CHAPTER APPLICATION TO TEMPERATURE CONTROL SYSTEMS

• Closed-loop control system

In contrast with the previous system, the action control is influenced or determined by the output signal, consequently, in this system exist a feedback exists. The main features of these systems are the following:

More complexity, but allows better parameterization. The output is compared with the input process variable.

40 Arduino based acquisition system for control applications

More stable when there are disturbances .

The main advantage of a closed-loop system compared to the other is the possibility to correct the disturbances affecting the system.

The application developed in this project has been implemented in accordance with the characteristics established in the closed-loop systems. The application selected requires that the output signal has an effect upon the process input to correct the disturbances or any other circumstance.

4.2. PID Controller

One of the most important elements in a control system is the controller. In this project has used a type of controller known as a PID controller [3], widely used in industrial processes.

In expression 4.1, it can see a typical structure of a PID control system, where the error signal e(t) (see expression 4.2) is used to generate the proportional, integer, and derivative actions, with the resulting signals weighted and finally added to form the definitive control signal o(t) applied to the plant model. In the formula x can see a mathematical representation of the PID controller explained before.

Output = o (t) = K P ⋅ e (t) + K i ∫ e(t) dt + K d ⋅ e (t) (4.1)

e (t) = Setpoint Measured - Variable (t) (4.2)

The output of the PID controller is generated from the sum of three components, which are calculated from the input error. These three parts are detailed below:

• Proportional

The proportional term is a basic part in any PID controller. This element provides a proportional corrective action to the error. As shown in expression 4.1, the error is multiplied by a constant K P .

• Integral

The integral term provides an integral corrective action to the error. However, the integral action also has a destabilizing effect due to the added phase shift. As it has shown in expression 4.1, the error is multiplied by a constant known as K i . The integral part can be calculated adding the error at each sample time. This element is very important because it tends to cancel the offset error.

CHAPTER 4. Application to temperature control systems 41

• Derivative

This last term provides predictive properties to the performance, generating a proportional action to the rate of change of the error. As

shown in expression 4.1, the error is multiplied by a constant K d . In contrast to the integral part, the derivative part tends to give stability to the system, but sometimes can generate large signal values.

The block diagram in Figure 4.1 shows the closed-loop system developed in this project. It is composed by different elements such as the sensor, the actuator or controller and the plant. In this project the controller or actuator will

be a potentiometer, the plant is a water jug and finally, a different temperature sensor.

Other important parameter is the setpoint that defines the limit of certain magnitude or variable. For example, in this system the setpoint is the temperature which the control system aims to reach.

As explained before, the output (o(t)) will contain three parts; proportional, integral and derivative, depending on the error induced by the difference between the error and the measurement value from the sensor.

Figure 4.1 Closed-loop system

It is important to notice that the disturbances induced in the plant can alter the output value. For this reason, it is appropriate to use a closed-loop system due to the corrective effect thorough the PID controller.

Consequently, it is necessary to obtain the parameters of the controller. Then, it uses an appropriate method called Ziegler-Nichols to find these parameters. This method is explained with detail in section 4.2.1.

42 Arduino based acquisition system for control applications

4.2.1. Ziegler-Nichols method

The main characteristics of the developed system allow using the step response method called Ziegler-Nichols method, which is characterized by two parameters, L and T, obtained from open loop response. Figure 4.2 represents

a sketch of a step response from a general system. For example, the step response of the plant model has been measured through

an experiment. This experiment consisted in submitting the overall system to a temperature change. In this case, the change produced was from ambient temperature to approximately 65 degrees. Consequently, it was obtained a step response similar to that shown in Figure 4.2.

Figure 4.2 Sketch of the step response about a general system

It should be noticed that this plot represents the step response of the system, and therefore, it can extract the parameters defined by the PID controller.

First of all, it is necessary to find the tangent line at the step response at its point of inflection. After, the intersection with the maximum value and the time axis, defines two points. This response is characterized by two parameters; L corresponds to the delay time and T, is the time constant. Finally, according to this method of tuning the PID controller, the parameters can be obtained through to the following equations:

CHAPTER 4. Application to temperature control systems 43

K c = 1.2 () T (4.3)

T i = 2 L (4.4)

T i = 0.5 L (4.5)

4.3. Temperature control

The application aims to control the temperature of a water jug thorough a PID controller. For this application is necessary to choose the appropriate temperature sensor [1]. Consequently, due to the multitude of temperature sensors on the market, it has decided to select two models widely used in different applications.

