Teaching Basic Control Concepts with a Home-made Thermal System

Diana Marcela Ovalle M, Luis Francisco Cómbita A. Engineering Faculty

Universidad Distrital Francisco José de Caldas Bogotá, Colombia

Abstract— In this work we show how to build a home-made

thermal system, and how we can use it in order to reinforce some basic concepts in control systems. Some of the concepts explored using the system are: identification based on step and frequency responses, the effect of basic control actions and the design, and implementation of analog controllers using operational amplifiers. In addition, we expose a set of advantages and disadvantages related with the laboratory experience documented here.

Keywords-component; thermal systems; laboratory experience;

open loop analysis; closed loop analysis; control system education.

I. INTRODUCTION This paper shows the work in the laboratory that has been

done with students of Control Systems at the fourth year in the Electronics Engineering Program at Universidad Distrital Francisco José de Caldas in Bogotá, Colombia. Since students should have proficiency in electronics design and implementation, we do not consider convenient to use typical control systems equipment, which is mainly oriented to work with systems through programs like Matlab® or Laview®.

The work in the laboratory presented here is oriented to students with some previous knowledge of dynamical systems. Specifically, students will need to have knowledge related to system models, transfer functions, transient and steady state time response, steady state error analysis, frequency response and classic system identification (through step and frequency response).

In the general scope of the course, students address the following topics:

• System stability analysis: using the Routh-Hurwitz criterion, the Nyquist criterion, and also from Bode and root locus plots

• Basic control actions: ON-OFF, proportional (P), integral (I), derivative (D), and its combinations (PI, PD and PID).

• Time domain and frequency domain design criteria.

• Controller design by the root locus method.

• Controller design by frequency response.

• Controller design in state space.

• Linearization.

The course is designed to take 16 weeks and a final exam. Weekly students have 2 lectures of 2 hours each, and 2 hours of laboratory work.

There are some basic systems that students can develop at a low cost like some Lego-based systems [1], DC motor speed or position systems [2], and thermal systems [3]. We decide to assign the students to develop a thermal system, since even though it has a slow dynamics its behavior is very close to what we want for the students to see, related to linearity and all the concepts we want for them to “feel” in a clear way. These concepts include time response, frequency response, basic control actions and various controller design techniques. It is important to emphasize that the work with the thermal system takes between 8 and 9 weeks, and the remaining laboratory work is done with a homemade DC motor speed system.

The students at the beginning of the course develop a thermal system, which they will work with the entire semester. The setup of the system, together with its physical and electronics implementations are shown in section II. In section III, we emphasize the expected achievements of each laboratory session. In section IV, we comment on the evaluation criteria for this laboratory work. Finally, after two years experience, we detailed in section V we conclude emphasizing the main advantages and disadvantages of this kind of approach for Electronics Engineering Program students.

Even though thermal systems are broadly studied in literature, there are not many references related to thermal systems used for teaching purposes, most of them are devoted to experiment with specific control strategies. The closest reference to this work is [8], where there is a system setup similar to the one proposed here, but again, they emphasize all the work in computer-based control structures, the same approach commercial laboratory equipment has.

II. SYSTEM SETUP The thermal system consists of a volume where we want to

control the temperature in, its temperature should be able to rise from ambient temperature to 50°C in 120 seconds, and we want to have temperature measures with 100mV/°C of sensibility. The setup of the thermal system consists on a heating chamber, an actuator, and a sensing and signal conditioning circuit. That set is what we call the augmented system, Fig. 1. Bellow, there is a short explanation on each of this subsystems.

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Fig. 1. Augmented system: actuator + system + senconditioning.

A. Heating chamber This is the volume where the tempera

controlled in. The dimensions of this vol4”x4”x6”, but there is no need to have a rectastudents must select the volume enclosingusually is Styrofoam.

Besides the volume characteristics, there select the heat source, which should work wits maximum power would be 30W. In almothe students select a bulb, and after some tchoosing a 12VDC – 20W one. Fig. 2 shthermal systems students implemented during

B. Actuator This is the part of the system that allow

amount of heating inside the chamber; it copower electronics stage. When working witstudents usually propose a power voltage foswitching the DC voltage over the bulb with (Fig. 4) or MOSFET, both of them using a PWthat the schematic for switching a MOSFET was in Fig. 4, but instead of a power transistoMOSFET and eliminate the 22 resistor betcollector and, in that case, the MOSFET gate

Fig. 2. Thermal system implementati

nsing and sensing

ature needs to be ume are close to angular shape. The g material, which

is also the need to with electricity and ost all of the cases, trials, they end up hows some of the g this year.

ws controlling the uld be seen as the th a DC bulb, the

ollower (Fig. 3), or a power transistor

WM signal. Notice would be the same or we use a power tween the 2N2222 .

ions.

