Embedded model control calls for disturbance modeling and rejection

Abstract

Robust control design guarantees closed-loop stability of a model-based control law in the presence of parametric uncertainties. Stability is guaranteed by introducing some ignorance coefficients and restricting the feedback control effort. Embedded Model Control shows that the model-based control law can be kept intact in the case of uncertainty, if the controllable dynamics is complemented by a suitable disturbance dynamics. The disturbance state must be driven by an unpredictable input vector, the noise, which can only be estimated from the model error i.e. the difference between plant and model output. The uncertainty-based design concerns the noise estimator, so as to prevent the model error from conveying uncertainty components which are command-dependent and thus prone to destabilizing the controlled plant. Separation of the components in the low and high frequency domain by the noise estimator itself allows stability recovery and guarantee, and the rejection of low frequency components. Two simple case studies help to understand the key assets of the methodology.

On the centrality of disturbance rejection in automatic control

“…Another form of rejector is the embedded model control approach proposed by Canuto [25] where the uncertainty is estimated online and canceled with control action. These are but a few examples, all of which can be well explained by the concept of total disturbance and the structure of DRC, shown in Fig.…”

The four-tank control problem: Comparison of two disturbance rejection control solutions

“…As a second extension, control algorithms are directly designed in the discrete-time domain on the basis of the so called embedded model, which is a kind of internal model at the core of the control unit. According to the Embedded Model Control (EMC, [25], [26]) methodology, embedded model must include suitable disturbance dynamics (not necessarily first order as in ESO and ADRC), which is driven by arbitrary bounded signals playing the role of driving noise. Model endowment with disturbance dynamics is a key tool for decoupling control strategies as shown in [27] and [28].…”

Embedded Model Control: Design separation under uncertainty

“…The model error has been shown by the Embedded Model Control (see [1], [2] and [3]) to be the key signal in designing control systems, being capable of separating uncertainty estimation and model-based control design. Error (1) is the key signal of the Internal Model Control ( [4], [5] and [6]).…”

“…The SISO case has been treated in [1], [2] and [3]. A case study, spacecraft attitude control accompanies the paper (see also [12]).…”

“…Only causal uncertainty enters the embedded model and must be estimated. Section 3 outlines the uncertainty estimator and the equations of the prediction error ˆy e in (2). The error equation is converted into a transfer function to express, in a compact form, the error as a result of uncertainty.…”