QNET Experiment #06: HVAC Proportional
Contents
1. 2 From the parameters of the heating transfer function G s estimated in Reference 3 calculate the numerical value of Ks 1 The heater constant offset voltage Vi of is included in Equation 13 in order to compen sate for the halogen lamp deadband The actuator behaviour resulting from such a dead band compensation will be more linear around small input voltages Vn ox has been esti mated in Reference 3 as the upper limit of the heating actuator deadzone The anti windup element in the feedback loop stops the integral action when the actuator saturates to prevent large overshoots in the response The HVAC heater saturates at Vi max When this limit is reached the surplus voltage is multiplied by the gain K and the result is removed from the integrator input The anti windup element is implemented using a dead zone nonlinearity with a slope of K as shown in Figure 2 Document Number 578 Revision 01 Page 10 PI Temperature Control Laboratory Manual 3 4 2 Blowing Control Loop Likewise for a more effective blowing control loop the basic PI scheme shown in Figure 1 above is complemented with a constant offset voltage used for actuator deadband compen sation and an anti windup scheme The resulting control scheme is illustrated by the block diagram shown in Figure 3 below amar Ve AK Ve mac Va ct Figure 3 Blowing Control Loop Active Iff Ve lt 0 It is reminded that the blowing or2. HVAC SISO Model Nomenclature As described in Reference 3 it is reminded that the temperature difference AT is the difference between the actual chamber temperature T and the assumed constant ambient temperature Ta The first order transfer function parameters of Equation 1 can be calculated as the average values of the model identified in Reference 3 This is shown below 1 1 1 1 Kse n 2 Kon Di A and Ta 2 Ta 2 T 2 1 From the system estimates obtained in Reference 3 obtain a numerical expression for the chamber open loop steady state gain Kss o and time constant Te as defined in Equation 2 Document Number 578 Revision 01 Page 2 PI Temperature Control Laboratory Manual 2 What is the type of the system What can you infer about the resulting steady state error 3 2 Pre Lab Assignment 2 Closed Loop Transfer Function The purpose of the laboratory is to design a controller that allows us to command the chamber temperature to a desired level with no steady state error Therefore a Proportional plus Integral PI control scheme is first chosen This results in a temperature closed loop diagram similar to the one illustrated in Figure 1 below Figure 1 Temperature PI Control Loop Document Number 578 Revision 01 Page 3 PI Temperature Control Laboratory Manual The PI control law implemented in the block diagram of Figure 1 can be formulated as follows V 1 K T 0 K
3. expressed in Equation 11 the square wave Amplitude to 2 C and Period to 150 seconds Specifically the setpoint properties parameters are expressed in Table 3 below Signal Type Te op C Amplitude C Period s Square Wave 32 0 2 0 150 0 Table 3 Temperature Setpoint Parameters Step 4 When you first open the ONET_HVAC_Lab_06_PI_Control vi controller file the default controller gains are not yet tuned An example of untuned controller parameters is provided in Table 4 below K K Kien Ta Ka Vh oft Vb orr VC VISSC VC PC C V V V 3 50 1 50 0 00 22 5 0 0 0 0 0 0 Table 4 Untuned Controller Parameters Run the LabVIEW VI Ctrl R to start the controller Ensure the initially green START push button is pressed and shown as a red STOP button to activate the controller This button can be used to pause the controller execution With the control action active the chamber temperature should now go up and down to roughly track the desired square wave setpoint You should obtain an untuned temperature response similar to the one depicted in Figure 4 above After a few periods you can stop the VI by pressing the red EXIT button on the front panel Step 5 Using the Numeric Controls of the Controller Gains box you should enter the system controller gains namely K Ki and K n that you have calculated in the pre lab section Also enter the ambient temperature Ta in C present outside of t
4. following standard form F426 sto 7 where s is the Laplace operator the damping ratio and n the undamped natural frequency Derive expressions for the proportional and integral gains K and Ki as functions of the system parameters the damping ratio and natural frequency O 3 For such quadratic systems it is reminded from classic control theory that the response peak time t can be expressed as T dE 8 Likewise the response Percent Overshoot PO can be formulated as Document Number 578 Revision 01 Page 5 PI Temperature Control Laboratory Manual i 3 9 Derive expressions for the proportional and integral gains K and Ki as functions of the system parameters the damping ratio C and the time to first peak tp PO 100e 3 3 Pre Lab Assignment 3 Controller Design 1 Additionally to exhibiting no steady state error to a step input the temperature closed loop response is desired to achieve the following design specifications in terms of peak time t and damping ratio t 20 0 s ana G 0 56 10 Calculate the proportional and integral gains Kp and Ki required to satisfy the design requirements stated in Equation 10 Document Number 578 Revision 01 Page 6 PI Temperature Control Laboratory Manual 2 What is the desired Percent Overshoot PO 3 Finally the designed PI control loop will operate around the following operating temperature leve
