Embedded model control: Reconciling modern control theory and error-based control design

The paper addresses the problem of reconciling the modern control paradigm developed by R. Kalman in the sixties of the past century, and the centenary error-based design of the proportional, integrative and derivative (PID) controllers. This is done with the help of the error loop, whose stability is proved to be necessary and sufficient for the close-loop plant stability. The error loop is built by cascading the uncertain plant-to-model discrepancies (causal, parametric, initial state, neglected dynamics), which are driven by the design model output and by arbitrary bounded signals, with the control unit transfer functions. The embedded model control takes advantage of the error loop and its equations to design appropriate algorithms of the modern control theory (state predictor, control law, reference generator), which guarantee the error loop stability and performance. A simulated multivariate case study shows modeling and control design steps and the coherence of the predicted and simulated performance.