Comparison of Digital Control Loops Analytical Models, Laboratory Measurements, and Simulation Results

Transcription

1 Comparison of Digital Control Loops Analytical Models, Laboratory Measurements, and Simulation Results Phil Cooke Rohan Samsi Tom Wilson 20 October 2009

2 Outline Application Circuit & IC Block Diagram Control Loop Model, Design, and Analysis PID Design Analytical Design Procedure Simulation & Experimental Circuit Schematics Time-Domain Simulation Model vs. Experimental Results Frequency Domain Comparison Summary Page 2

3 Application Circuit Optional I2C/PMBus Compatible Connection Input Voltage Decoupling Minimal External Passive Components Programmable Faults Slave Address Voltage and Current Sensing Networks MOSFET Gate Driver PX3511 or PX3515 Set Frequency and Output Voltage Page 3

4 IC Block Diagram Voltage Feedback Path Mux. to Feed in Voltage, Current, & Temp. Current Feedback Path Trimmed Ref. & Oscillator To Sync Converters PWM Command to MOSFET Driver Controller PID Post Filter DPWM Enable Outputs Internal Memory Internal Brain Input & Output OVP, UVP Peak, Average, Current Limit Internal/Ext. Temp. Alert/Shutdown Page 4

5 Control Loop Model: Mostly Small-Signal Line-to- Output Transfer Function Output Impedance Transfer Function Transfer functions in Continuous s or Discrete z frequency domains Lumped Total Delay Can include delay from DPWM block Feedback Gain 1, 1/2, 1/3 Control-to- Output Power Converter Averaged Model Page 5

6 Control Loop Design What Do We Want To Do Loop Gain Crossover Frequency Control-to- Output Phase Boost Controller -180º Page 6

7 Control Loop Design What Do We Want To Do Loop Gain Crossover Frequency Control-to- Output Phase Boost and Gain Adjust Controller -180º Page 7

8 Analysis: Small-Signal Equations Total Discrete Plant and Feedback These values (n 1, n 0, d 1, d 1, H) are known Discrete Controller G Z1 z = n 1 z+n 0 z 2 +d 1 z+d 0 H G C z =A az 2 +bz+c [ =A z 2 1+K FD z+k K I 1 FD 1 z K 1 P +K D 1 z 1 1 ] 1 K FD z 1 Loop Gain T z = G C z G Z1 z Solution: Solve at Crossover 20log G C z C G Z1 z C =0 or G C z C G Z1 z C =1 Page 8

9 PID Design Analytical Design Procedure 1. Select desired analog crossover frequency f C, this is the loop bandwidth, and calculate system resonance f O from the power converter reactive components 2. Set the analog post filter pole, f PA2, to 3 f C, and find K FD A reasonable starting range is from f PA2 = f C /2 to 3 f C K FD is one of the following {0.125, 0.25, 0.375, 0.50, 0.625, 0.75, 0.875, 1.00} for the PX7510D 3. Start with f X = 0.85 f O and Q X = 0.7 for the controller zeroes and find the required loop-gain (i.e., find α) to have T(z) crossover at f C f X should be equal to or less (for design margin) than f O, but not too low 4. Find α from: G Z1 z = n 1 z+n 0 Using H α= n 1 z C +n 0 z 2 +d 1 z+d 0 z 2 C +d 1 z C +d 0 H Page 9

10 PID Design Analytical Design Procedure Where G Z1 is the total discrete plant and feedback gain 5. From the discrete controller transfer function, find β Find β 6. Using pole-zero mapping (z=e st ), along with the discrete crossover z C, find γ G C z =A az 2 +bz+c z 2 1+K FD z+k FD z=e s T S z C =e jw C T S w C =2 πf C β= z C 2 1 +K FD z C +K FD analog maps to digital Find γ 1+s/Q X w X s/w X 2 z z ZN1 z z ZN2 γ= z C z ZN1. z C z ZN2 7. Solve for r using f X and Q X in: r=e π f X T S /Q X Page 10

11 PID Design Analytical Design Procedure 8. Finally the a, b, and c controller terms are: a= β α γ A b= 2 a r cos [2 π f X T S 1 1/ 2 Q X 2 ] c=a r 2 9. Alternatively, the K P, K I, and K D terms are: K D =c K I = a+b+k D 1 K FD K P =a K I K D Page 11

12 Time-Domain Simulation Model SIMPLIS Simulation Circuit & IC Model Power Converter PX3511D Gate Driver PX7510D IC Controller Model Page 12

13 Experiment Circuit Schematic Latest PX7510D Controller Integrated Driver and MOSFETs (PX4660) Page 13

14 Time-Domain Simulation vs. Experimental Results 5 A to 10 A Load Step SIMPLIS Simulation Model Imported Scope Data Page 14

15 Time-Domain Simulation vs. Experimental Results 10 A to 5 A Load Step SIMPLIS Simulation Model Imported Scope Data Page 15

16 Time-Domain Simulation vs. Experimental Results 5 A to 20 A Load Step SIMPLIS Simulation Model Imported Scope Data Page 16

17 Time-Domain Simulation vs. Experimental Results 20 A to 5 A Load Step SIMPLIS Simulation Model Imported Scope Data Page 17

18 Experiment Results: Time-Domain Actual Scope Plots All data was extracted to.csv file for comparison 5 A to 10 A Load Step 10 A to 5 A Load Step Page 18

19 Frequency-Domain Comparison: Original Design fsw is the Switching Frequency The MatLab model shown here uses a more accurate digital loop model Page 19

20 Frequency-Domain Comparison: Original Design The MatLab model shown here uses a simplified digital loop model Both the gain and phase are less accurate at the higher frequencies Page 20

21 Frequency-Domain Comparison: Design Procedure This is a more aggressive design The MatLab model shown here uses a more accurate digital loop model More phase boost throughout, higher crossover achievable Page 21

22 Summary Understanding Digital Control systems requires control loop models - The behavior can be better appreciated by analytical analysis aided with computer simulation tools in the time and frequency domain to gain further insight Page 22

23 Summary Understanding Digital Control systems requires control loop models - The behavior can be better appreciated by analytical analysis aided with computer simulation tools in the time and frequency domain to gain further insight Models for a typical digital PID voltage mode controller was provided Page 23

24 Summary Understanding Digital Control systems requires control loop models - The behavior can be better appreciated by analytical analysis aided with computer simulation tools in the time and frequency domain to gain further insight Models for a typical digital PID voltage mode controller was provided A digital design procedure starting from analog frequency domain specifications was given using these models to calculate the controller PID coefficients Page 24

25 Summary Understanding Digital Control systems requires control loop models - The behavior can be better appreciated by analytical analysis aided with computer simulation tools in the time and frequency domain to gain further insight Models for a typical digital PID voltage mode controller was provided A digital design procedure starting from analog frequency domain specifications was given using these models to calculate the controller PID coefficients Comparison of the time and frequency data was made between the models and simulation results to the real experimental data, simulation tools can further the accuracy of the validation before designs are released to production Page 25

26 Summary Understanding Digital Control systems requires control loop models - The behavior can be better appreciated by analytical analysis aided with computer simulation tools in the time and frequency domain to gain further insight Models for a typical digital PID voltage mode controller was provided A digital design procedure starting from analog frequency domain specifications was given using these models to calculate the controller PID coefficients Comparison of the time and frequency data was made between the models and simulation results to the real experimental data, simulation tools can further the accuracy of the validation before designs are released to production This represents a digital design example where all of the results are compared this provides confidence that these systems are understood and designs can be robust using these approaches Page 26