Fig. 3. Power v

Fig. 4. Switching a power tr

Fig. 5. Setup for LM35 and its sig

Related to the PWM geneapproaches, among them wemicrocontroller, by TL494, andin generating a ramp signal withe control signal.

C. Sensing and Signal ConditiThe sensing is performed b

sensor, with 10mV/°C of sensito increase sensor’s sensibiliamplifier with 10 of gain. important to follow the notes ithe power supply it has a very n

III. SYSTEM PERFORMEXPER

The system behaves as a fused to clarify concepts related

voltage follower.

ransistor with a PWM signal.

gnal conditioning to get 100mV/°C.

eration, students consider many e found PWM generation by d the more elaborated one based ith a 555 and comparing it with

oning by a LM35, a linear temperature ibility. Since the students need ity, they implement a voltage When using the LM35, it is in its datasheet, since only with noisily behavior, Fig. 5.

MANCE AND LABORATORY RIENCE first order system [4], and it is d to system analysis and design,

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from time and frequency response, passing through basic control actions, to finally focusing on controller design techniques.

A. Open loop analysis We include the following laboratory experiments related to

the system analysis:

• Identifying the system model based on its step response [5]. A first validation will be obtained by simulating system model, taking into account the external conditions (ambient temperature), which needs to be compared to the real system behavior. Estimated time: 1 week

The type of system the students should obtain is a first order one, with constant numerator, and where the ambient temperature should be taken into account either as another input or as a perturbation, that is

where is the temperature inside the chamber, is the input voltage, K is the system gain, is the system time constant, and is the ambient temperature.

One of the most common mistakes is not to consider the ambient temperature as an input, but as an additional constant term in the transfer function. Hence, the model students obtain is a first order one, but with a zero. Notice that both models show a similar behavior for a unitary step input. Nevertheless, since the ambient temperature is not inherent to the system, it cannot be considered into the model.

Another issue presented during the system model obtaining process is the calculation of the system gain. What usually happens is either the students do not take into account the ambient temperature, or they forget the fact that the step input is not unitary. Notice that the system gain is the relationship between the output variation and the input variation, that is

We illustrate these issues with an example. Fig. 6 shows a particular system model where K=0.8569, =227.8 and the ambient temperature was 23°C (equivalent to 2.3V), here ambient temperature was considered as an input. Fig. 7 shows a system with the same values, but considering the ambient temperature as an additional gain in the transfer function. Figs. 8 and 9 show unitary step response of each system. Notice that before the step starts, at 100 seconds, the system in Fig. 6 shows the ambient temperature, while the system shows 0°C. Nevertheless, the behavior after the step is very close to each other. The fact that the models are not equivalent, and only the model shown in Fig. 6 is the right one, can be evidenced when the input is not unitary. In Figs. 10 and 11, a step input of amplitude 6 is considered. Again, the model in Fig. 6 before the step starts shows the ambient temperature, and the model in Fig. 7 do not. Moreover, the behavior after the step start is

no similar, and it can be noticed that the model in Fig. 7 shows too much gain. Therefore, the model that adequately represents the thermal system dynamics is the one in Fig. 6.

Fig. 6. System model considering ambient temperature as an input.

Fig. 7. System model considering ambient temperature as a constant term

in the transfer function.

Fig. 8. System response to an unitary step input for the model in Fig. 6.

Fig. 9. System response to an unitary step input for the model in Fig. 7.

• Obtaining the temperature system frequency response to

validate the model obtained through the step response, estimated time: 1 week. This is not a straightforward task, since the system dynamics is very slow. Nevertheless, with modern signal generators or even by microcontroller programming, we can generate very slow sinusoidal

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signals over a DC level to obtain the system frequency response.

There are several cautions that should be take into account to obtain the data that allow us to build the frequency response of a system: 1. Since the thermal system cannot be excited with

signals that have negative amplitudes, it is necessary to add a level DC to the sinusoidal signal. The minimum and maximum instantaneous values of input signal should be between of the set of allowed values to excite the system.

2. Since the input signal is composed by a sinusoidal signal and a step signal then the DC level of the output signal also allows obtain the gain DC of the system transfer function.

3. To achieve obtaining the measurements needed to make the frequency response, it is necessary wait until the transient response decay approximate to zero, fact that can take several minutes after input with a signal with a specific frequency is applied to the system. In typical systems built for our students that time was between six and ten minutes.

