Embedded Model Control approach to robust control

Abstract

Robust control design is mainly devoted to guarantee closed-loop stability of a model-based control law in presence of parametric and structural uncertainties. The control law is usually a complex feedback law which is derived from a (nonlinear) model, possibly complemented with some mathematical envelope of the model uncertainty. Stability may be guarantee with the help of some ignorance coefficients and restricting the feedback control effort with respect to the model-based design. Embedded Model Control shows that under certain conditions, the model-based control law must and can be kept intact under uncertainty, if the controllable dynamics is complemented by a suitable disturbance dynamics capable of real-time encoding the different uncertainties affecting the 'embedded model', i.e. the model which is both the design source and the core of the control unit. To be real-time updated the disturbance state is driven by an unpredictable input vector, called noise, which can be only estimated from the model error. The uncertainty (or plant)-based design concerns the noise estimator, as the model error may convey into the embedded model uncertainty components (parametric, cross-coupling, neglected dynamics) which are command-dependent and thus prone to destabilize the controlled plant. Separation of the components into the low and high frequency domain by the noise estimator allows to recover and guarantee stability, and to cancel the low frequency ones from the plant. Among the advantages, control algorithms are neatly and univocally related to the embedded model, the embedded model provides a real-time image of the plant, all control gains are tuned by fixing closed-loop eigenvalues. Last but not least, the resulting control unit has modular structure and algorithms, thus facilitating coding. A simulated case study helps to understand the key assets of the methodology.