How are the Coefficients Calculated?

The Digital Compensator Design Tool (DCDT) uses mathematical approximations, such as the Bilinear-Tustin Approximation and the Backward Euler Approximation (applies to Proportional Integral Derivative (PID) compensator only) to calculate the coefficients for each of the supported compensators. By using these transformations, it is possible to simplify the computations required to map the s-domain (continuous time domain) transfer function of our compensator into the z-domain (discrete time domain).

Backward Euler Approximation Equation:

Backward-Euler-Approximation.PNG

Bilinear or Tustin Approximation Equation:

Bilinear-or-Tustin-Approximation.PNG

Where:
Ts is the sampling period.

The GUI will display the calculated coefficients for the selected compensator and these will be displayed in the Compensator Calculation tab, as shown in the figure below:

GUI-Calculated-Coefficients.PNG

Once the coefficients are calculated, these will be normalized and optimized for Fixed-Point math by the DCDT. The hardware can implement these coefficients using Microchip’s SMPS Control Library. This means that you can focus on the placement of the compensator poles/zeros to meet the desired system performance on the DCDT. The tool will generate the digital equivalent coefficients, that will represent the compensator, using a digital controller such as the Microchip dsPIC33 “GS” family of devices.

Hardware-GUI-Generated-Coefficient-Implementation.PNG
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