Real- -time Self Compensating AC/DC time Self Compensating AC/DC - PowerPoint PPT Presentation

Fusion Digital Fusion Digital Fusion Digital Fusion Digital Real- -time Self Compensating AC/DC time Self Compensating AC/DC Real Digitally Controlled Power Supply Digitally Controlled Power Supply Dave Freeman, Mark Hagen Texas Instruments Digital Power Group

Fusion Digital Fusion Digital Fusion Digital Fusion Digital Digital Control Digital Control • Problem: Determining optimal loop compensation given uncertainties of: • line, load and temperature variation • component tolerance, parasitics • step response • Solution: Utilize the processing power of a digital controller to measure the transfer function digital controller of the loop and from this measurement make adjustments to the digital compensation coefficients. 2 12Sep06

Fusion Digital Fusion Digital Fusion Digital Fusion Digital Transfer Function Measurement Transfer Function Measurement • To perform Transfer Function Analysis (TFA) we need to: – Generate a sinewave excitation signal – Inject that signal at a summing junction – Capture the response of the system to the excitation • From this response, calculate the open loop gain – From the open loop gain determine key performance metrics of bandwidth, gain margin and phase margin. • For a digitally controlled system the logical location to make the measurement is just before or just after the digital compensator. 3 12Sep06

Fusion Digital Fusion Digital Fusion Digital Fusion Digital Measurement Locations Measurement Locations Given the following basic system equations: = y Gu u' y' G(s) power stage = + u c d 2 = c Hx digital controller PWM ADC = + x e d 1 u y = − e r y d 2 d 1 The closed loop response for each node is - H(z) c x e r GH GH G = + + digital y r d d 1 2 + + + compensator 1 GH 1 GH 1 GH H H GH • Inject a sinewave at = + + u r d d + + 1 + 2 1 GH 1 GH 1 GH d 1 or d 2 H H GH = + − c r d d 1 2 + + + 1 GH 1 GH 1 GH • Measure response at 1 1 G = + − x r d d node e , x , c or u 1 2 + + + 1 GH 1 GH 1 GH 1 GH G • Solve for GH = − − e r d d 1 2 + + + 1 GH 1 GH 1 GH 4 12Sep06

Fusion Digital Fusion Digital Fusion Digital Fusion Digital Gain calc's calc's for various nodes for various nodes Gain Calculation of open loop gain G( f )H( f ) from measurements at each node: Transfer gains at each node: inject measure at inject measure at at at y u c x e y u c x e − − GH H H 1 GH e d 1 d 1 Hd Hd d 1 − Y 1 1 1 + + + + + + 1 GH 1 GH 1 GH 1 GH 1 GH d e − − − u 1 c 1 x D Y 1 1 − − − − − − G 1 GH G G c Hy Hx He d 2 d 2 d 2 − 1 + + + + + + 1 GH 1 GH 1 GH 1 GH 1 GH − d c + + d Hy d Hx d He u 2 2 2 2 • Note that the formula for calculating open loop gain contains the compensator gain H( f ) if the system is excited before the compensator and measured after, or vice-a-versa. • This is not a big problem since a digital compensator is completely deterministic and its frequency response can be calculated as: ( ) ( ) ( ) = = + z exp j 2 π f T cos 2 π f T j sin 2 π f T meas s meas s meas s + + 2 b z b z b ( ) = 0 1 2 H f (for a 2nd order compensator) meas 2 + + z a z a 1 2 5 12Sep06

Fusion Digital Fusion Digital Fusion Digital Fusion Digital Sinewave Generation Sinewave Generation • Use table look-up technique – TI digital controllers, including the UCD9501, have a build-in sinewave table in ROM. – For each sample step through the table with a step F size defined as = step N meas table F sample rate then = + tableIndex tableIndex step – When the end of the table is reached, wrap to the beginning of the table by subtracting the table length from the index. – By maintaining the fractional part of the table index and rounding to determine the table entry, very high frequency resolution can be obtained. 6 12Sep06

