments:
● Digital Multimeter: Measures electrical signals, including sensor and control outputs.
● Chronometer: Tracks time for calculating response metrics like rise time and settling
time.
● Set of Leads: Connects the components in the control loop.
Theory: Closed-Loop Proportional Control of Temperature

Overview of Closed-Loop Control Systems

Closed-loop control systems continuously monitor and adjust a process variable (like
temperature) to match a desired setpoint. Proportional control (PC) is a simple feedback
mechanism that adjusts heating or cooling power based on the difference (error) between the
actual and setpoint temperature.
5
Proportional Control Concept

Proportional control adjusts the output based on the error:

Control Output=Kp×Error\text{Control Output} = K_p \times \text{Error}Control Output=Kp

×Error

Where Kp is the proportional gain, and the error is the difference between the setpoint and
measured temperature. This system offers a quick response but may not eliminate steady-state
error.

Temperature Control Application

1. Error Detection: Measures the temperature and calculates the error.

2. Proportional Response: Adjusts the heating or cooling based on the error.
3. Stabilizing Temperature: Brings the temperature closer to the setpoint but typically leaves
a small steady-state error.

Key Aspects

1. Proportional Gain (Kp): Controls how aggressively the system responds. High Kp can
cause instability; low Kp may lead to slow response.
2. Steady-State Error: Proportional control cannot completely eliminate this error.
3. Disturbance Response: The system adjusts quickly to sudden changes but may take time
to stabilize after sustained disturbances.

Advantages and Limitations

Advantages:

● Simple to implement.
● Quick response to disturbances.
● Stable for applications with small error tolerances.

Limitations:

● Cannot eliminate steady-state error.

● Can cause instability with high Kp.
● Sensitive to changes in environmental factors.

Conclusion

Proportional control is effective for applications where fast response and stability are needed, but
may not provide high accuracy for critical processes. Proper tuning of Kp is essential for optimal
performance.

6
Procedure:
 Initial Setup:
● Set the process tank water level to 18 cm and ensure the heater is functional.
● Connect the temperature sensor leads to the interface.
● Set the proportional control knob to 0%, indicating no initial proportional control.
● Ensure all necessary connections are established as per the control circuit diagram.
 Setting Initial Conditions:
● Measure the initial temperature by connecting the digital multimeter to the temperature
sensor output. Record this starting temperature in °C.
● Set the proportional gain Kp at an initial value (e.g., 25%).
 Applying Proportional Control:
● Connect the control output to the heater driver. Start the chronometer to measure time.
● Observe and record the temperature every minute as the heater operates, noting the
temperature response over time.
● Repeat this procedure for increased values of Kp (50%, 75%, and 100%), recording
temperature changes at each setting in Table 6.1.
 Data Collection:
● At each Kp setting, monitor the temperature response and document the effect of each
proportional gain value on reaching and maintaining the setpoint temperature.
● Record data until the temperature stabilizes or reaches the upper limit of the system.
 Data Analysis:
● After data collection, plot the temperature response curves for each Kp setting against
time to visualize the effect of proportional gain on system performance.
●

Observations and Calculations:

Time Kp = 25% Kp = 50% Kp = 75% Kp = 100%

(min Temperature Temperature Temperature Temperature
) (°C) (°C) (°C) (°C)

7
 1 42.4 42.4 42.5 42.5

3 42.8 42.9 42.9 43

5 43 43.1 43.2 44

7 44.1 44.3 44.6 44.9

9 44.9 45.5 45.3 46

11 46.8 46.9 46 46.3

13 47.7 47.9 47.9 48

Graph:

49
48
47
46
45
44
43
42
41
40
39
0 2 4 6 8 10 12 14

Kp= 25 % Kp=50 % Kp = 75 % Kp=100 %

Graph Analysis

8
When plotting the data with Time on the x-axis and Temperature on the y-axis, the different
curves illustrate how varying Kp values influence the rate of temperature change:

● The curve with Kp at 100% will have the sharpest incline, quickly reaching the target
temperature of 50°C.
● As the Kp values decrease, the curves will show a more gradual rise in temperature, with
slower response times to the setpoint.

