Introduction to Embedded Model Control

The chapter is a brief introduction to the embedded model control methodology. Preliminary is Chapter 13 , where the state predictor and control law have been constructed and their errors studied. Crucial is the distinction between design model, where four classes of uncertainty (initial state, causal and parametric uncertainty, neglected dynamics) are included, and the embedded model, where only the initial state and causal uncertainty are retained. In Chapter 13 , a the separation theorem between state predictor and control law design completely ignored the neglected dynamics and postulated a perfect cancellation of the (nonlinear) cross-coupling terms affected by parametric uncertainty. Only initial state and causal uncertainty remained, and both of them were predicted and canceled from the design model except for bounded residuals. A design model with neglected dynamics and parametric uncertainty renders invalid the separation theorem of Chapter 13 and requires a revised pole placement. Because the additional uncertain terms do not enter the embedded model, state predictor and control law maintain the same structure as in Chapter 13 . Only their closed-loop spectra require to be redesigned. The revised pole placement of this chapter exploits the small gain theorem and simple bounding functions of the neglected dynamics and parametric uncertainty. The objective is to find a kind of separation (actually a sequential design) between predictor and control pole placement. The justification comes from the causality correction of Chapter 13 , which shows that a predictor sensitivity, which has been a priori designed (now by taking into account the additional uncertainty), does not significantly change, if the control law bandwidth (BW) is a posteriori chosen to be sufficiently wider than the predictor BW. The relevant design, referred to as standard design, was employed throughout book. An SISO attitude case study affected by a challenging neglected dynamics accompanies the theory illustration.