Adaptive Kalman filter for active magnetic bearings using softcomputing

Magnetic bearings can not only solve the bearing wear and life problems but also reduce the loss and noise of bearing. However, the strong disturbance and noise from the system affects the control behavior. Based on the Kalman filter the influence of noise will be reduced. But the strong nonlinear and uncertainty of parameter of the magnetic bearings make it difficult to establish the estimation / prediction equation in Kalman filter. This paper presents a design method of system estimation / prediction for Kalman filter with using soft computing. Firstly, linear local model for axial magnetic bearing overall system will be deduced. Then a few system parameters, which is relative with nonlinear and uncertainty, will be obtained by a intelligence function, which uses soft computing algorithm as system identification. Finally, the identified system parameters will be used in state equation in Kalman filter. It aims at better filter performance and state estimation than the conventional linear Kalman filter. A. Introduction Many works have shown, that AMBs have tremendous potential for many high speed industrial applications. The new approach aims to get a better filter performance and system observer by introducing a Kalman filter. Because of the intense nonlinear performance of the magnetically suspended bearings, the traditional linear system model is difficult to guarantee the accuracy in comparison with the actual system, when the system is far from the working point. As a result the filter function will be reduced. Thus a new approach for a precise system prediction for Kalman filter will be searched. The soft computing consists of fuzzy logic, artificial neural network, and neural fuzzy logic. In the method, the relationship between the large amount of input and output are established. As the widely used intelligent model, it is essentially one nonlinear model and is easy to describe a complicated dynamic system. It has been proved that soft computing model can identify arbitrary nonlinear system and system parameters with a high precision [2]. This paper demonstrates a soft computing variation of the system equation in Kalman filter, with experimental validation on a simulated active axial magnetic bearing. Despite its highly nonlinear and uncertain nature, the dynamics of AMB system are represented using an adaptive linear model with parameters that are identified by system identification with soft computing. In paragraph B a linear Kalman for this system will be introduced. In paragraph C the artificial neural networks are an important tool of the identification for the system parameters. In paragraph D a expert system, which is based on fuzzy rule, using a radial basis function and the result from identification, will be designed for a adaptive Kalman filter. Lastly the simulation’s result will be showed. Fig 1: concept of the adaptive Kalman filtering in closed loop B. Traditional linear Kalman filter for magnet bearing The first step of Kalman filter is to design the system state equation. This paragraph proposes linear discrete equation model on the basis of the force analysis of rotors and linearization of the magnetic force. The Kalman filter embodies the process and measurement noise. We design a Kalman filter with the constant noise. Detailed analysis is listed as follows. Force Analysis of the Single Degree Axial Magnetic Bearing Im magnetic bearing system, single degree magnet poles are usually assembled symmetrically as showed in Fig 2 a pair of electromagnetic forces opposite in direction is created simultaneously be adopting a pair of symmetric power amplification circuits and driving the electromagnet in differential mode. When the rotor is at the geometric center of the bearing, the distances between rotor and air gaps are 0 s . There is equal current 0 i , which is also termed as magnetic biasing current between the upper and lower magnet poles to set up magnetic field. An any working state, if the rotor bias is x, then the air gap between rotor and lower magnet is x s  0 . Accordingly, the air gap between rotor and lower magnet is x s  0 . So the resultant force generated by this pair of magnet poles is: [3] URN (Paper): urn:nbn:de:gbv:ilm1-2014iwk-031:9 58th ILMENAU SCIENTIFIC COLLOQUIUM Technische Universität Ilmenau, 08 – 12 September 2014 URN: urn:nbn:de:gbv:ilm1-2014iwk:3