Digital Control Measures In-System Response

Nov 1, 2006 12:00 PM
By Mark Hagen, Systems Application Engineer, and Dave Freeman, System Engineering Manager, Texas Ins

Digital Controller Design

Let's define a buck converter stage as shown in Fig. 2. The equation for the small signal ac transfer function for this converter is shown in Eq. 1:

For representative values, use

KDUTY = 24/100; V/% duty

R = 1800 Ω

C = 3 × 22 µF

RC = 0.001 Ω

L = 0.65 µH

RL = 0.058 Ω.

This produces a power stage with a zero at 2.4 MHz, and a complex second-order pole at 24.3 kHz with a Q of 1.68. The gain is defined for purposes of simulating the differences between measurement methods such that the input to the power stage is in percent duty cycle and the output is in volts.

The controller consists of a two-pole, two-zero digital compensator. In this example, the compensator zeros are both set to 30 kHz, and the poles are set to zero (to form an integrator) and 300 kHz. The gain of the compensator, defined at 1 kHz, is 43 dB. The digital sample rate is set to the PWM switching frequency of 700 kHz.

Fig. 3 shows the simulated open-loop transfer function for the representative system. So now let's use this system to evaluate the four transfer gains defined in Fig. 4. The G/(1+GH) trace has the lowest gain. At best its gain is -20 dB. This means that you would have to inject a large signal to get a small amplitude at the measurement location — not good. The 1/(1+GH) trace has a low gain at low frequencies, but a gain at or above 1.0 for high frequencies. Likewise, the GH/(1+GH) trace has good gain at low frequencies and low gain at high frequencies. Finally, the H/(1+GH) trace is the transfer gain seen when injecting the excitation signal at the input to the compensator and measuring it at the output of the compensator. In this case, we get to use the gain in the compensator, and it has the highest measurement gain.

Bode Analysis Design Tool

An in-circuit loop analysis was developed based on a TMS320F2808 and a PC-based design tool for a digital telecom rectifier reference design. The PC communicates to the power supply through an RS-232 interface. The telecom rectifier has three loops that can be analyzed with the system, the power factor correction (PFC) voltage loop, the PFC current loop and the dc-dc voltage loop. Commands are defined to select one of three loops in the power-supply system.

To characterize the system, an injection node and a response-measurement node are selected. The analysis start frequency, stop frequency, number of frequency steps, injection amplitude, number of dwell samples and number of measurement samples are specified. The PC test program sends commands to the digital controller to make a frequency response measurement for each frequency step. At the end of each measurement, the digital controller returns the two accumulated sine and cosine coefficients for that frequency. The PC program calculates the complex open-loop transfer function, and then plots the magnitude and phase for that frequency.

Because the power-stage compensator is digital, the test program queries the digital controller for the compensator coefficients, then calculates the exact frequency response of the compensator. Once the compensator frequency response is known, it is factored out of the open-loop transfer function to calculate the transfer function for the power stage.

Once these measurements and calculations are made, the user selects the display of frequency response of the power stage, the frequency response of the digital compensator, the frequency response of the open-loop system or the frequency response of the closed-loop system.

After the loop analysis measurement has been made and the frequency response of the analog power stage is determined, the Bode tool can be used to quickly explore the effect of changing the compensator coefficients, since the compensator is deterministic due to the digital nature.