[Paper Review] State Observers for Sensorless Control of Magnetic Levitation Systems

Alexey Bobtsov, Anton A. Pyrkin+2 more|arXiv (Cornell University)|Nov 7, 2017

Magnetic Bearings and Levitation Dynamics6 references3 citations

TL;DR

This paper proposes a novel sensorless control strategy for nonlinear magnetic levitation (MagLev) systems using adaptive state observers that estimate position and velocity from only voltage and current measurements. By combining parameter estimation-based observers with dynamic regressor extension and mixing (DREM), the method reconstructs magnetic flux and enables globally convergent state estimation, achieving performance comparable to full-state feedback control in simulations for both 1- and 2-degree-of-freedom systems.

ABSTRACT

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.

Motivation & Objective

• Address the challenge of sensorless control in nonlinear magnetic levitation systems where only voltage and current are measurable.
• Overcome the high cost and reliability issues of position sensors in MagLev systems by eliminating the need for direct position measurements.
• Develop globally convergent state observers for mechanical states (position, velocity) using only electrical measurements.
• Design a unified observer framework applicable to both 1- and 2-degree-of-freedom MagLev systems, despite their differing mathematical complexity.
• Ensure the proposed observer-based controller achieves performance indistinguishable from full-state feedback control in simulation.

Proposed method

• Use parameter estimation-based observers (PEBO) combined with dynamic regressor extension and mixing (DREM) to reconstruct magnetic flux from voltage and current signals.
• Leverage the reconstructed flux to design tailored nonlinear observers for mechanical coordinates (position and velocity) in both 1- and 2-dof MagLev systems.
• Apply a certainty equivalence principle by replacing full-state feedback control laws with estimated states from the observer.
• Utilize the IDA-PBC (Interconnection and Damping Assignment Passivity-Based Control) as the full-state stabilizing controller, which is then adapted for sensorless operation.
• Impose excitation conditions on the extended regressor signals to ensure convergence of the parameter estimation and observer design.
• Validate the design through simulation on both 1- and 2-dof MagLev systems, comparing sensorless performance to full-state feedback.

Experimental results

Research questions

• RQ1 Can a globally convergent state observer be designed for MagLev systems using only voltage and current measurements, without position sensors?
• RQ2 How can magnetic flux be accurately reconstructed from electrical signals in nonlinear MagLev systems using adaptive estimation techniques?
• RQ3 Why do 1-dof and 2-dof MagLev systems require fundamentally different mathematical approaches for observer design despite similar physical principles?
• RQ4 To what extent does the proposed sensorless controller match the performance of a full-state feedback controller in terms of transient response and stability?
• RQ5 What excitation conditions are necessary for the convergence of the DREM-based parameter estimation and observer, and how can they be practically satisfied?

Key findings

• The proposed observer successfully estimates position and velocity in both 1- and 2-dof MagLev systems using only voltage and current measurements, achieving global convergence.
• Simulation results show that the sensorless controller's performance closely matches that of the full-state feedback IDA-PBC, with negligible differences in transient response and trajectory tracking.
• The 2-dof system allows for a simpler observer design compared to the 1-dof system, which requires more complex parameter estimation and filtering due to structural differences.
• The method avoids invasive high-frequency signal injection, unlike some prior approaches, by relying on inherent system dynamics and DREM-based excitation.
• Convergence of the observer depends on excitation conditions on the extended regressor signals, which are shown to be satisfied under realistic assumptions about system energy and signal richness.
• The computational complexity of the observer remains a challenge for real-time implementation, particularly for the 1-dof case, suggesting a need for controller approximation in future work.