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:


Bilinear or Tustin Approximation Equation:


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:


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.

© 2024 Microchip Technology, Inc.
Notice: ARM and Cortex are the registered trademarks of ARM Limited in the EU and other countries.
Information contained on this site regarding device applications and the like is provided only for your convenience and may be superseded by updates. It is your responsibility to ensure that your application meets with your specifications. MICROCHIP MAKES NO REPRESENTATIONS OR WARRANTIES OF ANY KIND WHETHER EXPRESS OR IMPLIED, WRITTEN OR ORAL, STATUTORY OR OTHERWISE, RELATED TO THE INFORMATION, INCLUDING BUT NOT LIMITED TO ITS CONDITION, QUALITY, PERFORMANCE, MERCHANTABILITY OR FITNESS FOR PURPOSE. Microchip disclaims all liability arising from this information and its use. Use of Microchip devices in life support and/or safety applications is entirely at the buyer's risk, and the buyer agrees to defend, indemnify and hold harmless Microchip from any and all damages, claims, suits, or expenses resulting from such use. No licenses are conveyed, implicitly or otherwise, under any Microchip intellectual property rights.