In the selection of these sensors have been taken into account the initial requirements established. Due to the small signal obtained from the sensors, it must apply conditioning circuits to adapt it. The conditioning circuits are formed by active elements like operational amplifiers and regulators. For this reason it is necessary to provide energy to the system.

We studied two possibilities to develop the control applications: an autonomous system and a dependent system. The first one works independently, because the signal is acquired, processed and actuated in the own Arduino module.

The second one works different, in this case, the signal is acquired by an Arduino module and sent it to a laptop, which process it and after, returns an output control signal against a determinate system.

Both systems perform the same, but the control application code is different for each one. However, it may appreciate some differences in the final result caused by the delays of the some components involved in that system. Moreover, the application code can produce some differences between both systems. Another perturbation on the system can be produced by the serial communication (wireless).

These applications have been developed using two programming tools: IDE Arduino for an autonomous system, and LabVIEW for a dependent system.

For an autonomous system, the batteries seem the better option to supply the circuit, but, it is necessary to use other components to assure the stability of the supply voltage. On the other hand, the Arduino module provides a single ended voltage, but the operational amplifiers need a differential supply ± 5V. Then, another device is needed to a correct supply. Finally, a transformer with a power supply of 9 V gives energy to the action system, mainly composed by a relay and other components to ensure a proper operation.

In conclusion, the aim of this application is to maintain a temperature of a water jug using the control system explained previously. For this, a PID controller will

be implemented, whose function is to apply an output value according to the measurement from the sensor.

44 Arduino based acquisition system for control applications

In next paragraphs, the detail of each application for the selected sensor has been studied. First, the circuit used for the application is described, detailing all the components and because these have been implemented. Next, the constant values applied for each PID controller and the process to obtain them.

Finally, the test obtained for each application will be displayed trough a graphic, where the temperature and the output will be represented in the time domain.

4.4. Sensors

The system acquires signals from various sensors (see Figure 4.3). These signals are separated in channels according to the type of input established by Arduino module. In this case, the system developed in this project has four input channels.

NTC Thermistor Potenciometers

Switch

Pt1000

Figure 4.3 Conditioning circuits of the sensors on the protoboard

• Analog channel 1: NTC Thermistor sensor. • Analog channel 2: Pt1000 sensor or potentiometers. • Digital channel 1: Digital input emulated by a switch. • Digital channel 2: Digital input emulated by a switch.

CHAPTER 4. Application to temperature control systems 45

The purpose of this report is to develop an acquisition system composed by different inputs. For this reason, it has been applied a scenario that integrates two analog signals from temperature sensors or another from a potentiometer. According to this, the value of this input will be between 0 and 1024.

On the other hand, the digital signals are selected from a switch, which is a button. When the button is pressed, the sent value is 1, in contrast, this value is

0. Each sensor has a conditioning circuit consists of different components such as

resistors, capacitors, operational amplifiers, regulators, etc. In next paragraphs, it will explain in detail the performance of each one.

4.4.1. NTC Thermistor

The first application developed contains a NTC sensor in order to measure the temperature of the water jug, which will be connected to an acquisition system to obtain the data generated.

4.4.1.1. Characteristics

A thermistor is a resistive sensor of temperature. Its operation is based on the variation of the resistivity that shows a semiconductor with temperature. There are two types of thermistor depending on the sign of the coefficient, which are the following:

• NTC (Negative Temperature Coefficient) • PTC (Positive Temperature Coefficient)

In this case, we selected a NTC sensor to implement this prototype. The NTC sensor are mostly modelled by the following expression, where R T is the

resistance for a temperature (T), R 0 is the resistance for a reference temperature (T 0 ) and B is the characteristic temperature of the material. For more information, it can consult the main features on the Annex A.1. The temperature must be expressed in Kelvins:

The main inconvenient presented by the thermistor is its nonlinearity. This nonlinearity has been solved applying a specific circuit design as usual to improve linearity.

