The suspension module control system model has been established based on MIMO (multiple input and multiple output) state feedback linearization. We have completed decoupling between double suspension points, and the new decoupling method has been applied to CMS04 magnetic suspension vehicle in national mid-low-speed maglev experiment field of Tangshan city in China. Double suspension system model is very accurate for investigating stability property of maglev control system. When magnetic flux signal is taken back to the suspension control system, the suspension module’s antijamming capacity for resisting suspension load variety has been proved. Also, the external force interference has been enhanced. As a result, the robustness and stability properties of double-electromagnet suspension control system have been enhanced.
Maglev vehicle has minor noise, no pollution safety, and comfort many other advantages, so the maglev traffic has a bright prospect in the future. Maglev vehicle concludes several complex subsystems [
CMS04 mid-low-speed maglev vehicle.
EMS middle- and low-speed maglev vehicle applies modular suspension bogies, and one module concludes two suspension points. Double suspension points’ suspension task is accomplished by one suspension controller.
Assume the following: the leakage flux of magnetic winding is neglected; the magnetic resistances of the ferrite core and rail are neglected; namely, magnetic potential falls on air gap the inclination angle of magnetic rigid body is minuscule, and active point of magnetic force is considered invariable; the action line of load forces is superposed with direction of suspension gap measured; distribution of mass of the bracket is even, and the masses of two magnets are equal, so the action point of gravity is superposed on the geometry center
Based on above assumptions, the force analysis and geometrical relationship of maglev system are showed in Figure
Suspension system’s force analysis map.
Signs of Figure
Symbols in double suspension points system.
Signs | Signification |
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Number of magnetic coils |
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Magnetic resistance |
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Magnetic permeability of atmosphere |
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Acceleration of gravitation |
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Separation angle between electromagnet axis line and horizon |
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Electromagnetic force of suspension point |
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Disturbing force of suspension point |
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Total length of electromagnet |
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Current of magnetic coil in suspension |
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Voltage of magnetic coil in suspension point |
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Measured position value in suspension point |
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Average gap value between guideway and suspension point |
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Magnetic pole area |
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Suspension gap flux density |
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Total mass of suspension system |
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Rotation inertia of electromagnet for |
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Distance from guideway to |
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Electromagnetic force of suspension point |
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Disturbing force of suspension point |
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Disturbing force of arm relative |
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Current of magnetic coil in suspension point |
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Voltage of magnetic coil in suspension point |
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Measured position value in suspension point |
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Average gap value between guideway and suspension point |
When electromagnet module is in condition of balance, we can obtain the equation
Extract acceleration signals from (
Set
Simplify (
We can get geometrical relationship of parameters in Figure
Magnetic force equations are as follows:
Voltage balance equations of electromagnet winding are denoted in (
Substituting (
From (
On all accounts, the dynamic law of maglev system can be determined by the following equations:
Choose
Simplify (
MIMO affine nonlinear system is described as
Set the equilibrium point
Define the equilibrium point of maglev system
Namely, above equations satisfy
At the moment,
Therefore, Theorem
Compute the vector field generated by
Design feedback control value
We can obtain the control value after linearization from (
The diffeomorphic mapping matrix is
Choose the coordinates of transformation by matrix
In sum, maglev control system model after linearization is showed as follows:
Maglev system after feedback linearization is expressed by two-level integral subsystems:
Double suspension points’ closed control block diagram with magnetic flux feedback is showed in Figure
Double suspension points’ control construction diagram with feedback linearization.
Controlled matrix of system (
Because of
The geometrical relationship between measured positions and real physical positions in (
We can get
By now, double suspension points’ controller based on magnetic flux feedback was completed. Construction of the controller is described in Figure
Block diagram of double suspension points system.
Some experiments have been completed on CMS04 suspension bogie designed by NUDT (National University of Defense Technology), which is showed in Figure
CMS04 maglev control experiment platform based on magnetic flux feedback.
Standard maglev bogie’s parameters are given in Table
Standard maglev bogie parameters of CMS04 maglev vehicle.
Parameters | Values |
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653 |
|
324 |
|
0.0235 |
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0.5 |
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0.008 |
|
23 |
|
9.8 |
|
|
Decoupling property test comes true on one suspension point of maglev bogie. Set expected position 10 mm. When maglev system becomes stable, we add additional square signal with amplitude 0.5 mm and period 4 s. Observe suspension signals with two control algorithms S1 and S2. Experiment results are showed in Figures
Position curves of algorithm S1.
Position curves of algorithm S2.
Experiment results illustrate that when double suspension control system applies algorithm S2, the dynamic decoupling problem has been worked out. S2 raises the robustness and stability properties of maglev control system, but method S1 has no decoupling effect.
Double suspension control model has been founded with magnetic flux signal based on MIMO feedback linearization. The feedback linearization algorithm enables accurate linearizing model to keep all properties of original nonlinear system which overcome the disadvantages of Taylor’s expansion linearization method. In order to work out dynamic coupling problem and external interference problem of EMS mid-low-speed maglev vehicle, we take magnetic flux signal back to maglev control system and design double suspension compensable controller. Some experiments about new algorithm have been done in maglev vehicle CMS04 designed by NUDT. Experiment results demonstrate that double suspension module is precise based on MIMO state feedback linearization theory. With magnetic flux feedback, the maglev control system has better robustness and adaptability than traditional algorithm.
This work was financially supported by National Nature and Science Foundation of China (NNNSFC, no. 11202230) and the Twelfth Five-Year National Science and Technology Support Plan (2012BAC07B01).