Conclusion

The experiment clearly shows that a higher Kp results in a faster response from the temperature
control system, enabling it to reach the target temperature more quickly. However, higher Kp
values can cause instability, leading to oscillations around the setpoint. On the other hand, lower
Kp values provide greater stability but with a slower rate of temperature increase. Therefore,
selecting an appropriate Kp value for a practical control system requires a balance between the
need for a quick temperature adjustment and maintaining system stability, depending on the
application's specific demands and the allowable steady-state error.

Experiment: Closed Loop Proportional-Integral Control of Temperature

Objective:
● To verify the effects of the gain of the loop on the dynamic response of the system
● To draw the dynamic response curve of the system
List of equipments:
● Digital Multimeter: Measures electrical signals, including sensor and control outputs.
● Chronometer: Tracks time for calculating response metrics like rise time and settling
time.
● Set of Leads: Connects the components in the control loop.
Theory:
In control systems, particularly for temperature regulation, the objective is to maintain a desired
temperature by constantly adjusting inputs based on feedback. Closed-loop Proportional-Integral
(PI) control is widely used for accurate temperature management. Unlike open-loop systems that
operate without feedback, closed-loop systems dynamically adjust in response to deviations from
the target temperature. This experiment utilizes a PI controller to investigate how varying control
gains influence the system's response.

9
Figure 1: Lab Temperature Control Console

Proportional-Integral (PI) Control:

PI control combines two main actions to maintain a stable temperature:
1. Proportional Control (P):
● The proportional term adjusts the controller output based on the current error (difference
between setpoint and measured temperature).
● The larger the error, the greater the response, leading to faster correction.

● If used alone, proportional control often leaves a small steady-state error.

2. Integral Control (I):
● The integral term accumulates the error over time, making corrections based on the total
accumulated error.
● This action reduces the steady-state error, helping the system reach and stay at the
setpoint.
● Excessive integral action can lead to overshoot and oscillations.
The combined PI control action is defined by the control equation:
u(t)=Kp * e(t) + Ki ∫e(t)dt
where:
● u(t) is the control signal (input to the system)
● Kp is the proportional gain (determines the strength of the proportional response)
● Ki is the integral gain (determines the strength of the integral response)
● e(t) is the error (difference between setpoint and measured temperature)
The proportional gain Kp influences the speed of the response, while the integral gain K i helps
eliminate steady-state error, providing more precise control.
Experimental Procedure:
1. Set Up Initial Connections:

10
Connect the HEATER DRIVER bushes: bush 11 to bush 11, and bush 12 to bush 12. Also,
connect the temperature sensor: bush 1 and bush 2 to the interface bushes 1 and 2.
2. Prepare the Process Tank:
Check the water level. Ensure it is at 18 cm; if needed, add water through the inlet valve.
3. Power On:
Switch on the main system power.
4. Configure Set Point and Sensor Connections:
Connect SET POINT 2 to bush 4 of the PID controller. Also, connect bush 3 of the temperature
interface to bush 3 on the PID controller.
5. Measure Initial Temperature:
Use the digital voltmeter: place one terminal at bush 3 on the temperature interface and the other
at the earth bush. Record the starting temperature, converting the voltage to °C by multiplying by
10.
6. Set the Target Temperature:
Move the voltmeter to SET POINT 2 and adjust the voltage to 4V (representing 40°C).
7. Verify Reference Step:
Place the voltmeter on bush X2 of the PID controller. Confirm the voltage value represents the
difference between bushes 4 and 3.
8. Set Initial Proportional and Integral Gains:
Set the PROPORTIONAL knob to 50% and the INTEGRAL knob to 25%.
9. Activate System Control:
Press the RESET button to reset the integrator. Connect bush 6 to bush 6 and bush 8 to bush 8 on
the HEATER DRIVER. Start the chronometer as you begin data recording.
10. Record Temperature Over Time:
At set time intervals (e.g., every minute), measure and log the temperature from bush 3 of the
PID controller, converting to °C as needed. Continue until the system reaches a steady state.
11. Determine Steady-State Error:
Measure and record the steady-state error by placing the voltmeter on bush X2 of the PID
controller.
12. Repeat with Different Integral Gains:
After each test, drain and refill the tank to 16 cm. Repeat steps 9–11 with the INTEGRAL knob
at 50%, 75%, and 100%.
13. Power Down and Analyze:
Turn off the main switch. Plot the dynamic response curves for each INTEGRAL setting and
analyze the results.

