LCL Filter Design and Implementation for Improving Transient Position Tracking Control Performance of Voice Coil Motor

Voice coil motor (VCM) is widely used in high precision position servo control for its merits of high linearity and no cogging-torque. There are two conventional driving modes: PWM chopper drive and analog drive. PWM chopper drive usually results in current ripples, which could affect position control precision. Acceptable current ripple limits the increase in the DC bus voltage and could not achieve faster response. On the other hand, analog drive uses power amplifiers, which does not suffer from current ripple but can result in high power loss. Such power loss could also affect precision or result in cooling difficulty, especially for thermal-sensitive applications such as semi-conductor lithography. In this paper, a VCM chopping drive with an LCL filter together with filter design method is proposed. Unlike conventional LCL filter design for grid inverter that only focuses on steady state current quality, the proposed LCL filter design in this paper aims at transient position control, which considers the current ripple, transient position tracking time and additional volume. With the designed filter, position tracking time can be shortened with acceptable current ripple. To compensate the delay caused by LCL filter, the DC drive voltage is increased. And under the same current ripple level, with LCL filter and higher DC voltage can get faster position response speed than without LCL filter and lower voltage. The results are validated by simulation and experimental results.


I. INTRODUCTION
Voice coil motor (VCM) has been widely used in precision position servo control system because of its advantages of simple structure and fast response. VCM involves linear, rotary or planar motion types. The armature of VCM does not contain ferromagnetic materials, so that VCM has the merits of no cogging torque and high linearity. Typical applications include semiconductor lithography [1], precision instrument vibration reduction [2], impact test [3] and vibration test [4]. With the continuous increasing demand of performance, various studies on both motor and control has been carried out [5]- [12].
The associate editor coordinating the review of this manuscript and approving it for publication was Ton Do .
So that the analog drive has the merits of fast response and nocurrent ripple, but the main disadvantage is the power loss because that the power amplifier is operating in its linear region. Its high-power dissipation causes temperature rise, and then brings issues in both precision and cooling design, which is quite difficult to handle for precision-demanding systems, such as semiconductor lithography. Secondly, for PWM chopper mode, the power switching element is working in its saturation region, so the power loss is low. However, due to absent of ferromagnetic materials in the armature of VCM, the armature inductance is relatively small. The chopping could induce current ripples affecting positioning precision [13]. To achieve acceptable current ripple, the DC bus voltage must be kept low, resulting in the position tracking transient to be slower. Given the drawbacks of the two drive modes, this paper proposed the PWM chopper drive with LCL filter, which could provide both lower loss and smoother current. Compared with the case without filter, the position tracking speed is much faster for the same current ripple level.
Conventionally, LCL filters are widely used in gridconverter inverters [14]- [18], where major objective is to suppress switching harmonics and to ensure steady-state current quality that adapting different applications and concerns [19]- [22]. [19] uses a disturbance and state observer to alleviate the impact of computational delay and improve the ability against disturbance of grid-connected LCL filter. To further reduce the steady-state error and get better disturbance rejection capability of LCL filter, [20] proposes a comprehensive design methodology of the proportional resonant (PR) controller in an inverter with an LCL filter and validates the stability margin. In [21], discrete model predictive control (DMPC) is used to get better steady and dynamic performance. In [22], a novel PBC parameters design strategy based on the expectant limited steady-state error is proposed to simplify the high-order of LCL filter.
To sum up, the existing LCL filter design methods are mainly focused on steady-state current quality. LCL filter design for transient-state position tracking control performance has not been explored. Except for filter design, another difficulty that limiting LCL filter in transient position tracking might be the resonance damping [23], [24], especially in the transients of position tracking. However, with the increased studies on the resonance damping of LCL filter [25]- [27], the damping control performance could be satisfactory and can be excluded in the filter design considerations.
In this paper, a VCM chopping drive with an LCL filter together with filter design method is proposed. Unlike conventional LCL filter design for grid inverter that only focuses on steady state current quality, the proposed LCL filter design in this paper aims at transient position control, which considers the current ripple, transient position tracking time and additional volume. With the designed filter, position tracking time can be shortened with acceptable current ripple. And also the DC drive voltage is increased to compensate the delay caused by LCL filter. Under the same current ripple, with the LCL filter, DC bus voltage can be set to higher, which can help reduce the position response time. The cases of with LCL filter high DC voltage and without LCL filter low voltage are compare studied. The simulation and experiment results validated that even with LCL filter, faster position response speed can be acquired with higher DC voltage. This paper is structured as follows: in section II, the plant model and its transfer function are given. Section III gives the detailed design procedures of the LCL filter for position tracking. Then in section IV, simulation results for position control performance of the VCM using the LCL filter is given. Section V gives the experiment results. Finally, the conclusion is given in section VI.

