Analysis of Stability and Performance of a Cascaded PI Sliding-Mode Control DC-DC Boost Converter via LPRS

The analysis and design of a cascade proportional-integral (PI) sliding-mode control for a dc-dc boost converter using the locus of a perturbed relay system (LPRS) is presented in this article. The implemented system uses a sliding-mode controller for the inner loop and a PI controller for the outer loop to regulate the output voltage. An LPRS representation of the overall system is developed in this article. The latter is used to analyze the frequency and the amplitude of the chattering/ripple (self-excited oscillations) and relates them to the specifications. Besides, the LPRS-method-based analysis and design allows one to find the exact value of the equivalent gain, which is necessary for the analysis of disturbances propagation. Another important contribution is the detailed stability analysis of the two-loop controller through the LPRS method. System stability is analyzed for the two aspects, i.e., the chattering stability of the inner loop and the stability of the full-order two-loop averaged dynamics, through the concept of the equivalent gain. Furthermore, the LPRS is used to operate the converter at a specified switching frequency through defining the controller hysteresis value. Simulations and experimental results are provided to validate the theoretical analysis.