On stability of a cascaded PI-SM control DC-DC boost converter

Design and analysis of a cascade control DC-DC boost converter is proposed in this paper using the locus of a perturbed relay system (LPRS). The output voltage is regulated using a PI controller in the outer-loop and a sliding mode controller in the inner-loop. The chattering amplitude and frequency is analyzed using the LPRS method. The use of the LPRS method also allows one to exactly evaluate the equivalent gain, necessary for the disturbance (slow motion) analysis. Moreover, the stability analysis is evaluated in terms of two aspects: the orbital stability of the oscillations in the inner-loop (chattering stability), and the stability of the overall averaged dynamics. Besides, the SM controller is designed to operate at a specified switching frequency through the proper selection of the hysteresis value using the LPRS method. The theoretical analysis is verified through simulations and hardware implementation.