II. PLANT DESCRIPTION
A typical LCL filter consists of two inductors and one capacitor. A Rotary VCM is used in this study, the motor armature inductor can be used as one inductor and the overall size could be reduced. So the LCL filter designed for the PWM chopper control of voice coil motor is made up of the armature inductor L 2 , extra inductor L 1 and capacitor C, as in FIGURE 1.
where i 1 is the filter inductor current, i 2 is the motor armature current, u C is the filter capacitor voltage, u is the input voltage, R is the armature winding resistance, θ is the position angle of the rotor and w is the rotating speed. The parameters relating to the motor is given in Table 1. The transfer function between the armature current i 2 and the input voltage u can be expressed as (2).
where s is the Laplace operator. The block diagram of PWM chopper control with LCL filter proposed in this paper is shown in FIGURE 2. The control parameters are listed in Table 2.

III. LCL FILTER PARAMETERS DESIGN FOR VCM POSITION TRACKING
Based on the model in section II, the VCM armature inherent inductance is used as one inductor of the filter, and the LCL filter design for VCM position tracking is carried out considering the following 3 aspects.

A. FILTER PARAMETER INFLUENCE ON CURRENT RIPPLE
The use of LCL filter should reduce the current ripple that affecting positioning accuracy, this part explores filter parameters influence on current ripple.
The current ripple is also affected by many other factors, such as the switching frequency, PWM duty cycles and control algorithm. To simplify this problem, parameters are fixed with the following considerations. Firstly, no control strategy is used, the current ripple is compared with open-loop control. Secondly, the PWM duty cycle duty ratio is set to 50%, which leads to the largest current ripple compared with any other duty cycle values [28]. Thirdly, the switching and control frequency is set to 20 kHz according to the micro-controller ability to execute the control algorithm. After fixing these factors, the current ripple is evaluated with simulation.
The current ripples for different cases of without LCL filter and with LCL filter are given in FIGURE 3. It can be seen that for the case without LCL filter, the current ripple is about 130mA, as shown in FIGURE 3(a). For the case with LCL filter (with arbitrary filter parameter of L 1 = 1mH and   C = 1µF ), the current ripple is 11mA, which is less than 10% of the case without filter, as shown in FIGURE 3(b). It shows that the LCL filter can largely reduce current ripple.
To find out more detailed relations between filter parameters and current ripple, a potential feasible parameter variation range of L 1 0.3-3mH and C 5-50 µF are investigated in detail. FIGURE 4 shows the current ripple relation with the variations of L 1 and C. It can be seen that when both L 1 and C are small, the current ripple is large. When the parameter value increases, the current ripple decreases. It also seems that for the same product of L 1 C, the current ripples are almost of the same level.
The parameter product L 1 C influence is further evaluated, and the results are shown in FIGURE 5. It can be seen that the larger value the L 1 C, the smaller the current ripple. With the fixed value of L 1 C, the current ripples are almost in the same level, and the current ripple is only slightly larger with larger L 1 .
Another phenomenon worth noticing is the resonance. It is found out if the resonant frequency of the LCL filter is close to the switching frequency, the current ripple could increase. FIGURE 6(a) shows the case of L 1 C = 10 −10 , where the resonant frequency of the LCL filter varies from  16kHz to 26kHz. It can be observed that the ripple increases when the resonance frequency is close to switching frequency of 20kHz. For comparison, the current ripple for 100kHz switching frequency with the same parameters are given in FIGURE 6(b), and no resonance is observed. Thus, the resonance phenomenon should be avoided to get high performance filtering. And the filter resonance frequency should be set neither close to switching frequency in high frequency range, nor close to the position servo frequency in low frequency range.
Thus, the current ripple can be reduced by LCL filter parameters. The parameters should be selected to offer low current ripple and to avoid resonance.

