Abstract
A robust control design scheme using well-developed SISO techniques is proposed for maglev vehicles that are inherently unstable MIMO systems. The proposed seperate control method has basically two control loops: a stabilizing loop by a pole-placement technique, and a performance loop using a novel optimal LQ loop-shaping technique. This paper shows that the coupling terms involved in maglev vehicles with multimagnets should not be neglected but compensated for their stability and performance robustness. The robustness properties of the proposed control system are then evaluated under variations of vehicle masses and air gaps through a computer simulation. This paper also describes the reason why the proposed control technique can be suggested as a tool using only SISO techniques in controlling unstable MIMO systems such as maglev vehicles.
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Abbreviations
- f i :
-
Magnetic force in thei th corner of maglev vehicles
- z i :
-
Air gap in thei th corner of maglev vehicles
- z g ,zθ, andzϕ:
-
Air gaps with respect to heave, pitch, and roll
- \(\ddot z\),\(\ddot \theta \), and\(\ddot \phi \):
-
Accelerations with respect to heave, pitch, and roll
- F z :
-
Total magnetic force for heave direction
- T θ :
-
Torque for pitch direction
- T p :
-
Torque for roll direction
- M :
-
Total mass of maglev vehicles
- Iθ andIϕ:
-
Inertial moments about pitch and roll axes
- l andb:
-
Half length and width of maglev vehicles
- K z :
-
Circuit constant with respect to air gap
- K I :
-
Circuit constant with respect to current
- R i :
-
Resistance of thei th circuit transducer
- N :
-
Number of turns
- z0,y0, andI0:
-
Nominal values with respect to heave, guidance, and current
- |C ij |:
-
Coupling matrix of maglev vehicles
- {f ext (t)}:
-
Disturbance vector
- A ü :
-
System matrix for local control system
- A ij :
-
System matrix imposed by coupling terms
- b i :
-
Input vector
- Γ i :
-
Disturbance input matrix
- u l i (t) :
-
Local control law
- u c i (t) :
-
Complementary control law
- U p (t) :
-
Actual control law for a given plant
- G :
-
Optimal LQ loop-shaping control gain
- K :
-
Pole-placement control gain
- L :
-
Loop-shaping design parameter
- ϱ:
-
Scaling design parameter
- G F (S) :
-
Loop transfer function for a given plant
- Φ(S):
-
State transition function for a given plant
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Park, J.S., Kim, J.S. & Lee, J.K. Robust control of maglev vehicles with multimagnets using separate control techniques. KSME International Journal 15, 1240–1247 (2001). https://doi.org/10.1007/BF03185664
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DOI: https://doi.org/10.1007/BF03185664