Thermal System Closed-Loop Temperature Control aluminum plate thin-film resistive heater ceramic insulation conduction and convection heat transfer AD590 temperature sensor microcontroller on-off closed-loop control with relay support analog electronics 1
Objective of the Case Study Control the temperature of a thin aluminum plate, as measured by a temperature sensor positioned in the middle of the top of the plate, by regulating the voltage supplied to a resistive heater positioned under the plate. The temperature of the plate is to be regulated to a point 20 C above the temperature of the ambient air. 2
How Will We Accomplish The Objective? Apply the general procedure for a dynamic system investigation Understand the physical system, develop a physical model on which to base analysis and design, and experimentally determine and/or validate model parameter values Develop a mathematical model of the system, analyze the system, and compare the results of the analysis to experimental measurements Design a feedback control system to meet performance specifications Implement the control system and experimentally validate its predicted performance 3
Physical System Heated Thin Aluminum Plate 1/32 inch thick 2 in x 2 in k = 177 W/m-K Temperature Sensor Ceramic Tape Insulating Layer 1/8 inch thick 2 in x 2 in k = 0.055 W/m-K Thin-Film Resistive Heater between Thin Aluminum Plate and Ceramic Insulation Aluminum Support Plate 4
Properties of the Resistive Heater Specification Manufacturer Model Number Value Minco Products HK-5169-R185-L12-B Heater Resistance 185 ohms ± 10% Heater Area Heater Thickness 4 sq. in. 0.010 in. 5
Properties of the AD590 Temperature Sensor Specification Value Rated Temperature Range -55 C to 150 C Power Supply (min) 4 volts Power Supply (max) 30 volts Nominal Output Current @ 298.2 K 298.2 µa Temperature Coefficient 1 µa/k Calibration Error ± 2.5 C Maximum Forward Voltage 44 volts Maximum Reverse Voltage Case Breakdown Voltage -20 volts ± 200 volts 6
Material Properties of 6061 Aluminum Property Value Melting Point 775 K Density, ρ 2770 kg/m 3 Specific Heat, c p 875 J/kg-K Thermal Conductivity, k 177 W/m-K 7
Temperature Sensor Circuit 15 V 1 µa/k Sensor Voltage 1KΩ LF 411 K sensor (volts/k) = (1µA)(R sensor ) 8
Physical Model Ambient air q convection Sensor Thin Aluminum Plate Thin-Film Resistive Heater Ceramic Insulation Heat input q heater 9
Simplifying Assumptions Temperature of the plate is uniform No heat loss through the sides of the plate Thermal conductivity of the plate is constant Heat loss due to radiation is negligible compared to convective heat loss from the plate Convection coefficient is constant and is evaluated at the operating temperature of the plate Heat loss through the insulative layer is negligible Sensor dynamics are negligible Ambient air temperature is unaffected by the heat flux from the plate 10
Mathematical Modeling Define system, system boundary, system inputs and outputs Define through and across variables Write physical relations for each element Write system relations of equilibrium and/or compatibility Combine system relations and physical relations to generate the mathematical model for the system 11
Define System, System Boundary, System Inputs and Outputs Input: Voltage supplied to resistive heater Ambient air Output: Plate temperature as measured by sensor on top of plate q convection Sensor Thin Aluminum Plate Thin-Film Resistive Heater Ceramic Insulation Heat input q heater 12
Define Through and Across Variables Through Variable: heat flow rate q (J/s or W) Across Variable: temperature θ (K) Assumption: All points in the body have the same average temperature and temperature deviations from the average at various points do not affect the validity of the single-temperature model. 13
