Research on Control Strategy of 2-phase Interleaving Magnetic Integrated VRM

A kind of 2-phase interleaving coupled magnetic integrated VRM is studied and the corresponding passivity-based control strategy is put forward. The model of this kind of magnetic integrated VRM is constructed, and the performance of this 2-phase interleaving magnetic integrated VRM of passivity-based control is verified by simulation experiments. The results proved that this kind of passivity-based control strategy can decrease the steady state current ripple and the dynamic output voltage under load disturbance.


Introduction
Nowadays, the topology used in VRM is mostly multiphase interleaving Buck converter, in which the magnetic components have important effect on the performance of VRM.In order to increase the power density and efficiency of VRM, the magnetic integration technology is applied to it [1][2][3].However, each phase winding of the multi-phase magnetic integrated VRM has a self inductance, meanwhile, it can form coupled magnetic circuit with the other phase windings.Therefore, it is difficult to construct the model of VRM and the traditional linear control methods can not meet the demand of the performance [4].A kind of 2-phase negative coupling magnetic integrated VRM is studied in this paper and its circuit model is constructed using linear system control theory, what's more, the corresponding nonlinear passivity-based control strategy is put forward to realize the equality of each phase current and to improve the dynamic performance of VRM.

Model Building of 2-phase Interleaving Magnetic Integrated VRM
The model of 2-phase interleaving negative coupled magnetic integrated VRM is shown in Figure 1.There are 4 operation modes in each switch cycle, and the corresponding equivalent circuits are shown in Figure 2.

Passivity-based Control Strategy of 2-phase Interleaving Planar Magnetic
Supposed that the output state variables of VRM are " , where " 10 L I " and " 20 L I " are steady state average currents and " o " is static state output voltage.The equilibrium state of the system defined by equation ( 1) is supposed as " d V x " and is translated to the origin of state space.The error vector is defined as: Substituting equation ( 1) to ( 2), the error state equation of VRM model can be expressed as:  2 / 0 0 0 2 / 0 , 0 0 0 and define a matrix "E" as: Substituting equation ( 5) to (3), we have Supposing that the right-hand side of equation ( 6) is always equal to zero, then: A Lyapunov energy function can be established as follow: x Px  e 0 (8) The derivative of Lyapunov energy function is: According to the asymptotic stability criterion of the control theory, the origin is asymptotically stable in the system defined by equation (8).That is to say, if and only if the right-hand side of equation ( 6) is constantly equal to zero, the error zero point is the system's intrinsic steady point, then Using equation ( 11), we can derive the expressions of "λ 1 " and "λ 3 " as follow: Equation ( 12) and ( 13) are the passivity-based control strategy of 2-phase planar magnetic integrated VRM.
With this strategy, if the input voltage "V in ", the output voltage "V o " and the coupling coefficient "k" are known, the VRM can be controlled precisely to be on the steady operation point and is passive.This can guarantee that the VRM has a global stability.In addition, the dynamic response speed of the VRM can be regulated in certain range by adjusting the damping parameter "R 1 ".
According to equation ( 12) and ( 13), the steady state performance of the 2-phase magnetic integrated VRM with passivity-based control is simulated and compared with that of 2-phase discrete inductor VRM, as shown in Figure 3.The blue curves (I f1 , I f2 and I fo ) are the current waveforms of discrete inductor VRM, and the green curves (I h1 , I h2 and I ho ) are the current waveforms of planar magnetic integrated VRM.It can be seen that the current ripples of magnetic integrated VRM are smaller than that of discrete inductor VRM, and this means that the negative coupling magnetic integrated VRM of passivity-based control has better steady state performance than that of the discrete inductor VRM.

Load Disturbance Simulation
The simulation waveforms shown in Figure 4 are the simulation results of the process that the load resistance jumps from light load (R load =0.05Ω) to full load (R load = 0.025Ω) at the moment of 1ms and falls from full load to  light load at the moment of 1.5 ms.The blue curve (V f ) is output voltage waveform of discrete inductor VRM under load disturbance, and the green curves (V h ) is output voltage waveform of magnetic integrated VRM under load disturbance.It can be seen that the drop value and over-modulation of dynamic output voltage of 2-phase magnetic integrated VRM are smaller than that of 2phase discrete inductor VRM.

Conclusions
This paper brings passivity-based control method into 2-phase interleaving magnetic integrated VRM and puts forward a kind of passivity-based control strategy.The passivity-based control strategy is verified with MAT-LAB simulation.The simulation results prove that 2-phase interleaving magnetic integrated VRM with passivity-based control strategy can improve the steady state performance and the dynamic performance.Passivity-based control is a perfect control scheme for magnetic integrated VRM.

Figure 1 .
Figure 1.Equivalent circuit of two-phase negative coupled planar magnetic integrated VRM.

Figure 2 .
Figure 2. Four operating modes of 2-phase negative coupled planar magnetic integrated VRM.

Figure 3 .
Figure 3. Steady state current waveforms of 2-phase VRM with passivity-based control strategy.

Figure 4 .
Figure 4. Dynamic response of output voltages of 2-phase VRM with passivity-based control strategy.