11
Observations and Calculations:

Kp = 25% Kp = 50% Kp = 75% Kp = 100%

Time
Temperature Temperature Temperature Temperature
(min)
(°C) (°C) (°C) (°C)

0 44.6 44.6 44.4 43.5

12
 2 45 44.9 44.6 44.7

4 44.7 44.7 44.6 44.6

6 46.1 45.5 45.3 45.2

8 46.2 45.8 46.6 46.3

10 47.3 46.2 47.7 47.1

12 47.9 46.9 47.9 47.6

14 48.2 47.8 48.5 50

Graph:
52

50

48

46

44

42

40
0 2 4 6 8 10 12 14 16

Kp=25 % Kp = 50 % Kp= 75 % Kp = 100 %

Data Interpretation:

Based on the data collected from varying integral gain settings (Kp = 25%, 50%, 75%, and
100%), the following observations about the system's dynamic behavior can be made:

1. Response Speed (Rise Time):

○ At lower gain settings (Kp = 25% and 50%), the system exhibits a slower increase
in temperature, suggesting a more gradual response.

13
 ○ Higher gain values (75% and 100%) result in faster temperature rises, indicating a
quicker system response to changes.
2. Accuracy and Steady-State Error:

○ Increasing the integral gain helps reduce steady-state error, improving the
system's ability to reach the desired temperature. For example, at Kp = 25%, the
temperature peaks at 48.1°C, while at Kp = 100%, it reaches 50°C by the 14-
minute mark, showing better accuracy at higher gains.
3. Overshoot and System Stability:

○ As the gain increases, there is a noticeable risk of overshooting the setpoint and
potential instability. For instance, at Kp = 100%, the temperature exceeds the
target, indicating the system is overshooting and potentially oscillating around the
setpoint.
○ At lower gains (25% and 50%), the temperature increase is smoother and more
controlled, with a slower but steady approach to the target.
4. Oscillation Behavior:

○ Higher gain values (75% and 100%) result in more oscillations, which suggest an
aggressive response to errors but could lead to instability in the system.
○ Lower gain values (25% and 50%) show dampened oscillations, providing better
stability but slower convergence to the target temperature.

Key Takeaways:

This experiment illustrates that increasing the integral gain leads to a faster response and reduced
steady-state error. However, higher gains also increase the risk of overshoot and system
instability. Balancing the need for fast response with system stability is crucial when selecting
the appropriate gain settings.

Further Considerations:

The choice of integral gain settings should depend on the specific application needs. Systems
that require quick corrections might benefit from higher gains, while those demanding precise
temperature control should use lower gains. Future research could focus on combining
proportional, integral, and derivative gains (PID control) to achieve enhanced stability and
reduced oscillations.

Test Notes:

● Ensure the starting temperature is consistent for each experiment.

● Maintain the water level above 16 cm, as the heater will not function if the water level
falls below this threshold.
● The maximum allowable tank temperature is 50°C.

14
Experiment: Closed Loop Proportional-Differential Control of Temperature
Objective:
● To verify the effects of the gain of the loop on the dynamic response of the system
● To draw the dynamic response curve of the system
List of equipments:
● Digital Multimeter: Measures electrical signals, including sensor and control outputs.

15
 ● Chronometer: Tracks time for calculating response metrics like rise time and settling
time.
● Set of Leads: Connects the components in the control loop.
Theory:
Temperature Control in Closed-Loop Systems:
In control systems, particularly for temperature regulation, the objective is to maintain a target
temperature by adjusting inputs based on real-time feedback. A common method used to achieve
precise control in such systems is the Closed-Loop Proportional-Integral (PI) control. Unlike
open-loop systems that operate without feedback, closed-loop systems continuously adjust their
output in response to any deviation from the desired temperature. This feedback mechanism
allows the system to correct errors and maintain stable operation. In this experiment, we use a PI
controller to explore how varying control gains (proportional and integral) influence the system's
performance and response.

Figure 1: Lab Temperature Control Console

Proportional (P) Control

Proportional (P) Control:

Proportional control is a fundamental action used in PID controllers and is the simplest form of
continuous feedback control in a closed-loop system. In P-only control, the controller output is
directly proportional to the error, which is the difference between the measured variable and the
desired set point. This type of control aims to minimize fluctuations in the process variable but
does not necessarily bring the system to the exact set point.

