Disturbance Rejection Control for Active Vibration Suppression of Overhead Hoist Transport Vehicles in Semiconductor Fabs

Abstract

In modern semiconductor fabrication plants, automated overhead hoist transport (OHT) vehicles transport wafers in front opening unified pods (FOUPs). Even in a cleanroom environment, small particles excited by the mechanical vibration of the FOUP can still damage the chips if such particles land on the critical area of the wafers. To minimize the vibration excitation force transferred to the FOUP, this research focuses on controlling the vibration displacement level of an OHT hand unit interface between the OHT vehicle and the FOUP. However, since the OHT vehicle and the FOUP keep traveling, the target system is floating and there exists no external anchoring point for a controlling force source. In addition, no sensor attachments are permitted on mass-production FOUPs, which makes this vibration level suppression problem more challenging. In this research, a custom testbed is designed to replicate the acceleration profile of the OHT vehicle under its travel motion. Then, system modeling and identification is conducted using simulation and experiment to verify the fabricated testbed design. Finally, a disturbance observer-based controller (DOBC) is developed and implemented on a custom active vibration suppression actuator with inertia force-based counterbalancing to reduce peak vibration amplitude from 870 μm to 230 μm.

1. Introduction

The overhead hoist transport (OHT) system is the most widely used automated transportation system for 300 mm wafers in modern semiconductor fabrication plants. An OHT vehicle travels on tracks installed on the ceiling of a semiconductor fabrication plant. It transports wafers in a front opening unified pod (FOUP). A FOUP is a standard wafer carrier for 300 mm wafers and stores up to 25 wafers per carrier [1,2]. Globally, over 8000 OHT vehicles are operated in more than 28 fabrication plants in Samsung Electronics Co., Ltd. The overall traveling distance of all the OHT vehicles reaches 644,000 km per day. Since semiconductor manufacturing requires hundreds of process steps, a wafer must be transported via OHT vehicles multiple times between every process step. Thus, it is crucial to keep the wafers intact during transportation.

Ensuring a low vibration level on the FOUP during the transportation is essential. Previous researches in Samsung Electronics discovered that the transferred vibration from OHT vehicles to FOUPs has a negative effect on semiconductor yield. Dust inside the FOUP and from the bottom of the wafers can be excited with the vibration, land on critical areas of the wafers, and cause damage to the semiconductor products [3,4,5]. In Samsung Electronics, applying passive damping materials was the primary strategy to reduce the vibration level transferred from the travel motion of OHT vehicles to the FOUPs. Since improvement due to this strategy came to a certain saturation, active vibration control techniques are adapted for further vibration level reduction.

Vibration suppression is a broad research field with numerous applications such as construction, transportation, and precision engineering. Many types of tuned mass damper (TMD) systems were used as an innovative system for vibration control of building structures [6,7,8,9,10]. Moreover, active vibration isolation strategies based on a combination of sky-hook spring and sky-hook damper were investigated and applied to car suspension, scanning probe microscopy, and optical tables [11,12,13,14,15,16].

For active vibration suppression of the FOUP, Tsai et al. proposed an experimental OHT using a triplet of double-link arms to carry the FOUP in replacement of hoist cables for conventional OHT vehicles [17]. Applying a composite controller to this proposed model could reduce the transferred shock, tilt, or high-frequency excitation to the FOUP. However, this type of OHT cannot be applied to semiconductor fabrication plants in the real world with the presence of hoist cables.

To further improve controller performance for vibration suppression, Tokoro et al. proposed a state feedback control method based on actual observable states using suspension stroke sensors of a gasoline engine vehicle [18]. The proposed controller is successfully evaluated by experiment to suppress the pitching and bouncing motion of vehicle bodies. In addition, Yu et al. utilized a disturbance observer-based control method to control a four-wheel steering vehicle [19]. This disturbance observer-based control was helpful in ignoring nonlinear dynamics and handling exogenous disturbances.

There are two unique challenges for the FOUP vibration level suppression problem. First, unlike static building or optical table applications, the OHT vehicle and the FOUP keep traveling. Therefore there exists no external anchoring point for a controlling force source, and the target system is floating. Second, another challenge lies in the fact that the acceleration level of the FOUP cannot be directly measured as the control input, which makes this control problem different from the situation mentioned above. This is due to the current design of the existing semiconductor fabrication plants, where no sensor attachments are permitted on mass-production FOUPs.

To suppress the vibration on the FOUP during transportation, the main contributions of this work lie in three folds.

• Development and characterization of a vibration generation testbed for reconstructing the OHT hand unit motion.
• Design and implementation of an inertia force-based active vibration suppression system.
• Proportional Integral (PI) and disturbance observer controller design to suppress $70\%$ of the induced vibration.