4.4.1.2. Circuit design We designed a conditioning circuit to linearize the behavior of the sensor. For

this reason, the circuit selected to obtain a correct behaviour uses a series

46 Arduino based acquisition system for control applications

resistance throughout the expression 4.7, where R Tc is the equivalent resistance at the central point of the measurement range, and T c , the corresponding central temperature.

The final design includes four resistances: the thermistor and the sum of the rest, the series resistance to linearize the thermistor (R = R 2 +R 3 +R 4 = 755 ).

Then, it has used a voltage divider in order to relate resistance with temperature, and consequently, the temperature with the voltage. The expression for a voltage divider is the following:

For example, the simulation in Figure 4.4 shows the output voltage for different values of resistance (NTC sensor), on the left, at 20 degrees and on the right, at

Figure 4.4 Circuit simulation in Proteus at different temperature. On the left, simulation at 20 degree and on the right, at 80 degrees.

With the circuit simulation using Proteus, we obtained the corresponding output voltage represented in the following table:

CHAPTER 4. Application to temperature control systems 47

Table 4.1 Output Voltage at corresponding temperature Parameter

4.4.1.3. Control Application Figure 4.5 represents the block diagram of the application implemented in the

project. The following block diagram shows the evolution of each stage:

Figure 4.5 Application block diagram

48 Arduino based acquisition system for control applications

The first step in the application is to acquire data from the sensors connected to Arduino. Next, it proceeds to convert the voltage reading into temperature for the first analogue channel. Referring to the other channels, the reading is not modified. The established order to measure the readings must be the same appears in the application, without variation.

Below, in the next step, the algorithm interpolates the values obtained according to determined values established for each temperature in the range of measurement.

Next, the interpolated value is compared with the setpoint. If both values are the same, the output will be 0. Otherwise, if value is smaller than setpoint, the PID control is activated according to the parameters defined and the output will be determined between 0 and 1. In both cases, the output will be sent to Arduino to establish an action. The output value determines how much time should be on the power control.

Data processed from the channels through the Arduino, are displayed on the screen in the front panel, and are saved in a file. The values taken from each channel (analogue and digital) are represented while the system is running.

Finally, in the last step, the system returns to the first step without any delay, and the system acquire new values to start the process.

For this sensor, the electrical characteristic that describes it is resistivity. The range of resistors specified by the manufacturer for working within the range specified in this project is [276,40 – 2747,30] Ω for [20 – 80] ºC.

The following block diagram (see Figure 4.6) shows a closed-loop system developed for this application.

Figure 4.6 Close-loop system of the NTC temperature system

The next step in the process is to find the three parameters defined in a PID controller. In order to obtain these values, it processes to make an experiment based in submitting the plant to a step response from initial temperature of water jug until the maximum temperature reached, around 65 degrees. Next, the array of values obtained has been analyzed using MATLAB as it can see in Figure 4.7.

CHAPTER 4. Application to temperature control systems 49

Figure 4.7 Graphic behaviour of the plant with NTC Thermistor According to the Ziegler-Nichols method, it can obtain the tree parameters

detailed in the next table.

Table 4.2 Experimental parameters obtained for NTC

Parameter

Value

K C 171,49 (adimensional)

1,12 (minutes) T d 0,28 (minutes)

However, the algorithm used in the autonomous system does not accept a time constant for an integral and derivative parts. Then, these parameters must be converted using the following expressions:

K d = K p ⋅ T d (4.11)

50 Arduino based acquisition system for control applications

Table 4.3 Experimental parameters obtained for NTC ( gains )

Parameter

Value (adimensional)

K d 47,99

The temperature sensor has been calibrated using the experiment implemented to find the PID parameters which consisted in submitting the plant to an increment of the temperature until reaching a determined value. It has been used the expression extracted from the characterization. This curve expression relates the voltage measured with the resistance of the sensor. We used a reference temperature sensor in order to relate resistance with temperature, and consequently, the temperature with the voltage.

It is important to notice that all the experimental tests have been made using the prototype described in the chapter 3 and basically the acquisition system.

Then, using the same experiment, it has measured the corresponding voltage for each temperature with a multimeter. According to this, the following results have been obtained:

Table 4.4 Characterization values of NTC

Temperature Voltage

CHAPTER 4. Application to temperature control systems 51

4.4.2. Pt1000 sensor

The second developed application contains a Pt1000 sensor in order to measure the temperature of the water jug, which will be connected to the acquisition system.

