A practical loop-shaping approach for pole-placement in mechatronic systems

Manual design of feedback-controllers based on frequency-domain data is often used in industry to design low-order SISO controllers based on experimental data. Such design approaches are often either based on a data representation in the pole-zero plane, i.e. root-locus approaches, or a representation of the open-loop frequency response function (FRF), i.e. shaping of the sensitivity function. Both data representations however are not explicitly coupled during tuning to combine the advantages of both design methods. A new approach is proposed which combines both data representations into one controller design method such that loop-shaping in an extended form can be used to place closed-loop poles. By means of generalized stability, performance demands given in the pole-zero plane can be linked to phase and gain specification of the open-loop transfer-function. As a results, this method generalizes and refines the well known loop-shaping approach. Simulations and experiments with a two-mass-spring system show that transient behavior can be improved significantly compared to controllers that are designed on FRF data only.