One key benefit of P-control is its faster response compared to other controllers. The P-only
controller can initially react more quickly, sometimes responding within seconds, and as the
system becomes more complex, this faster response time could accumulate, allowing the P-
controller to respond even a few minutes faster than other types of control systems. However, the
main downside is the presence of an offset, where the system cannot achieve the exact set point.

16
This offset creates a steady-state deviation from the desired value, which is usually undesirable
in many applications.

The offset is analogous to systematic error in calibration, where the line never crosses the origin,
always maintaining a constant error. While P-only control is useful for many applications, it
cannot eliminate this offset on its own. To address this limitation, P-control is often combined
with other control actions, such as Integral (I) or Derivative (D) control, to reduce or eliminate
the offset and improve overall system performance. In summary, P-control provides a fast
response but needs to be complemented with additional control strategies to achieve precision in
maintaining the set point.

This P-control behavior is mathematically illustrated in Equation

Where,
● 𝑐(𝑡) = controller output
● 𝐾𝑐 = controller gain
● 𝑒(𝑡) = error
● 𝑏= bias
In this equation, the bias and controller gain are constants specific to each controller. The
bias is simply the controller output when the error is zero. The controller gain is the change
in the output of the controller per change in the input to the controller.
P-only control provides a linear relationship between the error of a system and the controller
output of the system. This type of control provides a response, based on the signal that
adjusts the system so that any oscillations are removed, and the system returns to steady-
state. The inputs to the controller are the set point, the signal, and the bias. The controller
calculates the difference between the set point and the signal, which is the error, and sends
this value to an algorithm. Combined with the bias, this algorithm determines the action that
the controller should take
Differential Control

Derivative control (D-control) anticipates future process conditions by analyzing the rate of
change of the error, aiming to minimize the error's rate of change and maintain a consistent
system behavior. The primary function of D-control is to resist changes in the system, especially
oscillations, making it valuable in controlling dynamic systems that are prone to rapid changes.

The main benefit of D-control is its ability to reduce or eliminate oscillations by calculating the
control output based on the rate of change of the error over time. The larger the rate of change of
the error, the more pronounced the controller's response. This characteristic helps dampen
oscillations and stabilize the system, especially when there is a rapid change in the measured
variable.

Unlike proportional and integral controllers, D-control does not directly guide the system to a
steady state. It does not address the steady-state error, making it less effective on its own for
achieving long-term stability. For effective control, D-control is typically coupled with
17
proportional (P), integral (I), or combined PI controllers. When combined, these controllers
leverage the strengths of each type to minimize both steady-state error and transient oscillations.

D-control correlates the controller output to the derivative of the error, which is the change in
error with respect to time. This means it responds to how fast the error is changing, making it
particularly useful for reducing rapid fluctuations and stabilizing a system that may otherwise be
prone to oscillations. However, D-control alone is not sufficient for most systems, as it needs to
be paired with other control strategies to achieve complete regulation.

● This D-control behavior is mathematically illustrated in Equation.

Where,

● Td is the derivative time constant

● c(t) is the controller output

● 𝑑𝑡 is the differential change in time

● de is the differential change in error

Proportional-Differential Control
Another combination of controls is the PD-control, which lacks the I-control of the PID system.
PD-control is combination of feedforward and feedback control, because it operates on both the
current process conditions and predicted process conditions. In PD-control, the control output is
a linear combination of the error signal and its derivative. PD-control contains the proportional
control’s damping of the fluctuation and the derivative control’s prediction of process error.
As mentioned, PD-control correlates the controller output to the error and the derivative of the
error. This PD-control behavior is mathematically illustrated in Equation

where
● c(t) = controller output
● Kc = proportional gain
● e = error
● C = initial value of controller
The equation indicates that the PD-controller operates like a simplified PID-controller with a
zero-integral term. Alternatively, the PD-controller can also be seen as a combination of the P-
only and D-only control equations. In this control, the purpose of the D-only control is to predict
the error in order to increase stability of the closed loop system. P-D control is not commonly
used because of the lack of the integral term. Without the integral term, the error in steady state
operation is not minimized. P-D control is usually used in batch pH control loops, where error in
steady state operation does not need to be minimized. In this application, the error is related to
the actuating signal both through the proportional and derivative term.
Experimental Procedure:
14. Set Up Initial Connections:

