Robust control stability using the error loop

The paper briefly formulates the error loop as a tool for designing robust stability control systems in front of structured and unstructured uncertainties. The error loop indicates that a tool for accommodating such uncertainties is the noise estimator, which is the unique feedback channel from plant to control. It is shown that the causality constraint preventing perfect cancellation of causal uncertainties (unknown disturbance), makes also control law to play a role, 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 parameter and requirements. A simple example is provided from a ball and beam plant.