4. Process for obtaining measurements for very low (i.e. 1x10–3 Hz) frequences takes long time. It is required a low frequency sinusoidal signal to be applied to the system and, then, it is needed to wait for the transitory response to banish and, at least, half of the sinusoidal signal cycle to appear in the output.

Fig. 10. System response to a step input of 6 for the model in Fig. 6.

Fig. 11. System response to a step input of 6 for the model in Fig. 7.

Fig. 12. Control System Scheme.

B. Closed loop analysis and design Once, the student is familiar to the open loop system

behavior, it is time to close the loop. Various closed loop techniques are explored:

• Design and implementation of an ON-OFF controller through a Smith trigger. The designing process involves mainly the selection of the hysteresis wide, [6]. Estimated time: 1 week.

Since this is the first controller the students implement, they still do not recognize the fact that the controller must act over the error signal. Hence, they do not adequately implement each one of the parts of a control system, Fig. 12. Instead of designing and implement a Smith trigger comparator to work with a tolerable error signal, they design a comparator to work with a desired temperature, the problem with this is that the control system is not going to work with any reference signal, but only with the value the system was designed for.

Related to the Smith trigger implementation, what is crucial for the comparator to work properly is to eliminate the voltage between the inverting and non-inverting operational amplifier inputs, otherwise the hysteresis window is not the one we designed.

A typical response for the closed loop system with an ON-OFF controller is shown in Fig. 13, where the input has been changed several times to verify the system behavior.

• Implementation of a proportional control action by an amplifier, visualizing how its saturation leads to an ON-OFF behavior, and its implication in the stationary state error. The system experimental root locus can be constructed here. Estimated time: 1 week.

Related to the implementation of the control action, there usually are not many issues. The problems are more conceptual. For example, students do not have a clear way of measuring the system position error. Another issue, specifically related with the type of controller under analysis, it is they try to accomplish more than one

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specification whit a proportional controller, which is not possible. Then, we emphasize in the fact that they would only achieve a certain settling time or certain steady state error with a proportional controller.

It is important for them to check how the system becomes faster and the position error decreases as they increase the proportional gain. In the same way, to realize that the system cannot be as fast as they want, due to the physical limitations, results into a nice discovery. Related to this, the presence of saturation in the control action, and how the proportional control action becomes into an ON-OFF one, it is the important thing to evidence. Another important fact for them to see is how, once the proportional control action is saturated, as they increase the proportional gain the gap for the ON-OFF controller decreases. It is here where it is important for students to start taking into account saturation phenomena in their simulations, which makes them more close to reality.

• Implementation of an integral control action with its implication in the stationary state error. The integral action is implemented with an integrator with operational amplifiers, where a large resistance should be in parallel to the capacitor in order to avoid the integrator saturation. The system experimental root locus can be constructed here. Estimated time: 1 week.

The integrator implementation is not as straightforward as one may expect. Usually, students do not have clearly identified the way the integrator is going to work, and they need help to determine what they need to do to assure the integrator is working properly. Once they have the integral action working with the system, it is interesting for them to see the system is never faster than the open loop system and, also, to check how the overshoot increases as they increase the integral gain. Therefore, the construction of the system root locus is a very constructive activity for them.

• Design and implementation of controllers using both root locus and frequency response techniques, in order to satisfy particular specifications. The implementation of the controllers could be done by analog filters, such as the ones shown in [7], chapter 5. Estimated time: 3-4 weeks.

Fig. 13. Closed loop system with ON-OFF controller.

Related to the root locus controller design, students are asked to design a controller that makes the closed loop system response has zero position error, a settling time 20% faster than the open loop one, as well as to have less tan 5% of overshoot. The designing strategy they use is the one propose in [7]. During the designing process, it is interesting for them to see how the presence of the controller zero(s) modifies the system time response. Hence, they need to design for more ambitious conditions to achieve the ones they really need. Once they have the simulation working, maybe the most important moment for them in the lab is to see the implementation works very closely to what they expected from simulation. Fig. 14 shows a typical system response for a controller that works adequately, in this case a PI controller. We can see the zero position error, a small overshot and a settling time of 200 seconds.

Related to the controller designed by frequency techniques, students are asked to design a controller that makes the closed loop system response to have zero position error, a phase margin of at least 70°, and to be faster than the open loop system. The designing strategy they use is the one propose in [5]. During the designing process, they start by realizing they will need to add an integrator to eliminate the error position. Once they include the integrator in the system dynamics, they design a lead controller in order to have a faster system. It results interesting for the students to visualize that the system behaves differently if they integrate the error signal and, then, implement the lead compensator than if the implementation is in the opposite way. The best results are obtained when the integrator precedes the compensator.