Fusion Digital Fusion Digital Fusion Digital Fusion Digital Response Measurement Response Measurement • The definition of a Discrete Fourier Transform (DFT) is: − N 1 ∑ − ≡ j 2 π nk / N K v e k n = n 0   − N 1  k   k  ( ) ∑ = ⋅  π − π      v cos 2 n j sin 2 n   n  N   N    = n 0 • This says that we can calculate the real and imaginary magnitude of the k th harmonic of a signal by multiplying that signal by a sine and cosine sequence and summing. • Since we've already generated a sinewave to inject into the loop as the excitation signal, the response measurement is simply: uCosSum += u*bcos; // Accumulate cosine // sum for measurement node u uSinSum -= u*bsin; // Accumulate sine // sum for measurement node u (Note that the cosine sequence is easily generated by adding an offset to the sine table index of 1/4 the table length.) 7 12Sep06

Fusion Digital Fusion Digital Fusion Digital Fusion Digital Example Calculation of G( G( f f )H( )H( f f ) ) Example Calculation of Inject at d 2 , measure at c Inject at d 1 , measure at e u' y' u' y' G(s) G(s) power stage power stage digital controller digital controller PWM ADC PWM ADC y y u u H(z) H(z) - - c e r x e r digital digital compensator compensator d cos cosSum cosSum d cos z -1 z -1 d sin sinSum sinSum d sin z -1 z -1 Return cosSum and sinSum for each ( ) − − + ⋅ e cosSum j sinSum injected excitation frequency. = = GH ( ) + + + ⋅ d e N / 2 D cosSum j sinSum Calculate open loop gain as follows: 2 cos ( ) ( ) − − + ⋅ c cosSum j sinSum − + + − 2 2 D E E E jD E = = GH = r r r i r i ( ) + + + ⋅ d c N / 2 D cosSum j sinSum + + + 2 2 2 D 2 D E E E 2 cos r r r r i ( ) − + 2 + 2 − D c C C jD C = r r r i r i 2 + + 2 + 2 D 2 D C C C r r r r i Where D cos is the base to peak amplitude Then plot magnitude and phase of G( f )H( f ) of the excitation and N is the # samples. to determine phase margin and bandwidth 8 12Sep06

Fusion Digital Fusion Digital Fusion Digital Fusion Digital Practical TFA measurements Practical TFA measurements • Windowing – The definition for the DFT produces the response just at harmonic frequencies. These frequencies produce an integer number of cycles in the measurement interval. At other frequencies you need to do something to reduce "leakage". 1. Window the measurement data. A raised cosine or triangle window are popular options. 2. Modify the measurement interval so that an integer number of cycles are measured. (What we implemented.) • Settling – We want just the forced response, so the controller needs to wait some number of samples for the natural response to decay. 9 12Sep06

Fusion Digital Fusion Digital Fusion Digital Fusion Digital TFA Physical Implementation TFA Physical Implementation Fully Digitally controlled Telecom Rectifier • 48V-1000W output, 85V-260V 50/60 Hz input • Interleaved Boost PFC stage • Phase shifted full-bridge DC/DC stage 10 12Sep06

Fusion Digital Fusion Digital Fusion Digital Fusion Digital Rectifier Schematic Rectifier Schematic Digital Controller • Implements 3 loops (PFC current, PFC voltage and DC/DC voltage), plus current sharing between PFC phases. • Sequencing, Soft start/stop and OC/OV/UV. • Manages serial interface and performs TFA. 11 12Sep06

Fusion Digital Fusion Digital Fusion Digital Fusion Digital Self- -Measured Bode Plots Measured Bode Plots Self • PC program issues serial bus commands to measure response at a given frequency. – command defines – frequency – amplitude – number of samples to delay – number of samples to measure – controller returns – cosine and sine coefficients for that frequency • Repeated from start to stop frequencies to produce Bode plot for each loop • Calculate plant transfer function and use this to explore effect of changes in compensation. 12 12Sep06

Fusion Digital Fusion Digital Fusion Digital Fusion Digital TFA (Bode) Design Tool TFA (Bode) Design Tool BW Select control loop gain margin phase margin Select which part of the loop to display Transfer Function Analysis (measure Bode) Digital magnitude coefficients plot Update coefficients based on PID gains Update coefficients based on analog poles & zeros phase plot Status 13 12Sep06