Non-linear control of a series direct current motor via flatness and decomposition in the bond graph domain

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A bond graph (BG) based methodology for non-linear control system synthesis is presented through its application to a speed-tracking problem stated on a series direct current motor. After a global flatness analysis of the motor BG model, a two-loop cascade control structure is decided and developed on the basis of a physical system decomposition in electrical, mechanical, and coupling submodels. Each loop of the cascade tracks a reference for a flat output that is local to a subsystem of the decomposition. Bond graph techniques are given for the three main components of the design methodology: system decomposition, flatness analysis, and tracking controller design. Theoretical and practical properties of the resulting control system are discussed, and its performance is demonstrated through simulation experiments. The methodology is applicable to the broader class of non-linear BG models where input-output system inversion is well defined.