The paper is organized as follows. In Section 2, the design and the specification of the vibration generation testbed (to replicate the real OHT track system) and the controller hardware implementation are introduced. In Section 3, a linear model is analyzed and characterized with system identification techniques to create models for controller design. The output force bandwidth of the vibration actuation is verified. In addition, a disturbance input force profile is also generated in Section 3. In Section 4, a disturbance observer-based controller (DOBC) is designed for active vibration suppression. By implementing the controller in Simulink and on the hardware, the performance results are presented in Section 5. Finally, the conclusions and future works are summarized in Section 6.

2. Hardware System Design

The hardware system design in this work primarily includes the vibration generation testbed and the active vibration suppression system. The design of these systems is centered around an OHT hand unit carrying a FOUP, as shown in Figure 1. As mentioned previously, the hoist cables on an OHT hand unit are inevitable since OHT vehicles must load or unload FOUPs at target locations that are nearly 8 m apart in height. Beneath this vertically hoisted hand unit, a pair of grips exist to clamp a FOUP. The vibration level transferred to the FOUP is mainly due to the travel motion of OHT vehicles. According to previous vibration transfer path analysis (TPA) studies conducted by the Samsung Automated Material Handling System (AMHS) team, it was discovered that the OHT hand unit is the dominant path of the vibration transferred to the FOUP [20,21]. Therefore, the OHT hand unit is set to be the design domain for active vibration control.

2.1. Testbed Mechanical Design

The vibration generation testbed is designed and fabricated to replicate the vibration of the OHT system. To be specific, the acceleration signal measured from an OHT hand unit (when an OHT vehicle was traveling on tracks within the factory) is replicated on the OHT hand unit of the testbed. As shown in Figure 2, the scope of this work focuses on single-axis vibration suppression along the traveling direction, whereas contributions from the other directions are assumed to be orthogonal to this access and neglected during the analysis.

Since it is not practical to reconstruct the entire OHT track system in the lab environment, only the design domain (i.e., hand unit assembly) is utilized, and a proper actuator is applied to excite input vibration. This system allows precise control of the vibration input force to simulate different track and driving conditions of the OHT system.

A proper actuator must be selected to generate the desired vibration signal. With a target bandwidth of 500 Hz, a voice coil actuator (VCA, VCAR0436-0250-00A; SUPT Motion) is chosen as the vibration generation actuator with its matching force, bandwidth, and travel bandwidth characteristics. The detailed specification is listed in

Table 1. VCA specification. “Actuation” refers to the vibration actuation VCA mentioned in Figure 2, while “Control” refers to the vibration control VCA.

	Stroke [mm]	Force Constant [N/A]	Peak Force [N]	Continuous Force [N]
Actuation	25.4	30	220	68.2
Control	22.4	6.8	33	13.5

. Here, the VCA is spring-loaded to establish a neutral position of the system. Using the actual OHT hand unit assembly, a modal stinger (2155G12; The Modal Shop, Inc., Cincinnati, OH, USA) is applied between the VCA and OHT hand unit so that the disturbance in perpendicular directions will not affect the alignment of the VCA to the OHT hand unit. Moreover, a linear encoder (IT3402L; Prologue Technology, O’Fallon, MO, USA) is assembled on the VCA for position measurement with a programmed precision at 1.25 μm per count, which gives sufficient resolution and a high allowed travel speed of up to 4 m/s. A triaxial accelerometer (3713F1110G; PCB Piezotronics) is mounted on the hand unit to measure the acceleration of the hand unit.

For the vibration suppression purpose, a smaller VCA (VCAR0033-0224-00A; SURP Motion) is chosen for inertia force-based counterbalancing application. The specification is also listed in Table 1. The linear encoder (IT3402L; Prologue Technology) is also assembled on this vibration control VCA for its position monitoring with equivalent performance. The vibration suppression system design considers the space constraint in an existing OHT system and can be transferred to the real system without significant modification.

2.2. Testbed Instrumentation

Data acquisition and actuator drivers with sufficient bandwidth need to be selected to interface with the vibration generation testbed. The National Instrument (NI) compact RIO system is chosen for this purpose (See Figure 3). The vibration generation subsystem is controlled by a cRIO-9074 chassis, and the vibration suppression subsystem is controlled with a cRIO-9038 with a more powerful field programmable gate array (FPGA) to implement relatively complex control logic. Various IO modules are added, including H-bridge motor drivers (NI9505), digital IOs (NI9402), an analog input (NI9205), and an analog output (NI9263) module. To be specific, NI9505 modules control VCAs, NI9402 modules measure digital signals from the linear encoders, the NI9205 module measures analog signals from the accelerometer, and the NI9263 module is used to synchronize two compact RIO chassis.

