Discrete-Time Framework for Stability Analysis and Controller Design in a Single-Inductor Multi-Output Buck Converter under Digital Current Mode Control

Single-inductor multi-output (SIMO) buck converters offer a compact solution for portable applications, in which digital current mode control (DCMC) can achieve fast transient and high efficiency over a wide load current and input voltage range. Using a discrete-time (DT) modeling framework, this paper shows that a practical sampling delay often leads to undesirable sub-harmonic instability in a DCMC SIMO buck converter, which may not occur using analog control. A peak current-based DCMC is used to control the input-side switch, whereas, the output-side switch is controlled using a digital voltage loop. With a practical sampling delay, DT large-signal and small-signal models are derived within two subsequent sampling instants. The accuracy of the DT large-signal model is verified using switch simulation. The closed-loop characteristic equation is derived, and the stability boundary is identified using a root-locus plot. It is shown that the sampling delay may lead to subharmonic instability even for a much lower duty ratio. A state feedback approach is adopted to design the digital controller and the controller gains are obtained by placing closed-loop poles at the desired location. This multivariable design approach is found to achieve reduced cross-coupling effects compared to that using a traditional output feedback design approach. Superior performance with stable behavior is shown using simulation results, which are also used to validate the analytical predictions.