In this paper we address the problem of state observation for sensorless control of nonlinear magnetic levitation systems, that is, the regulation of the position of a levitated object measuring only the voltage and current of the electrical supply. Instrumental for the development of the theory is the use of parameter estimation-based observers, which combined with the dynamic regressor extension and mixing parameter estimation technique, allow the reconstruction of the magnetic flux. With the knowledge of the latter it is shown that the mechanical coordinates can be estimated with suitably tailored nonlinear observers. Replacing the observed states, in a certainty equivalent manner, with a full information globally stabilising law completes the sensorless controller design. We consider one and two-degrees-of-freedom systems that, interestingly, demand totally different mathematical approaches for their solutions. Simulation results are used to illustrate the performance of the proposed schemes.
The recently proposed Dynamic Regressor Extension and Mixing (DREM) procedure has been proven to enhance transient performance in online parameter estimation and it has been successfully applied to a variety of adaptive control problems and applications. However, to use this procedure, a linear operator has to be chosen to perform the dynamic extension. A poor choice of the operator can reduce excitation of signals and hence it can compromise convergence properties. This paper presents a systematic selection of operators such that the excitation is always preserved. The paper also studies convergence conditions when the DREM procedure is combined with a least-squares estimator.
A new algorithm was proposed to estimate all parameters of the polyharmonic signal such as frequencies, amplitudes, phases, and shifts. Exponential convergence to zero of the errors of estimating the desired parameters was shown. The algorithm features noise-immunity to additive noise in the measurement channel. The dynamic dimensionality of the estimation algorithm is 3k, where k is the number of harmonics,
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