5. shown in Figure 4 below The default sampling rate for the implemented digital controller is 250 Hz However you can adjust it to your system s computing power Please refer to Reference 2 for a complete system s description The chamber temperature directly sensed by the thermistor is plotted on a chart in red as well as displayed in a Numeric Indicator located in the Chamber Temperature front panel box The values are in degrees Celsius QNET_HVAC Lab06_PI_Control_with_windup vi Quanser NI ELVIS Trainer QNET HVAC TRAINER HVACT Lab 1 PI Temperature Control Start Stop Control Om Setpoint Type Control Gains D Temperature degC gt Cam Constant Setpoint Properties Hfiso o s Temperature 1 1 1 1 1 1 1 200 225 250 275 300 325 350 lt Figure 4 Front Panel Used for the QNET HVACT Temperature Control Laboratory Step 3 The vertical toggle switch in the Setpoint Type box allows you to choose Document Number 578 Revision 01 Page 13 PI Temperature Control Laboratory Manual between a Square Wave or a Constant type of reference temperature Te Ensure that it is set to the Square Wave position The temperature setpoint is also plotted on the front panel chart in blue Use the Numeric Controls of the Setpoint Properties box to set the chamber operating temperature T op to 32 C as
6. Quanser NI ELVIS Trainer QNET Series QNET Experiment 06 HVAC Proportional LL EE R Integral PI Temperature Control Heating Ventilation and Air Conditioning Trainer HVACT Student Manual PI Temperature Control Laboratory Manual Table of Contents Iv Laboratory OD IC UVES oi A a aaa a tito 1 Rebis 1 o a A ie 1 3 1 Pre Lab Assignment 1 Open Loop Transfer Function i 1 3 2 Pre Lab Assignment 2 Closed Loop Transfer Function in 3 3 3 Pre Lab Assignment 3 Controller Design iii 6 3 4 Pre Lab Assignment 4 Final Controller Design i 8 SAU Ed Control A e aaa 8 34 2 Blowing Control Lope dd i aa 11 3 4 3 Final Temperature Control LaWs coocnooncnionncnonnconaconnonocnnnononccnoncnonon cana nconaconos 12 E A E 12 4 1 System Hardware Configuration u rina 12 42 Experimental PROC SAUL son ile A RO 13 Document Number 578 Revision 01 Page i PI Temperature Control Laboratory Manual 1 Laboratory Objectives The objective of this experiment is to design a temperature closed loop controller that meets required specifications The system should track and or regulate the desired chamber temperature with minimum peak time and overshoot A pre requisite to this laboratory is to have successfully completed the system identification experiment described in Reference 3 This laboratory is consistent with the sys
7. cooling control loop effectively commands the blower input voltage V and is only active if and only if V is negative The basic chamber com mand voltage V is calculated accordingly to the PI control law formulated in Equation 3 Also during the cooling process the heater input voltage remains constant and set to zero as expressed below V 1 0 15 where t is the continuous time The complete control law for blowing as depicted by the block diagram of Figure 3 above can be expressed as VC VL Vi og 16 where represents the absolute value function and V or is the blower offset voltage Since V is negative during blowing the absolute value is required to send a positive command voltage to the blower i e fan Document Number 578 Revision 01 Page 11 PI Temperature Control Laboratory Manual The blower constant offset voltage V os is included in Equation 16 in order to compen sate for the fan deadband V om has been estimated in Reference 3 as the upper limit of the fan deadzone The blower saturates at V max Similarly to the heating control loop the integrator is turned off when Vi max is reached to prevent large overshoots that can result from the integrator charging up too much The same deadzone nonlinearity slope K is used 3 4 3 Final Temperature Control Laws To summarize and reformulate the previous design considerations the two actuator input voltages are completely defin
8. ed below by Equations 17 and 18 Using Equations 13 and 15 the heater input voltage is calculated as defined below Vit Vi gD Y off 0 lt V t 0 V t lt 0 17 V t Likewise using Equations 14 and 16 the blower input voltage is determined as follows 0 0 lt V t HOT vol Vi or VAt lt 0 18 4 In Lab Session 4 1 System Hardware Configuration This in lab session is performed using the NI ELVIS system equipped with a QNET HVACT board and the Quanser Virtual Instrument VI controller file QNET_HVAC_Lab_06_PI_Control vi Please refer to Reference 2 for the setup and wiring information required to carry out the present control laboratory Reference 2 also provides the specifications and a description of the main components composing your system Before beginning the lab session ensure the system is configured as follows QNET HVACT module is connected to the ELVIS ELVIS Communication Switch is set to BYPASS DC power supply is connected to the QNET HVAC Trainer module Document Number 578 Revision 01 Page 12 PI Temperature Control Laboratory Manual The 4 LEDs B 15V 15V 5V on the QNET module should be ON 4 2 Experimental Procedure Please follow the steps described below Step 1 Read through Section 4 1 and go through the setup guide in Reference 2 Step 2 Open the VI controller file QNET_HVAC_Lab_06_PI_Control vi You should obtain a front panel similar to the one
