Development of an Automatic Elastic Torque Control System Based on a Two-Mass Electric Drive Coordinate Observer
- shock (impact) loads that result in fatigue destruction of mechanical equipment;
- vibrations that occur in the shaft lines of stands and in the electromechanical systems that are resiliently connected by the strip;
- instability of control systems due to torque limitations being applied to the electric drives.
2. Problem Formulation
- Earlier papers present research into electromechanical systems with two electric machines installed on the ends of an elastic shaft [42,43]. This enables control over the coordinates of both electric machines. These parameters include speeds and currents, which are used to calculate the torques of these machines as well as the elastic shaft torques. These coordinates are used in control algorithms.
- Dynamic processes should be presented in the form of continuously measured physical parameters yet require minimum computing.
- Controllable coordinates are motor speed and torque as well as the applied load torque. The output coordinates are the roll speed and the elastic torque of the spindle.
- The developed solutions should not require complex mathematics (computing) and should be implementable in the controllers already used by the rolling mill APCS (automatic process control system).
3. Materials and Methods
4.1. Development of the Closed Coordinate Control System for the Uncontrolled Mass
4.2. Simulation Results
- the amplitude margin is 10 dB, which is sufficient per Nyquist criterion;
- the phase plot is beak-shaped, no crossing through −180° to the left of the cutoff frequency; the phase margin is about 50°, which is also sufficient.
5. Experimental Results
- The system under consideration is a two-mass system where the first mass (the motor’s rotor) does not change its inertia.
- The stiffness of the elastic shaft (spindle) does not change either. This parameter depends on the length, diameter, and the properties of the metal that the shaft is made of. These parameters do not change even when the spindle is replaced.
- Second mass inertia depends on the mass of work and backup rolls, which is constant as well. The inertia of the rolled bar is 5% to 15% of the total second mass inertia. For configuration, use the mean bar inertia that deviates by 1.7% to 5%. Such deviations are commensurate with the error of the instrumentation sensors. Thus, they do not cause significant error in the configuration of the control algorithms.
5.1. Accuracy of Reconstructed Two-Mass Coordinates
- Greater gauge is associated with greater overshoot. Thus, at 9 mm, i.e., in the later passages, the ‘gapless’ amplitude is 35%, and the ‘gapped’ amplitude is 45%. In case of 30 mm gauge (the earlier passages), it is 240% and 212%, respectively.
- The torque component that stems directly from the gap-closing shock (impact) is relatively insignificant at 6.9% at 9 mm (1.55 and 1.45 p.u. of difference in amplitudes), 8.6% at 30 mm (2.4 and 2.21 p.u., respectively). This indirectly confirms that the ‘elastic’ torque component has the maximum impact on torque overshoot .
- Relative difference between actual and reconstructed values decreases as the gauge increases: 6.9% at 9 mm, 5.6% at 18 mm, and 4.1% at 30 mm.
5.2. Testing the Electric Drive Coordinates in the Developed Three-Loop System
- kSm was 1.8 with the initial configuration, changed to kSm = 1.2 after implementing the new algorithm. Thus, the algorithm reduced the torque amplitude by a factor of 1.5.
- kSm was 1.4 for the UMD torque MMT, 1.12 for LMD, i.e., reduced by a factor of 1.25.
- Elastic oscillations attenuated at least twice as fast. kSm was 1.4 for the UMD torque Mmt, 1.12 for LMD, i.e., reduced by a factor of 1.25.
6. Discussion of the Results
- in case of gripping with pre-closed angular gaps in spindle joints, difference in the amplitudes of the measured vs reconstructed torque averages at 5 to 7%;
- equivalent difference in case of open gaps hits 10%.
- proportional speed controller for the first mass, whose output is the target motor torque;
- proportional controller of elastic torque. This configuration is optimal because the object structure contains an integrator, and this controller provides high performance;
- proportional speed controller for the second mass, which features a corrective proportional integral element at the input. This element increases the slope of the Bode magnitude plot in the low-frequency domain and enables astatic control over the second mass speed.
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
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|Moment of inertia of the first moving mass (the motor)||J1||kg∙m2||125,000|
|Moment of inertia of the second moving mass (the roll)||J2||kg∙m2||114,571|
|Elastic coupling rigidity||c12||N∙m/rad||5,934,842|
|Eigenfrequency of elastic oscillations||ω12||rad/s||9.96|
|Electric drive acceleration||ε0||rad/s2||1–3|
|Mean elastic torque||M12||MN∙m||1.9|
|Speed controller gain||ksc||-||19.5|
|Speed controller time constant||Tsc||s||0.0041|
|Gauge||Measured Values||Observer Values|
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Radionov, A.A.; Karandaev, A.S.; Gasiyarov, V.R.; Loginov, B.M.; Gartlib, E.A. Development of an Automatic Elastic Torque Control System Based on a Two-Mass Electric Drive Coordinate Observer. Machines 2021, 9, 305. https://doi.org/10.3390/machines9120305
Radionov AA, Karandaev AS, Gasiyarov VR, Loginov BM, Gartlib EA. Development of an Automatic Elastic Torque Control System Based on a Two-Mass Electric Drive Coordinate Observer. Machines. 2021; 9(12):305. https://doi.org/10.3390/machines9120305Chicago/Turabian Style
Radionov, Andrey A., Alexandr S. Karandaev, Vadim R. Gasiyarov, Boris M. Loginov, and Ekaterina A. Gartlib. 2021. "Development of an Automatic Elastic Torque Control System Based on a Two-Mass Electric Drive Coordinate Observer" Machines 9, no. 12: 305. https://doi.org/10.3390/machines9120305