Write Physical Relations for Each Element Thermal Capacitance θ = a f a f 1 C q t q t in out Thermal Resistance Conduction t ( ) = θ( ) Convection R Radiation q t ka q( t) = [ θ1( t) θ2( t)] L q( t) = ha[ θ ( t) θ ( t)] 1 2 4 4 q( t) = C[ θ ( t) θ ( t)] 1 2 2 2 = C[( θ + θ )( θ + θ )][ θ ( t) θ ( t)] 1 2 1 2 1 2 Thermal Sources P V i V V h = h h = h = R h V R 2 h h 14
Write System Relations of Equilibrium and/or Compatibility Select the temperature of each thermal capacitance as a state variable and use: θ = a f a f 1 C q t q t in out to obtain the corresponding state-variable equation. The net heat flow rate into a thermal capacitance depends on the heat sources and heat flow rates through thermal resistances. Use a f 1 a f a f q t = θ1 t θ2 t R to express the heat flow rates through the resistances in terms of the system s state variables. 15
Combine System Relations and Physical Relations to Obtain the Mathematical Model a f 2 Vh qin t = heater input = R h a f 1 q t = θ θ = ha θ θ R 1 C q a t f θ = q t in out ) 1L C q a t f a f = NM 1 O θ in θ θ QP ambient R 1 1 RC C q a t f 1 θ + θ = in + θambient RC out ambient ambient 16
Predicted Dynamic Response Solve the mathematical equation both analytically and numerically to predict the dynamic response of the physical system and gain physical insight. dq τ dt o a f 1 1 1 θ + θ = + θ RC C q t in ambient RC τθ + θ = Rq ( t) + θ τ = RC in a f F + q = Kq q = Kq 1 e o i o is a f ambient Qo ω Q s K Qo τs Q i K = = i + 1 i ωτ + 1 tan 2 HG F H a f t τ I K I KJ 1 ωτ 17
Experimental Testing: Model Parameter Identification Two physical parameters need to be determined, one by calculation and the other by experiment. Thermal Capacitance C = Mc p = ρvc p = 4.96 J/K Thermal Resistance R = 1/hA Either measure τ = RC and solve for R or measure the steady-state temperature of the plate and use a 2 Vh θ θ qin = qout or = R R h ambient f 18
Control System Design Error To Workspace4 Qin To Workspace2 Temperature Reference + - Sum Controller: Relay u[1]^2/rh Electrical- Thermal Conversion R(s) RC.s+1 System Temp To Workspace Matlab / Simulink Block Diagram Thermal Closed-Loop Control System Clock time To Workspace1 19
Control System Simulation 25 20 temperature (degrees C) 15 10 5 0 0 20 40 60 80 100 time (sec) Simulation of Control about 20 C Setpoint with a 2 C Deadband 20
Experimental Set-Up & Control Implementation 21
Microcontroller Software Design Setpoint Read Sensor Signal Deadband Initalize Variables Read Sensor and Setpoint Signals Sensor Signal Less Than Deadband Bottom Sensor Signal Greater Than Deadband Top Sensor Signal In Deadband Compute Error Signal Yes Yes Yes Implement Logic Heater On Heater Off Issue Previous Command Command Actuator Decision Logic Flow Diagram 22
Microcontroller Real-Time Basic Program 100 REM set up Port A as an output, reset Port B 110 xby(0fd03h)=128:xby(0fd01h)=6 120 PRINT USING(####) 130 REM calibrate the A to D converters 140 XBY(0ff03h)=2 150 DO: SFR=XBY(0ff03h):WHILE SFR.AND.2 160 IF SFR.AND.40h THEN GOTO 140 165 MEMX=0 170 REM read current temperature 180 XBY(0ff00h)=1 190 CURTEMP=256*XBY(0ff01h) 200 CURTEMP=CURTEMP+XBY(0ff00h) 210 REM read setpoint temperature 220 XBY(0ff00h)=0 230 SETEMP=256*XBY(0ff01h) 240 SETEMP=SETEMP+XBY(0ff00h) 250 ERROR=SETEMP-CURTEMP 260 IF (ERROR<-82).AND.(MEMX<-82) THEN COMMAND=0 270 IF (ERROR>82).AND.(MEMX>82) THEN COMMAND=255 275 MEMX=ERROR 280 IF (ERROR>-82).AND.(ERROR<82) THEN COMMAND=COMMAND 290 XBY(0fd00h)=COMMAND 300 PRINT "CURRENT TEMP=",CURTEMP,"SET TEMP=",SETEMP 310 GOTO 170 23
Comparison of Predicted Dynamic Behavior with Actual, Measured Dynamic Behavior 25 20 Predicted: red curve (-) Measured: blue curve (--) temperature (degrees C) 15 10 5 0 0 50 100 150 200 time (sec) 24