18
 Connect, through leads, bush No, IT of the HEATER DRIVER 10 bush No. 11 and bush No.
12 to bush No. 12. Connect busher No. J and 2 of the temperature seniors to bushes No. 1
and 2 of the relevant interfaces.
15. Prepare the Process Tank:
Check if the water level in the tank is 18 cm; otherwise fill process tank: from water Inject
Valve until the water level has reached 18 cm.
16. Power On
Switch on the main system power.
17. Configure Set Point and Sensor Connections:
Connect the bush of SET POINT 2 t0 bush No. 4 of the PID controller and bush No. 3 of the
temperature interface to bush No, 3 of the PID controller.
18. Measure Initial Temperature
Insert one terminal of the digital voltmeter, set in de, to bush No, 3 of the temperature
interfaces and the other one in the earth bush. Read and write down the voltage value which
corresponds, multiplied by 10, to the starting temperature.
19. Set the Target Temperature:
Move the voltmeter to SET POINT 2 and adjust the voltage to 4V (representing 40°C).
20. Verify Reference Step:
Place the voltmeter on bush X2 of the PID controller. Confirm the voltage value represents
the difference between bushes 4 and 3.
21. Set Initial Proportional Gains:
Set the PROPORTIONAL knob to 50% and connect bush No. 5 of PID controller to bush
No. 5. Set the DERIVATIVE knob at 25%. Connect bush No. 7 of the PID controller to bush
No. 7 and bush No. S to bush No. 8 of the HEATER DRIVER and at the same time start the
chronometer.
22. Record Voltage Over Time
Write down the voltage value, after conversion in 0C, at equal time intervals up to the end of
the transitory (for example every minute).
23. Determine Steady-State Error:
Move the terminal of the digital voltmeter to bush N2 of the PID controller.
write down the voltage value which represents steady state error
24. Repeat with Different Integral Gains:
After each test, drain and refill the tank to 16 cm. Repeat steps 9–11 with the DERIVATIVE
knob at 50%, 75%, and 100%.
25. Power Down and Analyze:
Turn off the main switch. Plot the dynamic response curves for each DERIVATIVE setting
and analyze the results.

Observations and Calculations:

Time Kc = 25% Kc = 50% Kc = 75% Kc = 100%

(min) Temperature (°C) Temperature (°C) Temperature (°C) Temperature (°C)

1 32.5 32.4 32.5 32.2

19
 3 32.3 32.2 32.4 32.2

5 32.4 32.4 32.4 32.1

7 32.4 32.5 32.5 32.4

9 32.5 32.7 32.6 32.6

11 32.7 32.7 32.8 32.7

13 32.7 32.8 32.9 32.8

Graph:

33

32.8

32.6

32.4

32.2

32

31.8

31.6
0 2 4 6 8 10 12 14

Kc= 25 % Kc= 50 % Kc= 75 % Kc= 100 %

Analysis:

From the data gathered over a range of controller gains (Kc = 25%, 50%, 75%, and 100%),
several key observations about the system's dynamic behavior can be made:

1. Initial Rise in Temperature Variation: At lower Kc values, an increase in temperature

variation is noticeable. This suggests that while the system initially responds to increases
in controller gain, it may also experience higher oscillations or instability as the gain
increases from zero.

2. Peak Temperature Variation: A peak in temperature variation occurs at an intermediate

value of Kc (around 75%). This peak signifies the point where the system's response to
the controller gain is most pronounced. At this point, the system may exhibit maximum
oscillatory behavior or overshoot before it settles down.

20
 3. Decrease in Temperature Variation: When Kc is increased beyond the peak point (to Kc
= 100%), the temperature variation starts to decrease. This indicates that higher values of
controller gain contribute to stabilizing the system, reducing oscillations, and bringing the
temperature closer to the desired setpoint.

4. Stabilization: At very high values of Kc, the temperature variation begins to stabilize.
This suggests that the system becomes less sensitive to further changes in controller gain.
The stabilization can be attributed to the proportional action of the PD controller, which
effectively reduces the error and maintains the temperature consistently.

Conclusion:

The relationship between controller gain (Kc) and temperature variation is crucial for the proper
tuning of a PD controller. The analysis shows that there is an optimal range for Kc where
temperature variation is minimized, ensuring system stability and performance. Careful tuning
and continuous monitoring are necessary to optimize the PD controller, avoiding instability and
excessive oscillations while achieving desired control outcomes.

21