3. System Characterization

System modeling and identification is an essential step before the controller design. In this section, the dominating linear dynamic of the system is captured with lumped parameter models with corresponding parametric equations. Next, bode plots of the system are obtained with the sinusoidal input frequency sweep. Finally, a numerical transfer function is fitted to the bode plots based on the parametric equations.

In addition to the model of the mechanical system, characterization of the transducer is also performed. The VCA output force bandwidth is verified to exceed 500 Hz, which is significantly higher than the mechanical system bandwidth, so its dynamic model can be simplified as a gain for the frequency range of interest. Similarly, the encoder and accelerometer models can also be simplified as constant gains. An algorithm to produce the current reference profile for the VCA to generate the desired vibration acceleration profile is also presented in this section.

3.1. System Modelling

A lumped parameter model is developed to analyze the dynamics of the testbed in the mechanical domain. All the moving elements are represented as lumped masses, and connections between mass blocks are lumped as parallel connected springs and dampers. The physical system shown in Figure 1 can be modeled as the linear mass–spring-damper system as shown in Figure 4.

In Figure 4, $M_1$ is the centralized mass representation of the vibration actuation VCA and the hand unit, and $k_1$ and $b_1$ are the equivalent spring and damper connected between the VCA and the solid ground. $M_2$ is the lumped mass of the testbed frame, which can be modeled as a cantilever system, $k_2$ and $b_2$ are the lumped spring and damper of the cantilever system, and $k_3$ and $b_3$ are the equivalent spring and damper of the hoist cables connecting the hand unit and the frame. $M_3$ is the mass of the FOUP, and $k_4$ and $b_4$ are the equivalent spring and damper of the clamp between the hand unit and the FOUP.

While creating the above linear model, the following assumptions are made to simplify the system and linearize the nonlinear components. The approximate linear model can capture the main system dynamics but have a certain level of inaccuracy due to these simplifications.

• The testbed frame is modeled as a cantilever system, and only the first mode corresponding to the dominant pair of poles is considered and modeled as a single mass–spring-damper system.
• The dynamic of the high-stiffness stinger between the vibration actuation VCA and the hand unit is ignored for simplification. The VCA and the hand unit are lumped as a single mass $M_1$.
• Small angle approximation is assumed for the hoist cables that connect the hand unit and the frame to linearize the pendulum system. The elongation of the rubber-texture cables is also ignored.
• The stroke of the clamp-equivalent spring is assumed to be unlimited, thus the bumping between the clamp end and the FOUP is ignored.
• Since the displacement of the VCA coil is small, the VCAs are assumed to be linear (output force is proportional to the input current).

Since the force is transmitted from the hand unit to the FOUP through the clamp that can be modeled as a parallel spring and damper system ($k_4$ and $b_4$ in Figure 4), the acceleration of the FOUP is only related to the displacement and the velocity difference. Due to this reason, this research focuses on hand unit displacement control.

3.2. System Identification

To control the displacement of the hand unit, an appropriate model for the VCA-Stinger-hand unit system is needed. As analyzed in Section 3.1, the system can be modeled as shown in Figure 5.

The analytical transfer function relating the force F to the hand unit position $x_1$ is given by Equation (1).

$$\frac{X_1\left(s\right)}{F\left(s\right)}=\frac{m_2{s}^2+(b_2+b_3)s+k_2+k_3}{[m_1{s}^2+(b_1+b_3)s+k_1+k_3][m_2{s}^2+(b_2+b_3)s+k_2+k_3]-{(b_{3}s+k_3)}^2}$$

(1)

A frequency sweep from 0.2 $\mathrm{H}\mathrm{z}$ to 25 $\mathrm{H}\mathrm{z}$ with 0.1 $\mathrm{H}\mathrm{z}$ interval is implemented to determine the numerical values of the parameters that appear in Equation (1). A lock-in filter is used to obtain the gain and phase of the system under each frequency and to filter out the measurement noise (which is uncorrelated with the inputs). To be more specific, the system is excited at each frequency (f) for 10 periods, the product between the measurement and the sine wave ($x\left(t\right)sin\left(2\pi ft\right)$) and the product between the measurement and the cosine wave ($x\left(t\right)cos\left(2\pi ft\right)$) are calculated and integrated, which are the real part and the imaginary part of the transfer function at that frequency. The details are shown in Equations (2) and (3), where $\left|x\right|$ is the amplitude of the displacement, and $\varphi$ is the phase of the displacement:

$$\begin{array}{cc}\hfill \frac{1}{10T}{\int }_0^{10T}x\left(t\right)sin\left(2\pi ft\right)dt& =\frac{1}{T}{\int }_0^T\left|x\right|sin(2\pi ft+\varphi )sin\left(2\pi ft\right)dt\hfill \\ \hfill & =\frac{\left|x\right|}{2T}{\int }_0^T[cos\left(\varphi \right)-cos(4\pi ft+\varphi )]dt\hfill \\ \hfill & =\frac{\left|x\right|cos\left(\varphi \right)}{2}\hfill \end{array}$$