Fig. 15 shows a typical system response for a controller that works properly, in this case an integrator followed by a lead compensator. We can see the zero position error, a bigger overshot than the one obtained by the PI controller, and a small settling time, about 30 secs. Normally, the system working with a controller designed by frequency techniques trends to behave fast, since the control action keeps being saturated until the error is very small and, then, it regulates the control action to keep the temperature in the desired value. That is the reason the overshoot is bigger than in the case of the PI controller.

Fig. 14. Closed loop system with a PI controller.

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Without a doubt, once students probe that their design works in reality they become fans of control engineering.

IV. EVALUATION CRITERIA Students are asked to complete each assignment and to

write a report. In the report they should include:

• The electronics design needed, with simulation supporting the adequate performance and justification for component selection.

• Dynamics simulation, using Matlab® or similar software, showing that the model of what they design is useful addressing the assignment.

Fig. 15. Closed loop system with an integrator and a compensator.

• Real data and plots of the system behavior. We suggest

they compare real and simulated behaviors. When they do not manage the system to work properly, it is important they justify the reasons why.

• Conclusions and issues during every session.

It is curious to see students do whatever it takes to make the system to work in a proper way, but to put a little effort into the report. Even though, one of the things we emphasize is that the laboratory grade is equally divided between the proper addressing of each assignment and its report.

V. CONCLUSIONS The implementation of the thermal system and the analysis

and design laboratory experiments have been in use during the last two years in the control systems course, taken in the fourth year of the electronics engineering studies. Given the orientation of the academic program, this kind of laboratories is very useful, since the students clarify concepts not only related to control systems, but to electronics itself (power electronics, operational amplifiers applications, etc.). This is important, given that our engineers should have proficiency in electronics

design and implementations, that is the reason we do not consider the typical laboratory equipment useful to our students.

Even though the system dynamics is very slow and each test takes about 20 minutes, between heating and cooling processes, we continue using this kind of systems because its behavior is close to be linear, fairly easy to implement, a low cost application, and in almost all cases the students achieve all the objectives we expect.

One of the most common mistakes among the students is to think that the better the chamber isolation the quicker the temperature behavior, which instead of making the temperature dynamics fast, tends to behaves as a temperature integrator and, therefore, for a step input the temperature tends to increase very slowly during a very long time, which does not agree with the behavior we are expecting (first order).

Other disadvantages can be visualized when the students prefer to use AC bulbs, and when they do not pay attention to the restrictions on power or dimensions of the chamber. When one of these situations is present, the results include activation of the power supply protection for excess of current, ground problems, destruction of the chamber by overheat, temperature dynamics excessively slow, etc.

The kind of approach presented here clarifies and strengthens very important concepts of control system theory. Specifically system transient response and steady state response, steady state error, system frequency response, system identification through time and frequency response, basic control actions and controllers design and implementation. After achieving all the assignments proposed here, students have a solid background in basic control system theory and are ready to face advance controls courses.

REFERENCES [1] Wadoo, S. A.; Jain, R. “A LEGO based Undergraduate Control Systems

Laboratory”, IEEE Systems, Applications and Technology Conference. Long Island. 2012.

[2] Gunasekaran, M.; Potluri, R. “Low Cost Undergraduate Control Systems Experiments Using Microcontroller-Based Control of a DC Motor”. IEEE Transactions on Education. Volume 5. Issue 4. 2012.

[3] Atif Adnan, S.; Muhammad, A.; Shareef, Z. “Development of a Low Cost Thermal Feedback System for Basic Control Education.” IEEE 14th International Multitopic Conference. 2011.

[4] Close, C.; Frederick, D. K.; Newell, D. K. Modeling and Analysis of Dynamic Systems. 3rd Edition. Wiley. 2001.

[5] Chen, C. T. Analog and Digital Control System Design: Transfer-Function, State-Space, and Alebraic Methods. Oxford University Press. 1993.

[6] Coughlin, R. F.; Driscoll, F.F. Operational Amplifiers and Linear Integrated Systems. 6th Edition. Prentice Hall. 2000.

[7] Ogata, K. Modern Control Engineering. 3rd Edition. Prentice Hall. 1998. [8] Atif Adnan, S.; Muhammad, A.; Shareef, Z., “Development of a low

cost thermal feedback system for basic control education,” Multitopic Conference (INMIC), 2011 IEEE 14th International. 2011.

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