4.4.2.1. Characteristics In order to measure the temperature of a water jug, a resistive sensor is used,

as it exploits the predictable change in electrical resistance of some materials with changing temperature. These kinds of sensors are called: Resistance Thermometers or Resistive Thermal Devices (RTD). For this project, the Honeywell RTD HEL-700 has been chosen as temperature sensor. It is a Film thermometer (see Figure 4.8) based on platinum.

Figure 4.8 Honeywell HEL-700

The RTD are modelled by the expression 4.12, where R is the resistance for a temperature (T), R 0 is the resistance for a reference temperature (T 0 ).

Compared to thermistors, platinum RTDs are less sensitive to small temperature changes and have a slower response time. However, thermistors have a smaller temperature range and stability.

4.4.2.2. Circuit design The final model developed is based on a pseudobridge structure. This design is

divided in three main blocks: the power supply (regulator), the pseudobridge, and a voltage amplifier.

The structure of a Wheatstone bridge allows suppressing the offset generated by the nominal value of the RTD.

Notice that the value of R 0 can be so high, so, the variations of the signal are too low compared with the signal offset .

52 Arduino based acquisition system for control applications

Placing an operational amplifier like shows Figure 4.9, the output will be a linear function depending on the RTD value, because the current through the RTD will

be constant depending on the value of V s . The Figure 4.9 shows the overall design for the RTD (without the low pass filter

at the output). Notice that the useful signal is added by means of an inverting adder

operational amplifier structure. R 7 and R 8 are calculated to establish the gain for the useful signal. It has been selected an inverting amplifier structure, so the selected resistors are R 7 = 1150 and R 8 = 27 k . The final gain is:

Figure 4.9 Circuit simulation of the Pt1000 sensor at 60 degrees

Is important to find an experimental value closer to the theoretical value, so, two resistors in series have been used to achieve a resistance close to the calculated one (notice that the practical value is smaller than the theoretical one, it is that way to avoid the saturation of the amplifier).

With these values of the components, the following output rails are obtained through the next expressions:

CHAPTER 4. Application to temperature control systems 53

The Figure 4.10 shows the power supply circuit applied on the input conditioning circuit. It has been structured using two components, a regulator and an operational amplifier.

KA336 is the model selected for a regulator. These are useful as a precision 2.5

V low voltage reference for power supplies or op amp circuitry. The 2.5 V make it convenient to obtain a stable reference from low voltage supplies as needed in the supply stage.

The operational amplifier selected is the TLV272. It was used as a voltage follower because the voltage is transferred unchanged, the amplifier is a unity gain buffer and the output voltage follows or tracks the input voltage.

Moreover, the amplifier allows transferring a voltage from a circuit, which has high output impedance, to a second circuit with low input impedance. The interposed buffer prevents the second circuit from loading the first circuit unacceptably and interfering with its desired operation.

Figure 4.10 Power supply circuit implemented on the input conditioning circuit.

The closest commercial value to these resistors according to the requirement related to the current are showed in Figure 4.10, 4K7 and 2K7 in series connection with a power supply ( 5 V ).

Finally, with this configuration, we got a stable voltage on the input of the conditioning circuit.

54 Arduino based acquisition system for control applications

The range of the nominal values of the RTD at corresponding temperature is defined in the following table:

Table 4.5 Resistance and voltage values calculated from the expressions

4.4.2.3. Control Application For this sensor, the electrical characteristic that describes it is the resistivity.

The range of resistors specified by the manufacturer for working within the range specified in this project is [1075 – 1300] Ω for [20 – 80] ºC.

As said in the previous paragraphs, one of the main elements involves in a control system would be the PID controller. For this reason, it is important to find the three constants defined in a PID. In order to obtain these values, it processes to make an experiment based in submitting the plant to a step response from initial temperature of water jug until the maximum temperature reached, roughly 65 degrees. Next, the array of values obtained is analyzed using MATLAB as it can see in Figure 4.11.

Figure 4.11 Graphic behaviour of the plant with a RTD

CHAPTER 4. Application to temperature control systems 55

According to the Ziegler-Nichols method, we can obtain the three parameters detailed in the next table.

