ENGS 26 CONTROL THEORY. Thermal Control System Laboratory

Transcription

1 ENGS 26 CONTROL THEORY Thermal Control System Laboratory Equipment Thayer school thermal control experiment board DT2801 Data Acquisition board 2-4 BNC-banana connectors 3 Banana-Banana connectors ma power supply wire (for connecting ref to -15 V) Oscilloscope MATLAB 1. Objective Temperature control systems are found in a number of commercial products and in a number of situations. We find simple temperature control systems in our homes to regulate room temperature, oven temperature, and refrigerator temperature. Control systems regulate engine temperatures to maximize engine and lubricant life. More sophisticated temperature control systems are often required for tight regulation of temperatures during some chemical processes, in order to control reaction rates. Thermal control is also required to maintain precise operation of some transducers, whose offset voltage varies with temperature. This laboratory explores simple methods for controlling the temperature of an aluminum plate. In a later lecture example, we will explore digital control as a means for tighter temperature control of the plate. 2. Physical System The physical system that we will control is shown in Figure 1. It consists of a 2 x 2 aluminum plate, which is 1/32 thick. The plate is heated on its underside by a thin resistive heater, which is insulated from the mounting plate. The top of the plate is exposed to ambient conditions. A temperature sensor is mounted on the top, center of the plate. The sensor outputs a current proportional to temperature. Manufacturer s specifications for system components are given in Tables 1 and 2. This thermal-electrical system uses the resistive heater to convert electrical energy to heat. The aluminum plate conducts the heat through its volume, while the insulation prevents conduction from the underside of the plate to the base plate. Energy transfer as heat is convected from the exposed surface to air. Heat transfer conduction and convection equations can be used to model the system and determine its transfer function. In this lab, we will demonstrate basic control principles by using on-off control to maintain a temperature setpoint within some band. This is basically how a home, refrigerator, or oven temperature control system works. While a system model is not required to design the control law, the system model will be helpful in interpreting experimental results. 1

2 temperature sensor Heated plate on insulator heater leads base plate Figure 1 Physical System to be controlled Table 1 Properties of the Resistive Heater Specifications Values Manufacturer Minco Products Model Number HK-5169-R185-L12-B Heater Resistance 185 ohms + 10% Heater area 4 square inches Heater thickness 0.01 inches Table 2 Properties of the AD590 Temperature Sensor Specification Value Rated temperature range -55 to 150 C Supply voltage (min, max) 4 V, 30 V Nominal output current at K µa Temperature coef. 1 µa/k Calibration error at 25 C C Max. forward voltage 44 V Max. reverse voltage -20 V Case breakdown voltage V Figure 2 shows the circuit for the temperature sensor, which acts as a current source. When connected in series with a 10 kω resistor, the sensor produces a voltage proportional to temperature. The buffered output of the sensor is used as the feedback signal in our control system. The gain of the sensor is K sensor = 10 mv/k (1) Given this relationship, what should the output of the amplifier read at room temperature? 2

3 Figure 2 Temperature sensor and heater circuit 3

4 3. Experiment 3.1 Experimental apparatus In this experiment, we will use on-off control to maintain the temperature at the center of the plate at about 15 C above ambient. Heater circuitry is given in Figure 2, and a photograph of the apparatus is given in Figure 3. To familiarize yourself with the hardware, please identify the D/A input signal connection, temperature signal (which goes to the A/D connection), and the power amplifier on the experiment board and circuit diagram. The system operates by sending a (low power) input signal, either from the D/A converter or some other source, to the input of the power amp. The power amp is set to have a gain of 1.5. The output of the power amp drives one end of the heater between -15 and +15 V. The second end of the heater is connected to -15 V. The temperature sensor senses the temperature change and its voltage output changes accordingly. This output can be read with an A/D converter, voltmeter, or oscilloscope. The power amp gain is set to 1.5 because we want to control the heater with the D/A converter. The D/A converter provides a voltage output between +10 V, and the amplifier increases this range to +15 V. Note that the power amplifier is a noninverting amp, i.e., a -10 V D/A output produces a -15 V power amp output, and a 10 V D/A output produces a 15 V power amp output. (There is a small voltage drop across the amplifier, so the actual amplifier output range may be slightly less than +15 V.) The switch on the board provides the output of the power amp to the connectors labeled ref and amp output. With the switch in the LEFT position, the power amp output drives the heater. Please note that you must physically connect a wire from the ref connector to the -15 V connector, in order to connect one side of the heater to -15 V. If this wire is not in place, please put it in now. 3.2 System Identification We will first operate the apparatus to obtain a system response to open-loop step commands. To do this, connect the D/A from the silver data acquisition box to the board connectors using a BNCbanana cable. Connect the temperature sensor across to A/D channel 0, and supply +15 V and ground to the experiment board to power the circuit electronics. Find the.m file thermal.m in the ENGS-26 directory on the Thayer server. This program records the plate temperature at fixed time intervals, for a step heater voltage input. A copy of the program is given at the end of this handout. You will select the input voltage (between 0 and 30 V across the heater), the time step, and the total experiment time. Copy and rename the program to the C:\MATLAB directory or to your own directory on the Thayer server (D:\ drive). Start MATLAB, switch to the directory that you copied the program to, and run the program for 5 minutes and a full 30 V input across the heater. Choose a 1 second sample time. (If you are unfamiliar with running.m files, request assistance from you lab TA.) Make sure that the plate is at ambient conditions before you start! Print the temperature vs. time output plot. What type of response does the system exhibit? Using the model derived in lecture, estimate the heat transfer coefficient. An example experimental step response is given in Figure 4. Study the MATLAB program, then modify the program to obtain the step response in each direction as the plate heats, and as it cools. The commands to output a voltage to the D/A converter and to read a voltage from the A/D converter are as follows: p = path; % sets path needed to access MATLAB path(p, d:\engs-26 ); % commands for data acquisition dt2801(0, data); % sends data to D/A channel 0 % (data = voltage between -10 and 10 V) 4

