Flatness-Based Control of DC-DC Converters Implemented in Successive Loops

The article proposes a flatness-based control in successive loops for DC-DC converters. A model of a DC-DC converter connected with a DC motor is considered. Using a per-row decomposition of the state-space description of the system, the dynamics of the converter is shown to consist of a set of subsystems for which differential flatness properties hold. For the ith subsystem, state variable xi is shown to stand for the flat output while state variable xi+1 is shown to stand for a virtual control input. For each subsystem, a stabilizing virtual control input is computed. From the last row of the state-space model, the control input that is actually exerted on the converter’s model is found. This is shown to contain recursively all virtual control inputs associated with the previous rows of the state-space model. It is proven analytically that the tracking error of all state variables of the model gets asymptotically eliminated. Moreover, a stability proof for the control method is provided with Lyapunov analysis. The excellent tracking performance of the control method is further confirmed through simulation experiments.