Goranka Štimac

Comparative analysis of PSO algorithms for PID controller tuning

The active magnetic bearing(AMB) suspends the rotating shaft and maintains it in levitated position by applying controlled electromagnetic forces on the rotor in radial and axial directions. Although the development of various control methods is rapid, PID control strategy is still the most widely used control strategy in many applications, including AMBs. In order to tune PID controller, a particle swarm optimization(PSO) method is applied. Therefore, a comparative analysis of particle swarm optimization(PSO) algorithms is carried out, where two PSO algorithms, namely (1) PSO with linearly decreasing inertia weight(LDW-PSO), and (2) PSO algorithm with constriction factor approach(CFA-PSO), are independently tested for different PID structures. The computer simulations are carried out with the aim of minimizing the objective function defined as the integral of time multiplied by the absolute value of error(ITAE). In order to validate the performance of the analyzed PSO algorithms, one-axis and two-axis radial rotor/active magnetic bearing systems are examined. The results show that PSO algorithms are effective and easily implemented methods, providing stable convergence and good computational efficiency of different PID structures for the rotor/AMB systems. Moreover, the PSO algorithms prove to be easily used for controller tuning in case of both SISO and MIMO system, which consider the system delay and the interference among the horizontal and vertical rotor axes.

Modeling and experimental verification of a flexible rotor/AMB system

Purpose – In this paper, the aim is to present a modeling strategy for a flexible rotor/active magnetic bearing (AMB) system with non‐collocation. Special attention is paid to the vibration reduction and the stable passage through the first critical speed.Design/methodology/approach – The finite element method based on Euller‐Bernoulli beam theory is applied in the formulation of the rotor model. Since rotor/AMB systems are complex mechatronic systems, reduced order approach is used in the control system design. This study applies the modal decomposition method and the modal truncation method, thus retaining the lower order bending modes. The obtained numerical results are compared with the measured open loop frequency responses and the existing differences are compensated in order to obtain accurate numerical model.Findings – Frequency response of the entire system model (flexible shaft, actuators, power amplifiers and sensors) with amplitudes expressed in rotor lateral displacements can be verified by t...

Light Rotor-Stator Partial Rub Characterization Using Instantaneous Angular Speed Measurement

Instantaneous angular speed (IAS) measurement is recently recognized as a promising technique for condition monitoring of various rotating machines and their subsystems. There are various approaches considering counting techniques and processing of signal. This paper considers application of analog signals from toothed wheel encoder or zebra tape encoder and acquisition at low to moderate sampling rates. Such a system can experience problems with non-uniformity of encoder segments geometry, thus correction of encoder segment non-uniformity was performed. The rubbing often occurs in rotating machinery at position with small clearances and can sometimes cause catastrophic breakdown of machine. So it is important to develop reliable tools for rub diagnosis. As the rubbing process is nonlinear this paper beside conventional Fourier transform also considered potential of sifting operation of Empirical mode decomposition (EMD) method. EMD was employed to produce intrinsic mode functions (IMFs) and to further improve the detection capabilities of Fourier transform. Developed procedure for IAS measurement was successfully tested on laboratory test rig for rotor to stator contact dynamics investigation at speed transition from no rub to light rotor to stator partial rub condition.

Efficient approach for encoder geometry compensation in time interval measurement of torsional vibration

While it is usually a design goal to avoid torsional natural frequencies, there are systems where resonances will be encountered during normal operation. This paper considers time interval measurement of torsional vibration and problems connected with uneven encoder geometry. Such a problem is usually manifested as high-level order content in frequency spectrum. To prevent mentioned problem an in-situ segment compensation method is proposed that creates a time reference array representative of actual angular segments geometry. The method is experimentally tested on two different encoding devices. First was non-contact eddy current sensor and toothed wheel while the second was optic sensor together with zebra tape. The second encoding device showed better test results and less sensitivity on uneven encoder geometry.

Rotor-Stator Partial Rub Diagnosis Using Hilbert Huang Transform

Rotor–stator rubbing is occasional problem faced by rotating machines especially during startups and shut downs when passing through their critical speeds. The rubbing often occurs in rotating machinery at position with small clearances and can sometimes cause catastrophic breakdown of machine. So it is important to develop reliable tools for rub diagnosis. This paper investigates partial rub occurrence during constant and slightly variable speed operation and try to define vibration diagnosis patterns for its detection with Hilbert Huang Transform (HHT). The HHT is relatively new method which includes Empirical Mode Decomposition (EMD) and the Hilbert Transform. Diagnostic tool is tested on laboratory test rig for rotor to stator contact dynamics research at two different rotor operating conditions i.e. without rotor–stator contact and with partial rotor–stator rub. Measurements were performed with non-contact eddy current displacement sensors. Results are presented in the shape of HHT spectra of Intrinsic Mode Functions (IMF) and are compared to classical FFT spectra and spectrograms based on Short Time Fourier Transform (STFT). Rotor orbits are also presented to additionally verify rubbing condition.

Modeling, design and control of a flexible rotor supported by active magnetic bearings

In this paper an approach to analyze and stabilize a decentralized rotor/AMB system while passing the first critical speed is presented. Since the related difficulties emerge from the sensor/actuator non-collocation a set of finite element calculations and relevant rotordynamic studies are proposed and carried out. In such a way the adequate mechanical configuration of the system is found and proper controllability and observability is ensured. In accordance with the simulation results, the test rig is assembled. Finally, successful run up and run down analyses were carried out, which validated the efficiency of the presented procedure.