4 Modal Control of Magnetic Suspended Rotors 33 Step 2: Insert the worst cases in the optimization process in order to meet the design requirements for all models handled in the previous iteration. Then, return to step 1. It is important to mention that at step 0, the initial controller does not need to be based on the modal approach [17] employed as a starting point an initial controller designed on the basis of the H1approach. In step 1, which is dedicated to identifying the worst cases, the use of the analysis technique is quite attractive for the evaluation of robust stability due to the presence of structured uncertainties. 4.3 Model and Numerical Results The test rig presented in Fig. 4.1 is composed by three main parts: the flexible rotor supported by radial AMB’s, the controller and the external interface MBResearch™. It consists of a demonstration kit manufactured by SKF and is delivered with a control architecture based on a SISO PID controller, connected in series with a bank of filters. The shaft is supported by two identical radial AMB’s to provide a maximum load capacity of 283 N. Such components are energized by a bias current of 1.0 A, and are capable of supporting a maximum current of 3.0 A. The shaft is driven by an electric motor of 500 W, operating in the range of 0 to 12,000 rpm. The kit is also equipped with two conventional backup ball bearings, located at both ends of the shaft, devoted to support the rotor in the case of any failure in the magnetic levitation. The nominal clearance between the surface of the shaft and the inner ring of the backup bearings is approximately 0.1 mm. Table 4.1 presents the main parameters of the system. The first step was to develop individual computational models for each main component of the system (showed in Fig. 4.2) based on the design specification provided by the manufacturer. The following step was the assembling of those component models into a global one. Once the AMB’s stiffness parameters were determined, it was necessary to consider the subsystem represented by the rotor itself. In this case, the model was also based on the Finite Element method. For this aim, a proprietary software specially designed for handling rotordynamics problems was used, as developed in MATLAB environment. In order to properly represent this subsystem, the rotor was discretized into 51 Timoshenko beam elements, considering 4 dofs per Fig. 4.1 Experimental Test Rig Table 4.1 System parameters Parameter description Unit Number of turns per coil, N 276 – Air gap, g0 0.364 mm Pole cross sectional area, Ag 430.74 mm2 Maximum voltage 10 V Bias current, ib 1 A Current stiffness, ki 143.76 N/A Position stiffness, ks 0.395 N/m AMB load capacity 283 N Shaft length 645 mm Discmass 5.89 kg Motor power 500 W Operation range 0–12,000 rpm
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