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MSU ME 451 - Exp6_ThermalControl

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Pre-Lab Sample QuestionsME 451 : Control Systems Laboratory Department of Mechanical Engineering Michigan State University East Lansing, MI 48824-1226 ME451 Laboratory Experiment #6 Air Temperature Control ME451 Laboratory Manual Pages, Last Revised: June 10, 2007 Send comments to: Dr. Clark Radcliffe, ProfessorAir Temperature Control 2References: C.L. Phillips and R.D. Harbor, Feedback Control Systems, Prentice Hall, 4th Ed. 2.9 Temperature-Control System pg. 49-51 1. Objective The ability to accurately control a process is vital to numerous design efforts. For example, the automatic pilot in an airplane would not prove very useful, and potentially quite dangerous, if large deviations from the desired path could not be avoided. The Continuous Process Control laboratory will provide "hands on" experience with proportional control techniques. A performance evaluation of these methods of control will be conducted. The process to be controlled in this laboratory session is the temperature of a flowing fluid (air). The PT 326 Process Trainer will be employed in this investigation. The PT 326 is built by Feedback Instruments Ltd. and is discussed in section 2 of this document. 2. Definitions Figure 1 represents the basic components of a closed-loop process control system. CorrectingElementProcessMotorElementContr olli ngElementComparingElementMeasuri ngElementDetectin gElementSet ValuePlantContr ol E quipment Figure 1 Basic elements of a closed-loop process control system. The following list provides the definition of terms and information adapted from the PT 326 Process Trainer Manual: Process The term process is used to describe a physical or chemical change or the conversion of energy. The temperature of air flowing in a tube is the process this laboratory is concerned with. Air Temperature Control 3Detecting Element The detecting element is a bead thermistor connected to one leg of a bridge. The resistance of the thermistor changes as the temperature of its surroundings change. Measuring Element This change in resistance (due to change in temperature) causes the bridge output voltage to change. Thus, the bridge output voltage may be used to measure temperature. Measured value, q0 This is the voltage signal from the measuring element, which corresponds, to the value of the controlled condition. Set Value, qi This is the desired value of the controlled condition. The set value may be adjusted using a turn pot on the front panel or externally by providing a voltage between 0 and -10 volts to socket D. A decrease in voltage at socket D will cause a rise in process temperature. Deviation, D The deviation, D, is the difference of the measured value and the desired value. D = q0 - qi Set value Disturbance A step change in the desired value may be introduced when the INTERNAL SET VALUE DISTURBANCE is applied. Comparing Element The measured value from the bridge and the set value are compared with a summing amplifier. The internal signals of this equipment have been arranged to be of opposite sign. Therefore, the output from the summing amplifier represents a deviation. Socket B on the front panel may be use to monitor this deviation. Controlling Element A signal proportional to deviation is applied to the controlling element. A correcting signal is generated and sent to the correcting element. The PT326 is capable of continuous or two step control. Continuous Control Modes 1. Internal This provides proportional control only. Proportional control may be varied on the PT326 from 5 to 200 percent. Where the percent proportional control reflects the gain applied to the deviation signal. Gain Kp = 100 / %Proportional Therefore, a 100% proportional setting provides a gain of one to the deviation signal. Air Temperature Control 42. External The internal proportional band adjustment can be switched off to allow external control. Motor Element The motor element produces an output that is adjusted in response to the signal from the controlling element. In the PT326, the motor element supplies power (between 15 and 80 watts) to the correcting element. Correcting Element The correcting element directly affects the controlled condition. The correcting element in the PT326 is a wire grid, which heats the flowing air. 3. Equipment The PT 326 is a self-contained process control trainer. It incorporates a plant and control equipment in a single unit. In this equipment, a centrifugal blower draws air from the atmosphere and forces it through a heater grid. The air temperature is detected downstream of the grid by a bead thermistor before being returned to the atmosphere. The detecting (bead thermistor) and correcting (heater) elements have been placed sufficiently far apart to facilitate the investigation of "lag" time. The air stream velocity may be adjusted by means of an inlet throttle attached to the blower. The desired temperature may be set in a range from 30ºC to 60ºC. A toggle switch provides an internal step increase to the desired temperature signal. The PT 326 may be configured to run with either open- or closed-loop control. The process trainer also allows the connection of an external controller (the PID150Y). Figure 2- PT 326Air Temperature Control 54. Theory Figure 3 Model of the heater-flow system. A mathematical model of the temperature response for the system must be developed. A diagram of the system to be modeled is presented in Figure 3. An energy balance yields Heat stored = Heat in - Heat out (1) Replacing the terms of equation (1) by their thermodynamic equivalents yields []QTcPdtdTVcTVcdtdpppρρρ−== (2) where c= specific heat of air [energy/(mass×temperature)] (Joule per Kilogram Kelvin) p = flow rate [volume/time] (cubic meter/sec,..) Q ρ = density [mass/volume] (kilograms per cubic meter, gms/cm3…) = power [energy/time] (Joules per second, Watts,…) P V = volume from heater to thermistor [volume] (cubic meter, litres,…) T = temperature above ambient [temperature] (Kelvin, Centigrade, Fahrenheit...) Combining terms yields the first-order differential equation for the exhaust temperature: PVcTVQTdtdTp⎥⎥⎦⎤⎢⎢⎣⎡+−==ρ1& (3) Solving (3) yields: T(t) = (T0− Tf)e−t−t0τ⎛ ⎝ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ + Tf (4) Taking the Laplace of equation (3) gives: PVcsTVQssTp⎥⎥⎦⎤⎢⎢⎣⎡+⎟⎠⎞⎜⎝⎛−=ρ1)()( Air


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MSU ME 451 - Exp6_ThermalControl

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