(2)

$$\begin{array}{cc}\hfill \frac{1}{10T}{\int }_0^{10T}x\left(t\right)cos\left(2\pi ft\right)dt& =\frac{1}{T}{\int }_0^T\left|x\right|sin(2\pi ft+\varphi )cos\left(2\pi ft\right)dt\hfill \\ \hfill & =\frac{\left|x\right|}{2T}{\int }_0^T[sin(4\pi ft+\varphi )+sin\left(\varphi \right)]dt\hfill \\ \hfill & =\frac{\left|x\right|sin\left(\varphi \right)}{2}\hfill \end{array}$$

(3)

To keep the small angle approximation of the hoist cables valid (Assumption 3), the displacement of the hand unit should be kept at a small amplitude (200 μm in this test). Thus, the amplitude of the input sine current changes with different sweeping frequencies. To be more specific, as the sweeping frequency $f\left[k\right]$ approaches the resonant region, the input current amplitude $I\left[k\right]$ is reduced by a certain ratio $\mathrm{ratio}\left[k\right]$ to avoid large displacement amplitude. For each sweep frequency $f\left[k\right]$, the input current amplitude is first determined with Equation (4). After 10 periods, the lock-in filter calculates the corresponding measured gain $|H_{\mathrm{measured}}\left[k\right]|$ and phase $\angle H_{\mathrm{measured}}\left[k\right]$. With Equation (5), the real gain and phase of the system at frequency $f\left[k\right]$ can be determined. Since the frequency sweep interval is small (0.1 $\mathrm{H}\mathrm{z}$), here it is assumed that the amplitude $\left|H\right[k+1\left]\right|$ and $\left|H\right[k\left]\right|$ won’t differ much, thus a proper ratio for the next frequency $f[k+1]$ can be calculated with Equation (6).

$$\begin{array}{cc}\hfill I\left[k\right]& =\frac{I\left[0\right]}{\mathrm{ratio}\left[k\right]}\hfill \end{array}$$

(4)

$$\begin{array}{cc}\hfill |H_{\mathrm{real}}\left[k\right]|=\mathrm{ratio}\left[k\right]|H_{\mathrm{measured}}\left[k\right]|& ,\angle H_{\mathrm{real}}\left[k\right]=\angle H_{\mathrm{measured}}\left[k\right]\hfill \end{array}$$

(5)

$$\begin{array}{cc}\hfill \mathrm{ratio}[k+1]& =\frac{|H_{\mathrm{real}}\left[k\right]|}{|H_{\mathrm{real}}\left[0\right]|}\hfill \end{array}$$

(6)

The bode plot between the input force (F) and the hand unit displacement ($x_1$) is measured, and a numerical transfer function is fitted to the parametric expression in Equation (1). The Python SciPy package is used for the fitting. The logarithmic parametric equation is fitted to the logarithmic value of the measured magnitude with the method “Trust Region Reflective”. Both the measured value and the fitted model are plotted in Figure 6. The fitted linear transfer function is shown in Equation (7).

$$\frac{X_1\left(s\right)}{F\left(s\right)}=\frac{Gai{n}_1(s^2+3.23s+661.9)}{(s^2+2.18s+626.4)(s^2+25.55s+4411)}$$

(7)

As shown in Figure 6, the fitted model magnitude curve aligns well with the experimental data. The two measured resonant peaks at 4 Hz and 10.8 Hz accord with the two pairs of the conjugated complex poles on the denominator of the numerical model Equation (7). The measured anti-peak at 4.2 Hz also matches the pair of the conjugated complex zeros on the numerator. However, the fitted linear model has a certain phase lead compared to the measurement. This difference might come from the nonlinear behavior in the actual system.

The fitted linear model is verified by comparing the simulation and measurement results. A disturbance force profile is implemented on the disturbance actuator (VCA) to vibrate the hand unit, and the displacement of the hand unit is measured. The transfer function shown in Equation (7) is implemented and simulated in Matlab Simulink. The same disturbance force profile is input to the linear transfer function block. The simulated displacement is plotted together with the measurement in Figure 7.

