Robust Control of Plants with Parametric Uncertainties

Ulf Holmberg, Yves Piguet, LONGCHAMP Roland

Physical systems are often characterized by a set of parameters that must be measured or estimated experimentally. Naturally, measurement and estimation errors are inevitable; however, it is also often possible to bound the magnitude of the errors. For example, the least-squares method for parameter estimation yields the value of a nominal parameter vector and, in addition, it also produces bounds on the parameter estimation error. These can be expressed as ellipsoidal bounds . Two different robust control synthesis procedures have been developed for plants with ellipsoidal uncertainty bounds. One is an interactive pole placement approach. A special CAD program has been written that takes advantage of the human capability to interpret and feel changes of colors and shapes displayed on the computer screen. The other approach is non-interactive. It is based on multiple models that are chosen to well represent the uncertainty. The closed-loop poles that are outside a specified D stability region are repeatedly projected inside for each model at a time. This approach was successfully used in the identification for control strategy applied to a magnetic suspension system (Identification for Control). The latter approach, based on multiple models, can also be refined by using the multi-model techniques described in Multi-model Weighted Pole Placement Design and Multi-objective Design Using Multiple Models.

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Holmberg U., Y. Piguet and D. Bonvin. Robust Control Synthesis for Plants with Parametric Uncertainties. ECC’95, (September 1995), Rome, Vol. 4, pp. 3025-3030