B. FILTER PARAMETER INFLUENCE ON POSITION TRACKING TIME
Fast response is an important indicator for voice coil motor position servo system. This part evaluates the filter parameter influence on position tracking time.
In practice, the position tracking time is largely affected by control strategy. To exclude the influence of control algorithm, this paper evaluates the ''ideal'' position response time in discrete control form. The ''ideal'' performance is obtained by solving an optimization problem.
The optimization problem is formulated with the objective of tracking the position control reference, with respect to the plant model and DC bus voltage constraints.
subject to: where h is the step size, n is the discrete index, k is the maximum discrete index, θ * is the position tracking reference. The optimal position tracking data can be obtained by solving the optimization problem. A typical optimal position tracking response with detailed state variables is presented in FIGURE 7. The position tracking includes different phases of acceleration, deceleration and stabilization. The position tracking is with overshoot because it is the optimal way to reach the reference while maintaining speed and current at zero in finite discrete steps, that's why the stabilization phase is required. During the position tracking, the DC bus is fully used and the control relation is quite non-linear. The obtained optimal position tracking data is the ''best'' control performance for the given configuration, no other control strategy can obtain better result. Thus, it reflects the position tracking ability of the hardware configuration, and it can be used to evaluate filter parameter influence.
By defining the position control settling time as the time of reaching within ±5% of the reference, filter parameter influence on settling time can be obtained, as shown in FIGURE 8. Two cases of short stroke and long stroke are compared. It can be seen for different L 1 C product, the settling times are almost the same. It means L 1 has the major influence on settling time if compared with C. It can also be seen that with the same filter parameter, the settling time variation for short stroke is 8%, while 1% for long stroke. This is due to the fact that dynamic period (accelerating, decelerating) occupies a larger proportion in the short stroke.

C. FILTER PARAMETER INFLUENCE ON ADDITIONAL VOLUME
As VCM is often used in high precision applications, where the additional volume could also be a major concern in the precision structure. This section evaluates the filter parameter influence on the addition volume.
For inductor of the filter, it is manufactured by winding a coil on a magnetic core. The inductor volume is related with the inductor design, mainly involving magnetic core and winding turns. The capacitor volume is mainly related with the used capacitor. The photos of selected magnetic core and capacitor are shown in FIGURE 9. For inductor, the inductance can be expressed as in: where A l is the inductance coefficient, N is the winding turns, R M is the magnetoresistance.
To ensure the magnetic core is not saturated for the given condition, the flux density should be restricted using the following equation: where S is the core cross section, B max is the saturation flux density, I is the conducting current. The wire diameter is selected as 0.56mm according to our configuration. Because one core cannot satisfy all inductance values with minimum volume, so the inductor dimension varies for different cores. The magnetic core dimension covering the possible filter parameters are given in Table 3.
Another concern to design the inductor is to reduce the turn-to-turn capacitance, so single-layer winding is used. In this case, the winding turns should satisfy the following constraint: where, R is the wire radius, d is the coil inner diameter. The maximum inductance by this core can be fixed as: Considering the above constraints, the maximum inductance for a specific magnetic core can be obtained: Thus, given a desired inductance, the magnetic core offering minimum volume can be selected, and the volume can be calculated.
For capacitors, CBB capacitor are selected to withstand the AC voltage, the capacitor dimensions are also given in Table 4. The capacitor dimension is related with the capacitance value. After the two volumes relation is fixed, the total volume of the extra inductor and capacitor are evaluated with different filter parameters. The results are shown in in FIGURE 10. It can be seen that for our VCM configuration, the volume by different capacitor is larger than that by different inductor using different magnetic cores.
After comprehensive consideration over all the three factors of current ripple, position tracking time and additional volume, the final values of the filter parameters are chosen as: L 1 = 1mH, C = 1µF. With this configuration together with motor inductance 1.87mH as L 2 , the resonance frequency is 6.24kHz, which is within the control bandwidth for active damping. On the other hand, the resonance frequency cannot be set too low, or the filter size could be too large. The designed 6.24kHz resonance frequency is more than ten times higher than the position servo frequency of 150Hz.

IV. CONTROL PERFORMANCE WITH FILTER AND HIGHER DC BUS VOLTAGE: COMPARATIVE STUDY BY SIMULATION
The designed filter is expected to reduce current ripple and ensure position tracking time. However, the use of LCL filter will inevitably bring delay. This part tries to compensate the position tracking delay by increasing the DC bus voltage. The comparison with the case of without filter and lower voltage is also provided.
To make the two cases comparable, conditions must be similar. Needless to say, the control parameters must be the same. Besides, similar current ripple level is also another prefixed condition. As the LCL filter can reduce current ripple, the same acceptable current ripple for the configuration of the LCL filter can tolerate a higher DC bus voltage, and thus the position tracking can be faster.
In this section, the increased DC bus voltage for the configuration with filter is firstly studied, then the position servo settling time is compared with simulation.