5 Figure 3 Experimental Apparatus dt2801(0,data,chan); % sends data to D/A channel chan,chan=0 or 1 y = dt2801(1); % reads a value from A/D converter channel 0 y=dt2801(1, 7.5E-5,1); % reads a value from A/D channel 1 Find the step response and heat transfer coefficient based on a variety of voltage inputs ranging from approximately. 10 volts across the heater to 30 V across the heater. For example, find the response for 10 V, 20 V and 30 V. Do heating and cooling for the highest voltage only. Is the system time constant the same for both heating and cooling? Why or why not? 3.3 On-off control The goal of an on-off control law is to switch the actuator between two states, based on a measured error signal {desired temperature - actual temperature}, or, in terms of the voltage output of the temperature sensor, {desired output voltage - actual output voltage}. Figure 5 gives an illustration. Initially, the error is large, and the heater remains on until the error reaches the upper range of the system deadband, as shown in the Figure. When it is detected that the deadband is exceeded, the heater is turned off, and when temperature reaches the lower deadband limit, the heater is turned on again. In this manner, the temperature oscillates between two limits. This characteristic, known as limit cycling, is a characteristic of on-off control, which is a form of nonlinear control. Turning the heater on and off could be accomplished using a mechanical-electrical switch, as in a home thermostat, but here we will use the D/A converter and the power amplifier to turn the heater on and off. 5

6 Figure 4 Example transient response measured at 1 second intervals Now, we will regulate the temperature of the plate using on-off control. Referring the circuit diagram in Figure 3, the heater is turned on when the D/A voltage is +10 V, and it is turned off when the D/A voltage is -10 V. We will use the D/A converter to turn the heater on, and we will simultaneously record the plate temperature using A/D channel 0. We will control the D/A and A/D converters using MATLAB and the shareware MATLAB functions for driving the data acquisition board presented above. We will also be able to choose our setpoint and deadband from within MATLAB. The basic structure of your MATLAB program will be as follows: 6

7 heater off deadband setpoint temperature heater on time Figure 5 On-off control response p = path; path(p, d:\engs-26 ); dt2801(0, -10); loop(0); seconds = 300; deadband = xxx; setpoint = yyy; sample_time = zzz; data = zeros(seconds,3); % sets path needed to access MATLAB % commands for data acquisition % turn heater off % loop is a command that delays a % fixed number of seconds. % This is an initialization command % for the loop function. % number of seconds to sample % choose a deadband parameter % temperature or voltage setpoint % sample time, seconds (integer only) % A place to store data dt2801(0,10); % turn heater on and start loop for i=1:seconds y = dt2801(1); % reads a value from A/D converter { Write code to determine if upper limit of deadband is exceeded. If so, turn heater off } { write code to determine if temp. is below lower limit of deadband. If so, turn heater on. } data(i,2) = y; % store A/D data data(i,3) = { Last output to D/A converter } % store D/A data loop(sample_time); % wait 1 sample time end; dt2801(0, -10); % turn heater off before exiting 7

8 Once you understand the programming commands, write a MATLAB program to implement on-off control. This will be a matter of adding setpoint and deadband variables, and using if-then statements to determine whether to change the heater status. (If you are unfamiliar with how to use if-then statements in MATLAB, please request help from your lab TA.) Connect the D/A to the heater input, and connect the output of the temperature sensor to A/D channel 0. Choose a deadband corresponding to about 4 C (+2 C around the setpoint), and choose a setpoint of about 15 C above ambient. (Note that your setpoint should be chosen below the steady-state temperature of the plate for a 30 V input across the heater. Why?) Run your program with a sample time of 1 sec. What happens? Explore the system behavior by varying the setpoint and deadband, and answer the following questions: What is the smallest deadband (tightest control) that you can achieve? Why? What happens to temperature control tolerance if you increase the sample period significantly (e.g., to 10 seconds)? What are the limitations of on-off control? Is achievable deadband different for a lower or higher setpoint? 4. Optional Experiment (for extra credit) Some digital thermostats have adaptive control algorithms that learn the dynamics of the system, and use the learned behavior to adaptively estimate the time required to turn on a furnace in the morning, after a night setback. For example, if I would like the temperature to be 72 F at 7 AM in the morning, and the setback temperature is 62 F, the time required for the building to reach the desired temperature depends on the thermal mass of the building and how well the building is insulated. The time required also depends on the outdoor temperature, which is normally not known. Since digital thermostat manufacturers do not have thermal models for every building in which their product will be used, they implement an algorithm that will adaptively estimate the system time constant. For example, they may store temperature response data for a transient response from a setback temperature and subsequently compute a time constant based on a firstorder model. Design and implement an adaptive control algorithm that allows a setpoint to be reached at a specified time after your system is turned on. Test your algorithm for two different conditions: 1) free convection, and 2) forced convection (you can use a piece of cardboard to blow air over the plate). Does your algorithm identify a different time constant in each case? Is it able to adjust and meet the specified setpoint at the specified time? 8