As shown in Figure 7, the simulated displacement signal shows an acceptable match compared with the measured displacement signal. The simulated displacement peaks always appear earlier than the measured ones, which match with the model phase lead found in Figure 6. The model phase lead of the peaks near 0.66 s is calculated for verification. Here, the time of the two peaks of the simulated displacement ($t_1$ and $t_2$) and the time of the second peak of the measured displacement ($t_3$) are labeled in Figure 7. The phase lead of the model is calculated with Equation (8) and (9). The calculated $16.{98}^{\circ }$ phase lead matches with the estimated ${15}^{\circ }$ lead shown in the right plot in Figure 6.

$$\begin{array}{cc}\hfill \omega & =\frac{\pi }{t_2-t_1}=57.02[\mathrm{rad}/\mathrm{s}]\hfill \end{array}$$

(8)

$$\begin{array}{cc}\hfill \mathrm{model}\mathrm{lead}& =\omega (t_3-t_2)=0.296\left[\mathrm{rad}\right]=16.{98}^{\circ }\hfill \end{array}$$

(9)

The linear model captures the main behavior of the system, despite some non-linear components and errors in the model. The controller algorithm will be developed based on this linear model.

3.3. Output Force Bandwidth Verification

As the required bandwidth is 500 Hz, the force output from the vibration actuation VCA should first meet this requirement. An initial testbed is designed for the output force bandwidth verification, as shown in Figure 8. The VCA unit is connected to the stinger. The other end of the stinger is connected to a force sensor attached to a wall. The back bar that connects the VCA with the ground is the same one that appears on the testbed shown in Figure 2, which serves as a cantilever.

A frequency sweep from 10 Hz to 1000 Hz with 1 Hz interval is implemented with the lock-in filter introduced in Section 3.2. The bode plot relating the VCA input current to the stinger output force is shown in Figure 9. The resonant peaks and the anti-resonant peak show that the whole system is composed of several mass-spring-damper connected together, potentially with dynamics from the aluminum frame structures and the spring-loaded VCA mechanical dynamics.

The anti-resonant peak initially observed is below 500 Hz and restricts the output force bandwidth. We hypothesize that the back bar behind the VCA and the front wall are not sufficiently rigid. After reconfiguring the support structures by narrowing the distance between the two support bars and strengthening the front wall, the frequency of the anti-resonance peak has been successfully pushed beyond 500 Hz (as shown in Figure 9), which satisfies the design requirement.

3.4. Disturbance Force Generation

The vibration generation VCA input current profile needs to be designed to reproduce the acceleration of the lab hand unit collected from the actual systems running in the Samsung plant. In particular, the current profile will be operated in an open loop so that the suppression system can compensate for this vibration. Therefore, the main objective of this task is to generate a suitable current profile, which will vibrate the hand unit with the desired acceleration when the vibration suppression system is not activated.

With the repeatable nature of the vibration generation testbed (the same input will result in the same output), an iterative learning controller is investigated. The iterative learning controller will update the input current command repeatedly to optimize the actuated acceleration to reproduce the measured signal in the actual plant. The controlled input is recorded and will be operated in an open loop in the later vibration suppression controller design section (Section 4).

The basic controller comprises a feedforward controller and a feedback controller with small gains. Since the dynamic between the input force and the hand unit acceleration has the same number of poles and zeros (not a strictly proper system), due to the sensor error and delay in the hardware, a large feedback gain will excite high-frequency oscillations. Despite the small gain, the feedback controller is still trying to compensate for the error between the acceleration measured and the reference during each iteration. Thus the controlled acceleration from both feedforward and feedback will be more similar to the acceleration reference than the acceleration from the feedforward controller only. After getting a new control effort (current) from the controller, it would be smoothed to suppress the high-frequency component, then become the feedforward part of the next iteration. Figure 10 shows the best iterative learning result.

With the iterative learning controller, many of the acceleration high peaks are reached, which can be used for vibration suppression control. The control effort (current) was input to the vibration actuation VCA in an open loop during the later vibration control section.

4. Active Vibration Suppression Controller Design

In this section, the design process for the control algorithm to suppress the vibration displacement of the hand unit is presented. The first step is to analyze the characteristics of the vibration signal to be suppressed and determine the suitable type of control technique to use. The initial controller candidates being considered include:

• Proportional integral derivative (PID)
• Disturbance observer
• Repetitive control
• Iterative learning control
• Data-driven learning

The PID controller is the selected benchmark solution as an initial starting point. The disturbance observer is the primary algorithm to handle the generic vibration force input as a disturbance rejection problem. As verified in Section 3.2, the system is primarily linear without significant nonlinearity from system identification. This is a nice feature for implementing the disturbance observer controller, making it the chosen algorithm in this problem.

The remaining algorithms can be effective in certain situations where the vibration signal to be suppressed has specific properties. After further analysis of the vibration signal from the factory plant measurement data, these algorithms are deemed inappropriate for this specific application. The vibration data does not show dominant frequency components but spans the whole frequency range, thus, the repetitive control technique might not be suitable for this particular application. Due to the different initial conditions and the different disturbance sources (gaps on the track, motion changes of the OHT vehicles, etc.), the time domain acceleration profiles of each test from the Samsung plant are different. This makes the application of iterative learning control relatively challenging. The data-driven learning algorithm may still be a good candidate to be explored in the future but would require a significant number of datasets from the OHT hand unit in the factory.