9. fred t dt 3 where the temperature error Te e can be expressed as shown underneath T t AT 0 AT 09 T 0 T0 4 The corresponding control loop gains and variables are enumerated in Table 2 below Symbol Description Proportional Gain Integral Gain Reference Chamber Temperature i e Setpoint Chamber Temperature Error Table 2 PI Control Loop Nomenclature The sign of the command voltage V as calculated in Equation 3 can then be used to implement the switching strategy between the plant two possible inputs that is to say Vn and V Specifically the sign of V determines whether the chamber needs to heated up i e Va is controlled by the PI loop and V is set to zero or cooled down i e Va is set to zero and Vs is controlled by the PI loop Such a switching strategy is formulated by Equation 5 below V t 0 lt V t 0 0 lt V t V t 0 V t lt 0 and V t V t V t lt 0 5 1 The resulting closed loop transfer function Tci s of the PI control system is defined in the Laplace domain as follows T s T 5 6 Tals Using the control block diagram 1 and or Equation 3 derive the expression of Te s as a function of the system parameters Kss and Te and the PI controller gains K and Ki Document Number 578 Revision 01 Page 4 PI Temperature Control Laboratory Manual 2 Tens should be a second order system whose denominator can be expressed under the
10. hart top left corner Fill up Table 6 as shown below You should have plotted two iterations of both step types i e heating and blowing First measure the corresponding Percent Overshoot PO and peak time t for all 4 step responses as specified in Table 6 Tc peak is the overshoot value Then take the average of PO and t over the 2 iterations of each step type Finally combine and average the results of both step types What are your final values for PO and t Step Type Iteration Ti peak C PO t s Heating 1 2 Average X Blowing 1 2 Average X Average Values X Table 6 Step Response Actual Performance Step 14 Do the measured Percent Overshoot and peak time meet the required specifications Explain your observations Step 15 If the design requirements defined by Equation 10 are still not satisfied you should manually fine tune the controller parameters of Table 5 until the response performance improves to the desired level Include in your laboratory report your final tuning parameters experimental plots and results as well as the measured system performance criteria satisfying the specifications Step 16 Once all your experimental results are obtained shut off the PROTOTYPING POWER BOARD switch and the SYSTEM POWER switch at the back of the ELVIS unit Unplug the module AC cord Then stop the VI by pressing the red EXIT button Document Number 578 Rev
11. he HVAC chamber Set the value of K to 0 0 C V which effectively turns off the integral anti windup element in the feedback system Finally the deadband compensation parameters Vr or and Vo of should also be properly set to the values that you estimated in Reference 3 Do so by using the Numeric Controls of the Deadband Compensation box on the front panel Summarize your final tuned controller parameters by filling up Table 5 as shown below Document Number 578 Revision 01 Page 14 PI Temperature Control Laboratory Manual K K Kern Ta Ka Vh oft Vo orr V C E Ol V C C C V V V Table 5 Tuned Controller Parameters Step 6 Start the controller by running the LabVIEW VI Ctrl R in order to try your calculated gains on the actual system The software applies square wave temperature setpoints to the closed loop control system and plots both setpoint and actual chamber temperature over a 350 second time range Observe the way the system switches between the two actuators i e lamp and fan in order for the chamber temperature to track the desired square wave setpoint around the operating level T op Step 7 Let the system run until you have plotted on the chart the temperature response to 2 heating steps and to 2 cooling steps at least the overshoot and peak time part of it Step 8 Make a screen capture of the obtained step response plot and join a printout to your report Document Number 578 Revis