A. DC BUS VOLTAGES FOR THE CASES OF WITH AND WITHOUT THE LCL FILTER UNDER SIMILAR CURRENT RIPPLE
With the same current ripple level, different DC bus voltages are applied for the cases of with and without LCL filter. According to our VCM configuration, for the case without LCL filter, the DC bus voltage is 15V. For the case with LCL filter, the DC bus voltage can be set to 24V. This 24V value is selected offer the similar current ripple in experimental, as given in the next section.
With the above configurations, the current ripple of two cases by simulation are shown in FIGURE 11. It can be seen that the current ripples are not exactly the same in simulation, but they are of similar level.
Even with increased DC bus voltage, the current ripple of the case with LCL filter is still smaller than the case without LCL filter.

B. POSITION TRACKING TIME COMPARISON
The above configurations are compared with the same control parameter for three typical step size of minor-stroke (0.01rad), short-stroke (0.1rad) and long-stroke (0.3rad).
In minor-stroke test, the simulation results are shown in FIGURE 12. The settling times are 22ms for the case without filter and voltage of 15V and 10ms for the case with LCL filter and voltage of 24V.
The short-stroke test performance is given FIGURE 13. The settling time for the response time of 15V DC voltage without LCL filter is 16ms; the response time of 24V DC voltage and with LCL filter is 12ms.
For long-stroke test, the settling times are 22ms for the case without filter and 18ms for the case with LCL filter, as shown in FIGURE 14.  It can be seen that for both stepping size, the settling time for the case with LCL filter is faster and with less current ripple.

V. CONTROL PERFORMANCE WITH FILTER AND HIGHER DC BUS VOLTAGE: COMPARATIVE STUDY BY EXPERIMENT
The position control performance with the designed LCL filter is validated by experiments with comparison to the case without filter.
The experiment rig is shown in FIGURE 15. The three-loop PID control algorithm is implemented in a TI TMS320F28069 controller. The encoder resolution is 0.0012566 rad. The position setting and tracking signals are transformed from controller data into analog signals through digital-to-analog circuit. According to the parameters design based on three aspects (current ripple, position tracking time and additional volume) in Section III, in the experiment, the inductance value is L 1 = 1mH; the capacitor value is C = 1µF.
As aforementioned, the case without LCL filter is driven by 15V DC bus voltage and the case with filter is 24V. Both cases have the same current ripple level, as shown in FIGURE 16.    It can be seen that the current ripple for both cases are almost the same, but the waveforms are different. FIGURE 17, FIGURE 18, and FIGURE 19 give the position tracking performance for minor-stroke test, short-stroke test and long-stroke test with the same controller parameter. It can be seen both cases have smooth response and without overshoot for the two steps. The settling time for minor-stroke test is 28ms (with LCL filter, 24V) and 40ms (without LCL filter, 15V) respectively; for short-stroke test is 8ms (with LCL filter, 24V) and 12ms (without LCL filter, 15V) respectively; for long-stroke test, the settling time is 15ms (with LCL filter, 24V) and 25ms (without LCL filter, 15V). And because the rotational corner of the voice coil motor used in experiment is limited in a small range, bigger position step cannot be implemented.
Thus, with the same current ripple level, the designed LCL filter can get much faster response with increased DC bus voltage. For VCM, the implementation LCL filter brings advantages on both current ripple and position tracking time. Besides, the losses are low because the power devices are working with chopper mode.
It is worth mentioning that in the experiment for 0.01rad, the settling time of both with and without LCL filter is even longer than that of bigger step sizes 0.1rad and 0.3rad. That is because for the PID controller in linear mode, the output is purely error driven. When the error is smaller, the output amplitude is low and the changing rate is slower. As a result, in this case a small step response takes much more time.

VI. CONCLUSION
In this paper, an LCL filter design and implementation method is proposed for improving both steady-state and transient state position tracking control performance of voice coil motor.
The LCL filter design in this paper is aiming at both steady-state and transient-state position control performance that considering current ripple, position tracking time and filter volume. The relation between filter parameter and the above concerns are revealed. The parameter design based on the three factors are proven to be effective.
To compensate the delay caused by LCL filter, the VCM can be driven with higher DC bus voltage while offering less or similar current ripple and faster position tracking speed, as has been validated by simulations and experiments. Thus, this LCL filter design and implementation can be beneficial for VCM position control, which offers the merits of low current ripple, faster response and low loss.