During controller design, practical limits on the hardware transducer also need to be considered. The limited force and stroke of the controller VCA is the main constraint of our controller hardware. The limited force makes it impossible to have arbitrarily high controller gain and constrains the settling time of the controlled signal. The limited stroke (see Figure 11) is a potential extra-disturbance source that may exacerbate the vibration problem. When the VCA moving mass reaches the limit of the stroke and thus hits the hand unit, the impact will cause an extra sharp vibration peak.

For the vibration suppression controller design, there are two main tasks to accomplish:

• to actuate the controller VCA moving mass to gain inertia force;
• to keep the controller VCA moving mass within a certain range to avoid extra disturbance when the moving mass reaches the movement limit.

A disturbance observer-based controller (DOBC) is designed to accomplish the two tasks. The disturbance observer is implemented to estimate and suppress the majority of the real-time disturbance. A proportional integral (PI) controller is added to compensate for other types of error. Another PI controller is also implemented to control the displacement of the controller VCA moving mass. The block diagram of the controller structure is shown in Figure 12. Here, $r_{\mathrm{HU}}$ and $r_{\mathrm{MM}}$ are the reference value of the hand unit displacement and vibration control VCA moving mass displacement. $G_{\mathrm{HU}}\left(s\right)$ and $G_{\mathrm{MM}}\left(s\right)$ are the transfer function between the vibration control VCA input current and the hand unit displacement, and the transfer function between the input current and the VCA moving mass displacement. $H_{\mathrm{HU}}\left(s\right)$ and $H_{\mathrm{MM}}\left(s\right)$ are the dynamic of the measurement of the hand unit displacement and the VCA moving mass displacement. The $\frac{1}{{\overline{G}}_{\mathrm{HU}\left(s\right)}}$ and the filter block (denoted as D.O. in Figure 12) represent the disturbance observer, where ${\overline{G}}_{\mathrm{HU}}\left(s\right)$ is the modified version of $G_{\mathrm{HU}}\left(s\right)$ and the filter is the low-pass filter used to stabilize the output, which will be elaborated in Section 4.2. It deserves to be noticed that the observed disturbance is the combination of the disturbance and the control effort of the last iteration. Thus, to suppress the disturbance in the current iteration, the control effort of the previous iteration needs to be added.

It needs to be noticed that the VCA is supposed to be linear (see Assumption 5). Thus the vibration control VCA input current is proportional to the inertia force. Moreover, the hand unit and the vibration actuation VCA are lumped as one mass (see Assumption 2). Thus $G_{\mathrm{HU}}\left(s\right)$ is the same as the transfer function shown in Equation (7) with an extra constant gain due to the VCA force constant.

4.1. PI Controller

A proportional integral (PI) controller is first implemented for the displacement control. It is composed of a proportional gain and an integral term of the difference between the reference and the measurement, as shown in the blue region in Figure 12. The proportional gain increases the speed of convergence. The integral gain helps to eliminate steady-state error. The proportional gain and the integral gain are tuned for the best performance. As the gains are increased, the hand unit displacement is suppressed better, but the moving mass of the inertia force actuator (the magnet of the VCA) travels a longer distance. To avoid the extra vibration caused by the bumping between the moving mass and the mounting base of the VCA coil (see Figure 11), another PI controller is added to control the position of the moving mass to prevent it from moving too far away from the center position, as shown in the orange region in Figure 12. The performance will be discussed in Section 5.1.

4.2. Disturbance Observer-Based Controller

In this section, a disturbance observer-based controller (DOBC) is designed to suppress the hand unit displacement better. It is designed based on a disturbance observer (shown in the black region in Figure 12), which will estimate and eliminate the major disturbance. The double PI controller mentioned in Section 4.1 is also implemented to suppress the error further.

The performance of the DOBC is expected to be better compared to a regular PI controller. The PI controller is designed to react to the error of the measured displacement signal (difference between the measured displacement and the reference) and generate a force input using the VCA to the mechanical system, which has a limited effect due to the lag in the mechanical system dynamics. On the other hand, the disturbance observer estimates the real-time disturbance force and responds directly with added control effort. By demanding the inertia force actuator be a force with the same amplitude but opposite direction as the estimated disturbance force, large displacement peaks can be attenuated better.

