Title: Robust control stability using the error loop

Authors: Enrico Canuto; Wilber Acuña-Bravo; Carlos Perez Montenegro

Addresses: Politecnico di Torino, Department of Control and Computer Engineering, Corso Duca degli Abruzzi 24, 10129 Turin, Italy ' Politecnico di Torino, Department of Control and Computer Engineering, Corso Duca degli Abruzzi 24, 10129 Turin, Italy ' Politecnico di Torino, Department of Control and Computer Engineering, Corso Duca degli Abruzzi 24, 10129 Turin, Italy

Abstract: This paper formulates the error loop as a tool for designing robust stability control systems in the presence of structured and unstructured uncertainties. The error loop indicates that uncertainties can be accommodated through the design of the noise estimator, which is the unique feedback channel from plant to control. The real-time model that is embedded in the control unit and the noise estimator constitute a state predictor. The embedded model consists of a controllable dynamics plus a disturbance dynamics fed by the noise estimator. It is shown that causality constraint prevents perfect cancellation of causal uncertainties (unknown disturbance), but makes the control law which is fed by the state predictor to play a role, thus offering a further degree of freedom. Employing asymptotic expansions of the closed-loop transfer functions, simple, explicit design formulae derive from stability inequalities. They relate closed-loop eigenvalues to model parameters and requirements, and define an admissible frequency band for the state predictor bandwidth. This paper restricts formulation to the univariate case. A simple example is provided with simulated and experimental data.

Keywords: robust control stability; closed loop; error loop; embedded model control; uncertainties; modelling.

DOI: 10.1504/IJMA.2013.053403

International Journal of Mechatronics and Automation, 2013 Vol.3 No.2, pp.94 - 109

Available online: 17 Apr 2013 *

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