Table 4.6 Experimental parameters for a RTD

Parameter

Value

K C 88,12 (adimensional)

1,22 (minutes) T d 0,30 (minutes)

However, the application code implemented in autonomous system does not accept a time constant for an integral and derivative parts. Then, these parameters must be converted to a gain constant using the expressions described in the paragraph x. With these expressions, it obtains a gain constant for each part of the PID controller (see Table 4.7).

Table 4.7 Experimental parameters for a RTD ( gains )

Parameter

Value (adimensional)

73,18 K d 18,29

The temperature sensor has been calibrated using the experiment implemented to find the PID parameters. It has been used the equation extracted from the characterization (see Table 4.8). This curve equation relates the voltage measured with the sensor’s resistance. It has used a reference temperature sensor in order to relate resistance with temperature, and consequently, the temperature with the voltage.

56 Arduino based acquisition system for control applications

Table 4.8 Characterization values for RTD

Temperature Voltage

4.5. Experimental tests

4.5.1. Autonomous system

In the first scenario studied in this project (see Figure 4.12 and Annex B.1), the data is acquired from the Duemilanove Module, and a part of the application code implemented is used for data processing, resulting in an output.

This output is applied directly to digital pin contained in the module. Finally, the data is sent to receiver by Xbee communications, which can be represented later in a notebook.

The receiver gets the data and after, these are transferred to a computer by serial communication. Then, it can be represented by an application, with LabVIEW or Processing.

CHAPTER 4. Application to temperature control systems 57

Sensor

(Circuit)

Acquisition, Processing and Actuation Display

Figure 4.12 Autonomous system

4.5.1.1. NTC sensor The Figure 4.13 shows the temperature evolution. In this measurement, it can

be observed that the temperature increases slowly until reaching 30 ºC approximately. During a period of time, the temperature increases and then, it reach a setpoint temperature, where the system maintain a constant temperature.

Figure 4.13 Autonomous system testing (using NTC sensor). Temperature vs

Time.

58 Arduino based acquisition system for control applications

In this case, the Figure 4.14 shows the output established for the control application developed. The value is between 0 and 1, and represents the period of time during the power supply is active. When the temperature reaches the setpoint, the output value is 0 during certain periods of time.

Figure 4.14 Autonomous system testing (using NTC sensor). Output vs Time.

4.5.1.2. Pt1000 sensor The prototype for the autonomous system using the RTD sensor (see Annex

C.1) is the same than the implementation used for the NTC sensor. It has been made a test in order to prove the general system.

The Figure 4.15 shows the temperature evolution. In this measurement, it can

be observed that the temperature increases slowly until reaching 30 ºC approximately. During a period of time, the temperature increases and then, it reach a setpoint temperature, where the system maintain a constant temperature.

Figure 4.15 Autonomous system testing (using RTD sensor). Temperature vs

Time.

CHAPTER 4. Application to temperature control systems 59

In this case, the Figure 4.16 shows the output established for the control application developed. The value is between 0 and 1, and represents the period of time during the power supply is active. When the temperature reaches the setpoint, the output value is 0 during certain periods of time.

Figure 4.16 Autonomous system testing (using RTD sensor). Output vs Time.

4.5.2. Dependent system

In this scenario (see Figure 4.17 and Annex B.2), the role has been modified. The data is sent to receiver by XBee communication without processing. In this case, the receiver gets the data by XBee communication in order to process and represent the data with an application which has been developed in LabVIEW.

Sensor

(Circuit)

Acquisition Processing, Action and Representation

Figure 4.17 Dependent system

60 Arduino based acquisition system for control applications

4.5.2.1. NTC sensor Figure 4.18 shows the evolution of the temperature measured as in the

autonomous system.

T(ºC) 35 30 25 20 15 10

Figure 4.18 Dependent system testing (using NTC sensor). Temperature vs

Time.

Figure 4.19 shows the evolution of the output control in real time.

Figure 4.19 Dependent system testing (using NTC sensor). Output vs Time.

4.5.2.2. Pt1000 sensor The prototype for the dependent system using the Pt100O sensor (see Annex

C.2) is the same than the implementation used for the NTC sensor. It has been made a test in order to prove the general system.