To estimate the input force, the system transfer function 7 is inverted and simplified by removing similar terms shown in the numerator and denominator. Two low-pass filters at 150 rad/s are added to avoid the instability caused by differentiating the measurement signal and the more zeros than poles. The disturbance observer transfer function is shown in Equation (10).

$$\frac{I\left(s\right)}{X\left(s\right)}=\frac{Gai{n}_2(s^2+25.55s+4411)}{{(s+150)}^2}$$

(10)

To implement the disturbance observer on hardware, z-transform is implemented to get a discrete transfer function by substituting s to $\frac{2(z-1)}{T(z+1)}$, as shown in Equation (11). As the main loop running on the FPGA has a loop rate of 10 kHz, the sampling period is set to T = 0.1 ms.

$$\frac{I\left(z\right)}{X\left(z\right)}=\frac{Gai{n}_4(400515411z^2-799991,178z+399493411)}{(406022500z^2-799955000z+394022500)}$$

(11)

To implement this z-domain transfer function on hardware, $x\left[k\right]z^{-1}=x[k-1]$ is applied and Equation (11) can be rewritten as Equation (12). The implementation in Simulink is shown in Figure 13.

$$\begin{array}{ccc}\hfill I\left[k\right]& =& 1.970223I[k-1]-0.970445I[k-2]+{\mathrm{Gain}}_4(0.986436x\left[k\right]\hfill \\ & & -1.970312x[k-1]+0.983919x[k-2])\hfill \end{array}$$

(12)

The verification of the disturbance observer in Simulink and the performance will be discussed in Section 5.2.

5. Results and Discussion

In this section, the simulation and actual performance of the PI-only controller and the disturbance observer-based controller (DOBC) are compared and discussed.

5.1. Pi Controller

The gains of the PI controller, $K_P$ and $K_I$, are tuned for the best performance. The proportional gain $K_P$ of the hand unit displacement ($x_{\mathrm{HU}}$) controller is first tuned and increased to attenuate $x_{\mathrm{HU}}$ until the peaks rise again. After that, the integral gain $K_I$ of the $x_{\mathrm{HU}}$ controller is tuned. As the gains increase, the displacement of the controller VCA moving mass also increases and will reach the stroke limitation, as mentioned in Section 4. Thus at the same time, the gains of the moving mass controller are also tuned with the same procedure. The final gains are:

$$\begin{array}{cc}\hfill K_{P,\mathrm{HU}}& =0.006\hfill \\ \hfill K_{I,\mathrm{HU}}& =0.025\hfill \\ \hfill K_{P,\mathrm{MM}}& =0.0002\hfill \\ \hfill K_{I,\mathrm{MM}}& =0\hfill \end{array}$$

The PI controller is verified both in Simulink and on the testbed. In Simulink, different input signals (step, sinusoidal, pre-designed current profile) are tested. On the testbed, the pre-designed current profile mentioned in Section 3.4 is tested.

In Simulink, a step response is first tested and the result is shown in Figure 14a. Then, three sinusoidal inputs are tested at three vibration characteristic frequencies (3 Hz, 8 Hz, and 20 Hz), and the results are shown in Figure 14b–d.

The performance of the PI controller on hardware is shown and compared with the Simulink simulation in Figure 15a. A 30% of the maximum displacement threshold is plotted as a blue region. Since the vibration characteristics that an OHT vehicle experiences while traveling is mostly impacts, the peak reduction is a good indicator of the vibration suppression quality. Thus, the ratio between the controlled displacement peaks of the hardware setup and the open loop displacement peaks is plotted in Figure 15b to show the suppression of the PI controller on the vibration peaks. Smaller ratios correspond to better vibration suppression performance. The ratio is also summarized in

Table 2. Displacement peaks value and the peak reduction ratio of Open Loop, PI controller, and disturbance observer-based controller.

Peak	Open Loop [$\mathsf{\mu }$m]	PI [$\mathsf{\mu }$m]	DOBC [$\mathsf{\mu }$m]	PI Ratio	DOBC Ratio
1	298.75	225	148.75	0.753	0.498
2	−71.25	−22.5	−46.25	0.316	0.649
3	435	313.75	230	0.721	0.529
4	−573.75	−163.75	−150	0.285	0.261
5	140	−11.25	71.25	0.080	0.509
6	−196.25	−78.75	−90	0.401	0.458
7	237.5	136.25	56.25	0.574	0.237
8	−271.25	−198.75	−140	0.733	0.516
9	245	228.75	−17.5	0.934	0.071
10	−586.25	−282.5	−201.25	0.482	0.343
11	648.75	408.75	110	0.630	0.170
12	−870	−315	−222.5	0.362	0.256
13	620	295	73.75	0.476	0.119
14	−425	−28.75	−103.75	0.068	0.244
15	413.75	188.75	135	0.456	0.326
16	−277.5	−87.5	−31.25	0.315	0.113
17	95	21.25	40	0.224	0.421
18	−220	−53.75	−113.75	0.244	0.517

and compared with the disturbance observer-based controller result in Section 5.2.

