Variable Structure Control for Power Electronics
: Limitations in the Structured Construction of Sliding Mode Controllers

  • Georgios Kafanas

Student thesis: Doctoral ThesisDoctor of Philosophy (PhD)


This thesis analyzes the effects of the motion in the boundary layer of some sliding surfaces in the performance of sliding mode controllers for power electronic converters. In converters with multiple inputs and multiple internal states a sliding mode controller stabilizing the system imposes sliding on a manifold residing in the intersection of multiple switching surfaces. Systems sliding in the intersection of multiple surfaces can exhibit jitter, a phenomenon which causes abrupt changes in the sliding speed along the sliding manifold. But even in a system with a single sliding surface there can be distortion in the motion in the sliding layer due to unmodeled dynamics. Time delays introduced by sensors were reported to distort the motion in the boundary layer resulting in steady state drift and excessive ripple. Two converters were instigated to determine the effects of the motion in the sliding layer in the dynamics of the controlled system.

A sliding mode controller was designed for the voltage fed trans-Z-source DC-DC converter that can stabilize the full state of the system. The controller operates by imposing sliding in the intersection of two surfaces. Jitter was observed in the sliding motion for some hysteresis switching controllers. Two switching manifolds where tested. The dynamics on the sliding mode were found to be affected significantly by the selection of the switching manifold and the switching logic. An extended convex hull was used to describe the range of dynamical behaviors that can be expected for any switching manifold used to implement the sliding mode of the trans-Z-source converter.

To investigate the effects of the sensors on the motion in the sliding layer, a buck converter with sensors was analyzed. A model representing the sensors of power converters as first order integrators was used to model the non-ideal behavior of the sensors. The sliding mode in the resulting dynamics is proven to be unstable. Time domain simulations reveal a limit cycle that appears in steady state operation. A relation between the quality of the sensors and ripple in steady state operation is determined numerically. This relation allows for a less conservative selection of the sensors of the converter.

Many new methods are being developed for the design of sliding mode controllers. Applying the resulting controllers in power electronic converters requires a careful design of the switching algorithm. In converters with multiple switched inputs, a careful design of the switching surface and the switching logic can improve the performance of the controlled system. Unmodeled dynamical behavior such as the dynamics of sensors can also affect the performance of the converter significantly. Numerical simulations are a useful tool for detecting the viable designs with respect to the range of acceptable unmodeled behavior.
Date of Award28 Nov 2019
Original languageEnglish
Awarding Institution
  • The University of Bristol
SupervisorMike R Jeffrey (Supervisor) & Xibo Yuan (Supervisor)

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