CHAPTER 4. Application to temperature control systems 61

Figure 4.20 shows the evolution of the temperature measured as in the autonomous system.

T(ºC) 35 30

Figure 4.20 Dependent system testing (using RTD sensor). Temperature vs

Time.

From the comparison between the other studied scenarios, it can be observed some disturbances. This difference is consequence of parameters not taken into account such the delay produced by the computer and LabVIEW or other parameters can come from components as the protoboard and the cables. These components produce some capacitance effects and increase the period in the same quantity for all the values measured.

Figure 4.21 shows the evolution of the output control in real time.

Figure 4.21 Dependent system testing (using RTD sensor). Output vs Time.

62 Arduino based acquisition system for control applications

5. CONCLUSIONS

5.1. Overall conclusions

The overall system meets all the objectives proposed in this project. The hardware and the control algorithms implemented are capable of acquiring data from the sensors. Moreover, it can process data in both directions, consequently is a bidirectional system.

At the end of this project, a series of prototypes are available for using as an acquisition system for different applications. The final prototypes are the following:

• Acquisition system connected directly a computer via USB. • Autonomous acquisition system • Acquisition system connected to a computer via wireless (Zigbee or wifi

protocol).

It is important to notice that an autonomous scenario studied in this project offers advantages compared with the dependent system, because it does not need another element to process the data. However, the dependent system offers the possibility to apply an algorithm less closed than the algorithm deployed on the autonomous system due to the limitations on the programming language.

Therefore, the platform selected has allowed studying a lot of possibilities related to the communication, circuit design and the algorithm through different tools such as IDE Arduino, LabVIEW or Processing. In conclusion, the development of this project has allowed an interdisciplinary knowledge in different areas of the technology.

Nowadays, Arduino represents an appropriate tool capable of solving engineering problems such as the application developed due to its main characteristics. Due to this, the Arduino environment is being introduced as a tool in education to support for solving determinated problems in engineering.

Moreover, we have used a tool as Matlab to evaluate the values obtained from the experiments or tests implemented.

Also, this way of working supports a pedagogical model of learning process where the student is an active participant in the whole process, from the conception of the idea until the final product or prototype.

On the other hand, rather than the Zigbee communication, we have deployed a scenario with a wifi communication. This is a very important element due to the accessibility offered by this kind of communication.

The tests performed on both systems verify the correct performance of the acquisition system and the algorithm developed for the temperature control

Conclusions taking into account the entire factors involved on the application, such as the

PID parameters. All the conditioning circuits for both sensors have to be designed in order to fulfil

all the specifications, and there are several trade-offs that have to be resolved in an optimal way.

Always exists a limit in terms of resolution and errors, either for signals or analog signals. The system has to be designed with a limited resolution. There are also many external and internal factors than can affect to the performance, like the protoboard, the tolerance or the connections used. Another limitation can be caused by the Arduino module due to the number of bits of the converter.

Many of the interfering factors can be diminished by means of using more accurate elements. Obviously, this would represent and increment in price. Due to this trade of between price and quality, it is very important to characterize and have knowledge of the global behaviour.

Finally, in future works could treat the following concepts: • Improve the conditioning circuits. • Apply new plants. • Characterize the uncertainty.

5.2. Environmental study

Nowadays, engineering projects must take into account the environmental impact.

At the end of the life of each device, those must be deposited in containers of waste electrical and electronic equipment for recycling.

The use of batteries as a power source, for different components is harmful to health and the environment, if the batteries are not recycled correctly. These batteries contain heavy metals which are very harmful to health. The layer which protects them is readily decomposed and if these batteries are located into an inadequate location such as on the ground, the waste is filtered and consequently, it may pollute the water. Moreover, it recommends using rechargeable batteries or direct connection to power source, allowing a long period of duration, and prevents continuous replacement of batteries.

The protoboard is the most problematic component due to its constitution. The board is made of bakelite, a thermostable type. This plastic is infusible and insoluble. However, those present a high resistance compared to thermoplastics. Consequently, the recycling of these components is more difficult.

All the components used in the development of this project meet with the RoHS Directive which aims to restrict certain dangerous substances commonly used in electronic and electronic component.

64 Arduino based acquisition system for control applications