Experimental validation of the Newton observer for a nonlinear flux-controlled AMB system operated with zero-bias flux

ABSTRACT

The paper presents the results of experimental validation of the Newton observer for estimation of the magnetic flux within the feedback control of a nonlinear active magnetic bearing (AMB) system. In the preliminary work the Newton observer was adapted for the exact discrete-time model of the simplified one-degree-of-freedom AMB system, operated with zero-bias flux and under the voltage switching strategy, and showed good results in case of numerical simulations. The objective of this paper is to confirm these results on the basis of experimentation. The experiments were conducted on the AMB test rig, developed and manufactured at Bialystok University of Technology.

KEYWORDS:

• Active magnetic bearing
• Newton observer
• zero-bias
• flux control

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

A. Mystkowski http://orcid.org/0000-0002-5742-7609

Ü. Kotta http://orcid.org/0000-0002-7697-769X

V. Kaparin http://orcid.org/0000-0002-4968-2474

Notes

1. In the case when the number of equations exceeds the number of states, the inverse in (5) should be replaced by a pseudoinverse.

2. Note that though we use the full-order Newton observer (estimating all three states), in (6(6) $u=-3x_1^2{x}_3-2x_2\left|x_3\right|-3x_1{x}_2{x}_3-x_3+u_0,$(6) ) the measured value of the state $x_1$ is employed.

3. Note that the plots throughout the paper depict the trajectories of the physical parameters x, $\dot{x}$, and φ but not the non-dimensionalised variables $x_1$, $x_2$, and $x_3$. The physical parameters can be easily obtained from the non-dimensionalised variables using the relations (1(1) $\begin{array}{rl}{x}_1& :=\frac{x}{g_0},x_2:=\frac{\dot{x}\sqrt{\kappa }}{{\mathrm{\Phi }}_{\mathrm{sat}}\sqrt{g_0}},x_3:=\frac{\phi }{{\mathrm{\Phi }}_{\mathrm{sat}}},\\ u& :=\frac{v\sqrt{g_0\kappa }}{N{\mathrm{\Phi }}_{\mathrm{sat}}^2},\tau :=t\frac{{\mathrm{\Phi }}_{sat}}{\sqrt{g_0\kappa }},\end{array}$(1) ).

4. The disturbance is the external load/force acting on the shaft supported by AMB. This force is used to test the shaft stability. For simplicity we represent the disturbance as voltage. The power amplifier converts this voltage into the disturbance current with amplitude ±1 A, resulting in the disturbance force generated by the electromagnets.

5. Hereinafter, with a slight abuse of notation, we will use the symbol y for the vertical axis and not to denote the output of the system, as in Sections 2 and 3.

Additional information

Funding

The scientific work of A. Mystkowski and A. Kierdelewicz was realised in frame of work no. S/WM/1/2016 and financed from research funds of Ministry of Science and Higher Education. The work of V. Kaparin was supported by the Estonian Centre of Excellence in IT (EXCITE), funded by the European Regional Development Fund.