BIOEN 302: Introduction to Biomedical Instrumentation Autumn 2010

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1 Project 4: PID Controller for a Resistive Heating Element Objective: Develop a control system that uses feedback to maintain a target temperature. Background Just as medicine involves both understanding a patient s needs and acting on them, a medical instrument is most useful when it can both read information and use that information to establish some condition such as position, force, temperature, or drug concentration. Any piece of equipment that is intended to modify its environment ranging from a hot plate to a computerized robot can be loosely divided into the part that actually takes the action (the actuator) and the part that determines how hard the actuator will work (the controller). The controller usually has two input signals, one that indicates the condition of the environment (from a sensor) and one that indicates the desired condition (from a user or program). Together, the properties of the controller, the actuator, and the environment will determine how the system will respond to a command from the user. Control systems can be divided into two types. Open loop systems supply an output in response to some user input but do not monitor the result that the output is having on the system or environment. One example is a burner on a typical stove. The user selects the power input to the burner, but the actual temperature at the burner will depend on the burner characteristics as well as the condition of the material that is being heated and the temperature of the surrounding air. Effective open loop control requires that the user understand how the input affects the system output. Closed loop systems compare the user input to a value measured from the system to determine the output to send to the actuator. One simple example is an oven with a thermostatic switch. The user needs only to set the desired temperature and the switch controls the average power input by turning the heat on and off. The use of feedback in a closed loop control system can accommodate a large degree of ignorance of the system characteristics. However, in order to create a control system that follows the desired output closely, we usually want to apply some knowledge of how the system responds to actuation. In addition, highperformance control systems usually respond to the difference between the desired and measured values (the error), not just to being too high or too low. For the following discussion, let us name the error E, and each gain component as G. The subscripts P, I and D, stand for proportional, integral and differential. The simplest feedback control system is proportional: output = G P E. To improve system performance, integral and differential terms can be added, such that de vout GPE G I Edt GD dt This type of system is known as a proportional integral differential (PID) controller. The flow chart for every PID controller is the same, and the gains G P,I,D are adjusted to produce the desired system behavior. print date: 11/3/2010 1

2 Note that the gains G P,I,D are scalars, but the overall system gain V SENS /V CMD is usually complex and is represented by a transfer function H(s), where s = + j. In today's lab exercise we will set up a heater circuit and start a process called system identification, in which we model our system based on knowledge about its physical construction, and on data that we have collected from it. Next week we will use this model to design a controller and test it on our thermal system. Nomenclature E Error: difference between measured and desired sensor value Proportional gain G P G I G D NTC V SENS V CMD Integral gain Differential gain Negative temperature coefficient Sensor voltage, hence the environmental value that the controller is trying to control Command voltage, the input from the user or program Pulse width modulation The maximum power that an actuator can apply to a device is limited by the controller voltage range, power supply, fuses, wiring, and actuator itself. Except at startup, however, it is seldom desirable to work at maximum output over a significant period of time. A standard oven does alternate between fully on and fully off, but this method of control may result in large excursions away from the target temperature. The target temperature can be followed more closely if the average power output is based on the error, E. One way to do this is to have the instantaneous output power be exactly equal to the desired average output power. This method can require accurate amplification of relatively large currents, which is possible but potentially costly. In addition, this method is inefficient because part of the voltage from the power supply must be dropped somewhere other than the load itself. Therefore, there is excess power consumption and unnecessary heating of the controller circuitry. An alternative method of power control is pulse width modulation (PWM). PWM controllers provide an output that is either off or at full power, but with timing that is determined by the error signal. Whereas an oven with a standard on/off thermostat would be at full power all of the time as the temperature rose from T target 20 to T target 1, an oven with a proportional thermostat using PWM might be at full output 80% of the time when the temperature deficit is 20, but only 5% of the time when the temperature deficit is 1. The fluctuations are typically rapid, cycling several times per second. The heat capacity of the material acts as a lowpass filter, damping out the thermal oscillations. At locations away from the actual point of heat application, it is impossible to tell that the heat has been applied in pulses. The use of pulse width modulation permits us to choose either the analog outputs or the digital outputs from our data I/O device. The analog outputs can be varied in very fine increments over a wide voltage range. In PWM mode we could use the print date: 11/3/2010 2