12. he heating control loop effectively commands the heater input voltage V and is only active if and only if V is positive The basic chamber command voltage V is calculated accordingly to the PI control law formulated in Equation 3 Also during the heating process the blower input voltage remains constant and set to zero as expressed be low V t 0 12 where t is the continuous time The complete control law for heating as depicted by the block diagram of Figure 2 above can be expressed as V t V t Vi gD Vi og 13 where Vi or is the heater offset voltage and Vn ir is the heater feed forward voltage as defined by Vi gO Ke TO T 14 with Ta the ambient temperature outside of the chamber T e the desired chamber temperature and Ky n the heater feed forward gain Feed forward action is necessary to bring and maintain the chamber temperature to the de sired level It compensates for the standard air cooling in the chamber due to natural heat Document Number 578 Revision 01 Page 9 PI Temperature Control Laboratory Manual dissipation The PI control system compensates for small variations e g disturbances from that operating point 1 Using the definition of the heater steady state gain Kss n characterize the heater voltage feed forward gain Ky 1 as defined in Equation 14 Hint It is reminded that in the steady state Vn is the voltage required to maintain T at the desired level T
13. ion 01 Page 15 PI Temperature Control Laboratory Manual Step 9 Does the closed loop system track the desired square wave setpoint accurately Is there any steady state error Comment on the symmetry or lack of of the temperature response between heating and blowing steps Explain Document Number 578 Revision 01 Page 16 PI Temperature Control Laboratory Manual Step 10 Set the value of K to 0 2 C V which corresponds to slope of the integral anti windup deadzone to 0 2 C V and keep the same values for the other control parameters entered in Table 5 Start the controller by running the LabVIEW VI Ctrl R in order to try your calculated gains on the actual system using the anti windup element Observe the effects on the response of having an anti windup element Then adjust K to improve the response and enter the tuned parameter in Table 5 above Step 11 Let the system run until you have plotted on the chart the temperature response to 2 heating steps and to 2 cooling steps at least the overshoot and peak time part of it Step 12 Make a screen capture of the obtained step response plot and join a printout to your report Step 13 You should now measure and determine your system performance from the Document Number 578 Revision 01 Page 17 PI Temperature Control Laboratory Manual actual response plot as displayed on the VI Front Panel Do so by using the Graph Palette located on top of the C
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15. l T op T op 32 0 degC 11 Cc If the chamber temperature setpoint variation AT is a square wave of 2 degree Celsius amplitude around T op to what values do you expect the temperature to overshoot to Document Number 578 Revision 01 Page 7 PI Temperature Control Laboratory Manual 3 4 Pre Lab Assignment 4 Final Controller Design The temperature Proportional plus Integral PI control scheme previously developed and illustrated in Figure 1 above is improved in this section to better suit the characteristics of each of the heating and cooling processes both composing the HVAC system Therefore al though based on the same standard PI loop two slightly different control schemes are de signed hereafter in order to better accommodate the physical particularities of each process As previously defined in Equation 5 it is reminded that the switching logic between the heating and cooling control loops is still determined by the sign of V 3 4 1 Heating Control Loop For a more effective heating control loop the basic PI scheme shown in Figure 1 above is complemented with a feed forward action an offset voltage and an integrator anti windup element as illustrated by the block diagram shown in Figure 2 below Document Number 578 Revision 01 Page 8 PI Temperature Control Laboratory Manual Control Saturation Figure 2 Heating Control Loop Active Iff V 0 It is reminded that t
16. tem nomenclature used in Reference 3 2 References 1 NI ELVIS User Manual 2 QNET HVACT User Manual 3 QNET Experiment 05 HVAC System Identification 3 Pre Lab Assignments A This section must be performed before you go to the laboratory session 3 1 Pre Lab Assignment 1 Open Loop Transfer Function In a first approach and in the present laboratory the HVACT system is assumed to be a Single Input Single Output SISO plant This is motivated by the fact that both heating and blowing processes have first order transfer functions Gn and Gy respectively with similar system parameters While the controlled output is always the chamber temperature T the controlled input is either the heater or the blower voltage but not both simultaneously depending on whether the chamber needs to heated up or cooled down Such a switching mechanism results in a decoupling between the the two inputs The remaining HVAC input voltage is disabled Document Number 578 Revision 01 Page 1 PI Temperature Control Laboratory Manual and set to zero Therefore the HVAC open loop chamber transfer function G s from input voltage to chamber temperature difference can be defined such as A TA s Ko c C V s E T S 1 1 where the model variables are defined in Table 1 below Description Chamber Command Voltage Chamber Open Loop Steady State Gain Chamber Open Loop Time Constant Laplace Operator Table 1
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