Effect of inertia variations for active vibration isolation systems
Introduction
Owing to the developments in modern industries, there is an increasing demand for high precision systems and vibration control technologies. Microvibrations can degrade the quality and yield of products in numerous precision processes, such as photolithography, wafer inspection, and flat-panel-display manufacturing [1,2]. Microvibrations are considered to be disturbances in the process of normalizing and solving a system, and they result in an unpredictable model. In addition, microvibrations can cause errors while an output signal follows an input reference signal. Thus, vibration control is required in precision processes to minimize errors and consequently improve production performance [[3], [4], [5]]. Microvibrations can be categorized as unstandardized vibrations, which are applied from the outside of equipment, and standardized vibrations, which are generated inside equipment. These microvibrations can be stabilized through control using an active vibration isolation system (AVIS) [[6], [7], [8]]. However, previous studies have not analyzed the effects of inertia variation on an AVIS and have only set specifications for the performance of the system. The performance of a conventional AVIS can decrease owing to a change in the system model. Furthermore, the model, performance, and optimal gain of the system may change with inertia. Generally, control gain allows optimal control performance for a specific model. However, the system model changes based on the position of the stage mover. Consequently, the control gain may not be optimal. If inertia variation is significant, it is divergent owing to the critical point of the system. This problem is limited by the gain value.
To overcome these limitations, the influence of inertia variation on the AVIS and active control of the AVIS depending on the inertia variation in a target system were analyzed here. In addition, the robustness and performance of the system were studied when the inertia of the actual model of the system was changed. As a result, the system related to the rotational motion led to model changes, according to the behavior of the system, which required further updates. The adaptive linear quadratic Gaussian (LQG) controller was applied to update the model. The adaptive LQG is a control algorithm based on the state space. It is easier to update the model using the LQG that using the conventional error-based PID controller. The LQG is also suitable for analyzing the response characteristics of a multi-input multi-output (MIMO) system. The performance comparison of the PID and LQG controllers has been studied previously [9].
In this study, an AVIS with six degrees of freedom (6-DOF) and an adaptive LQG controller is used. The system comprises four pneumatic isolators and eight optimized voice coil motors (VCMs). Six position sensors and eight geophone sensors (velocity) are used for the 6-DOF system. The AVIS is developed and validated using a dSPACE controller. The remainder of this paper is organized as follows: Section 2 presents the modeling of the proposed system. The verification of the adaptive LQG algorithm and the state–space modeling are described in Section 3. Section 4 presents the evaluation of the performance of the system according to inertia variation using the proposed control algorithm. Section 5 presents the conclusions and the direction of future work.
Section snippets
System configuration
In this study, a module including a drive unit, sensor unit, and pneumatic passive element was constructed to design the AVIS. This system was divided into a lower frame for supporting the lower end, an upper plate that matched the resonance frequency of the system and fixed a target system, and a target system that required vibration isolation [[10], [11], [12]].
Microvibrations were applied to the upper plate through a drive and measurement module, beginning with the lower frame. As shown in
6-DOF state–space modeling for AVIS control
This section describes the application of the modeling and kinematics of the proposed AVIS to control the system using the state–space algorithm, which consists of a combination of state and output equations. The state space can be divided into a regulator that stabilizes the system through a state variable and an observer that follows the state of the system [[17], [18], [19]].
Fig. 5 depicts a block diagram of the entire system with the state space. The process of updating the observer model
Performance evaluation of the AVIS with respect to inertia variations
The inertia of the system inevitably changes owing to the position of the mover. This sections describes the investigation of the effect of inertia variation on the robustness and control performance of the system. Inertia is affected by the weight and distance between the center of gravity and the mover of the stage. However, the test bed used in the experiment has a short driving distance, and the mass of the mover is small. Thus, it is not easy to show the inertia variation due to the
Conclusion
This study describes the modeling, state–space algorithm design, and experiments conducted for the AVIS. In addition, the performance of the system is evaluated with respect to inertia variation. The proposed control algorithm is based on the state space based LQG controller. The bandwidth and stability are analyzed by evaluating the followability and characteristic equations through the state equations. It is easy to ensure the bandwidth of the observer when the bandwidth of the observer is
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
This work was supported by Korea Institute of Industrial Technology (KITECH) and Korea Institute for Advancement of Technology (KIAT) grant funded by the Korea Government (MOTIE) (P0008458, The Competency Development Program for Industry Specialist).
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