3 software to set the output voltage and then to turn its output on or off. The digital outputs are either 0 or 5 V, so they are effective only with a PWM controller. Each digital output is one bit of a binary number, so to use these outputs for thermal control we simply turn the desired bit on or off at the appropriate rate. In either case, the current supplied by the data I/O device is small, so it is necessary to amplify the current with a transistor before applying it to the heater. Equipment Breadboard & connecting wire TIP121 or TIP115 or 2N6292 or 2N6107 power transistor with heat sink 4.7, 5, or 10 resistor, rated for 1 W ( 2), called low value resistor below Thermistor: FAG J01, LAG J01, or similar 1 k resistor ( 2) 1 or 10 k trim pot for Wheatstone bridge Power supply USB 6009 data I/O device Computer with LabView Procedure The goal of this lab project is to create a PID controller that regulates the temperature of a resistor thermistor. This controller can then be the basis for the thermal control system in an environmental control chamber. The major steps in this project are: Assemble a circuit that can be used to heat a resistor and measure its temperature; Acquire step response data and use it to create a Laplace domain model of the heater system; Determine appropriate PID gains both analytically and by trial and error; Create a feedback controller using Labview; Test the behavior of the controlled system. Circuit setup a) Prepare the low value resistor and thermistor by sliding wire insulation over the leads; this provides electrical isolation. b) Join the resistor and thermistor with heat shrink tubing. c) Create a Wheatstone bridge for the thermistor, using the 1k resistors, the trim pot, and the thermistor. The output from this bridge is the input to your data I/O device. d) Connect the low value resistor(s) in series with the power transistor, i.e. between the emitter and ground. The input to the transistor's base will be the voltage from one of the analog outputs from Labview. e) Test the operation of the circuit with a power supply and multimeter, or power supply, function generator, and oscilloscope. Test the output voltage from the bridge as you vary the voltage at the base of the transistor. Don t burn yourself! print date: 11/3/2010 3

4 Software setup a) Plug the USB 6009 data I/O device into an available USB port on your computer. Complete the installation steps if necessary. b) Create a LabView VI that contains one data acquisition channel and a pulsewidth modulation output for one analog output channel. Create the front panel controls necessary to set the output duty cycle manually. This VI can be built around the VI that you created for the colorimeter, but you are going to need a lot of help with the PWM part. We will give it to you, and will provide an example. System identification Once the circuit and software are complete, our first goal is to estimate an impulse response and a transfer function for the heater system. a) Apply a step change to the duty cycle and measure both the input and output voltages until an equilibrium voltage is reached. Estimate the time constant of the transient response, e.g. by measuring the slope at t=0. This time constant will probably be different for the cooling and heating cases; although you will not control the cooling phase, it will be interesting to compare the two results. Therefore, perform at least one experiment for each case. In each one, record the command voltage V CMD (i.e. the voltage applied to the base of the transistor) and the sensor voltage V SENS (i.e. the voltage from the bridge). b) Use the input and output voltage signals with the VI that fits transfer functions to response data. You will be shown how to do this in lab. Obtain three transfer functions: 1) first order, 2) second order with no zeros, and 3) second order with one zero. Choose one of the transfer functions with no zeros to proceed with PID control development. PID controller development a) Plug your coefficients into the closed loop PID control simulation VI and experiment with the PID gains. Your goal is to minimize the rise time and settling time, and overshoot. The overshoot can be most important in a biological control system, because excessive concentrations or temperatures can kill. b) Plug your coefficients into the general form for a transfer function in a PIDcontrolled system (assuming two poles and no zeros), and solve for PID constants that produce a critically damped system. Test those constants in the closed loop PID control simulation VI. c) Add a PID control loop to your input/output VI. You may do these calculations with mathematical icons, express (interactive) math functions, or by using a MathScript node, which allows you to enter MATLAB script that operates on the LabView variables. LabView also includes a variety of PID control functions that do not require you to do your own mathematical programming, but they do not print date: 11/3/2010 4

5 tend to work any better and you might not learn as much if you rely solely on LabView functions. Your VI will need to include a conversion from the voltage produced by your PID controller into output duty cycle. d) Set the gains determined previously and test the response of the system to a step input. Lab write-up: 1. The report for the PID control project is due on November 12, either in your quiz section (on paper) or by 3:15 p.m. (on line). These are team reports with teams of either 2 or 3. Teams of 4 will have grades scaled accordingly, so plan to write 33% more if you have a 4 person team. Please state in the report how the workload was distributed among the team members. The goal is two pages of text at 1.5 line spacing, plus 3 4 figures. You may write more if you like. The report should be formally written and formatted. Writing style will contribute to your score. Proofreading will not, but if your report is full of proofreading errors we may return the report to you, ungraded. 2. Describe the purpose and general principles of a feedback control system. Describe the effect of each of the gains in a PID controller. 3. Include a schematic diagram of your circuit, including component characteristics such as tolerance (probably 5%) and wattage rating. 4. Include 1 2 figures that illustrate how the system response changes according to the values of G P, G I, and G D. You may put more than one response curve on each figure. One additional figure should show an underdamped response, and illustrate your measurement of the steady state error, the overshoot, and settling time (defined here as the time it takes for V SENS to reach and stay within 5% of the final value after a step change in input). 5. Show how you would implement the PID controller in hardware (i.e. as a circuit on a breadboard). Include a schematic diagram of the circuit using four, five or six op amps. This diagram may be hand drawn, but neatness does count. In conclusion By the end of the project, you should have learned... In any system that needs some input just to stay at a constant value, a proportional control system will produce a steady state error. The integral gain in a PID controller can eliminate the steady state error. The differential part of a PID controller can reduce overshoot, allowing you to use higher proportional and integral gains. A feedback controlled system with only one energy storage element (e.g., the heat capacity of the resistor+thermistor) can act like a second order system. print date: 11/3/2010 5