The Simulink result (the yellow curve) overlaps with the hardware measurement (the red curve) very well, which verifies the correctness of the model. The positive peak is decreased from 648.75 μm to 408.75 μm. The negative peak is reduced from −870 μm to − 315 μm. However, as shown in Figure 15a, some peaks of the PI-controlled displacement still exceed the 30% threshold, thus a better control algorithm is needed.

5.2. Disturbance Observer-Based Controller

The disturbance observer-based controller shown in Figure 13 is verified in Simulink. The measured disturbance is inputted into both the continuous and discrete disturbance observer transfer function, and the observed disturbance is compared with the actual input current. It is shown in Figure 16. It deserves to be noticed that the disturbance actuation VCA is supposed to be linear (see Assumption 5). Thus the observed current is proportional to the observed disturbance.

As shown in Figure 16, the measured current follows the overall trend of the actual input well. When taking a closer look at the signal, there is a certain level of phase lag due to the low pass filter added for stability. To further study this phenomenon, two regions are zoom-in and highlighted in Figure 16. For each region, the time of the two peaks of the actual current ($t_1$ and $t_2$) and the first lagged peak of the observed current ($t_3$) are labeled. The phase lags are then calculated and compared with the theoretical phase lag of the low-pass filter as shown in

Table 3. Theoretical and measured phase lags of the two peaks highlighted in Figure 16.

	Frequency $\mathit{\omega }$ [rad/s]	Theoretical Lag [${}^{\circ }$]	Measured Lag [${}^{\circ }$]
peak 1	296.5	126.3	126.9
peak 2	432.3	141.7	161

using Equations (13)–(15).

$$\begin{array}{cc}\hfill \omega & =\frac{2\pi }{t_2-t_1}\hfill \end{array}$$

(13)

$$\begin{array}{cc}\hfill \mathrm{theoretical}\mathrm{lag}& =\angle \frac{1}{{(j\omega +150)}^2}\hfill \end{array}$$

(14)

$$\begin{array}{cc}\hfill \mathrm{measured}\mathrm{lag}& =\omega (t_3-t_1)\hfill \end{array}$$

(15)

After implementing the disturbance observer on the vibration suppression hardware, the PI controller is also added in parallel to compensate for the error from the disturbance estimate for better performance. The result is shown in Figure 17. The displacement is successfully suppressed and never exceeds 30% of the maximum open loop peak. The positive peak is decreased from 648.75 μm to 110 μm. The negative peak is reduced from −870 μm to −222.5 μm. Similar to the PI controller analysis, the peak ratio between the controlled displacement peaks and the open loop ones is plotted in Figure 17b to show the suppression of the DOBC controller on the vibration peaks. It is also listed in Table 2 and compared with the PI controller result.

6. Conclusions and Future Work

In this paper, a custom active vibration suppression actuator with an inertia force-based counterbalancing technique is implemented on a custom-built vibration testbed to suppress the vibration level of the OHT hand unit. In semiconductor fabrication plants, the vibration transferred to the FOUP via the OHT hand unit originates from the travel motion of an OHT vehicle on tracks. As the first step, a vibration generation testbed without the entire track is designed and verified to replicate the OHT travel vibration in lab environment. Using the fabricated vibration generation testbed, a vibration control VCA with the inertia force-based counterbalancing technique is utilized to suppress the vibration displacement of the OHT hand unit in the OHT travel direction. A double-PI controller is introduced to control the counterbalancing motion of the VCA without undesired boundary bumping. For better performance, a disturbance observer-based controller (DOBC) is designed. Both controllers are first simulated and verified in Simulink and later are implemented and compared on the testbed. The double-PI controller has a 64% decrease in maximum peak displacement (870 μm to 315 μm). The disturbance observer-based controller results in a 74% reduction in maximum peak displacement (870 μm to 230 μm).

By successfully suppressing the vibration level of the FOUP, the wafers will be kept intact during OHT transportation and the defect of semiconductor chips will be significantly decreased. Moreover, the active vibration suppression techniques presented in this work can also be applied to a broader range of applications where a low level of vibration is desired.

For future work, based on successful displacement level control of the OHT hand unit, the immediate next step is to analyze the actual vibration acceleration level on the FOUP. Although the acceleration level of the FOUP cannot be used for control, its real value is considered as the target variable to be controlled. Since the clamping mechanism between the hand unit and FOUP can be approximated as a parallel spring and damper system, transmitted force on the FOUP is expected to be directly affected by controlling the vibration displacement level of the hand unit. The acceleration value can potentially be observed through techniques such as Kalman filters. In the long term, the future plans primarily include two aspects: (1) multi-axis displacement level control of the OHT hand unit and (2) adaptation of flexure design to improve vibration transfer characteristics of the clamping mechanism between the hand unit and FOUP.