# Noninteracting Control Design for 6-DoF Active Vibration Isolation Table with LMI Approach
## 1 Introduction
Vibration attenuation performance was presented, but only for one direction, whereas the response in other directions was not shown, hence, overall performance could not be concluded. In [5], the authors proposed a sheet current model that considers the end effects of the VCMs used in the design of a 6-DoF AVIS, and the parameters of the AVIS were identified using the hybrid functions approach. And then, a composite nonlinear feedback (CNF) controller was designed following the modal decomposition method. The CNF controller was designed for each pair of input-output, so there were six individual controllers in total. However, the identified model is incompatible with the dynamic characteristics and the interaction isolation performance of this control system was not discussed. Generally, the modal decomposition is well known to obtain the diagonal form of a system model, but it is a rather analytic method than a decoupling control approach. Another method treats the interactions as disturbances affecting the system. [PERSON] et al. [7] proposed an \(H_{\infty}\) control with a direct disturbance suppression technique and the effectiveness of the control strategy was verified using a 2-DoF AVIS. Unfortunately, this approach is only effective for the 2-DoF system and is difficult to implement for more complex systems. Moreover, other decoupling techniques have been studied such that only one controller is designed for the whole system and all the interactions are effectively isolated. For instance, diagonal decoupling by static-state feedback [9], decoupling with dynamic compensation [10], noninteracting constraints [11], robust noninteracting control [12], input-output energy decoupling [13], row by row decoupling [14], and noninteracting control based on the relaxed control [15], as well as other decoupling controllers [16; 17; 18], have been applied in various applications. Nevertheless, the common issue with these control system designs lies in the analytical methodology of deriving the proper control matrices that not only decouple the interactions but also achieve the desired performance. Therefore, in this paper, a new robust noninteracting control system design method for a 6-DoF AVIS system is proposed. The key point of the approach is that the resulting system configuration affects the control input in a way that each reference signal controls the corresponding control output without influencing the other ones. The proposed controller is designed based on an integral-type servosystem, which consists of state feedback and unity feedback. Conditions on the controller matrices are analyzed to obtain noninteracting performances. Even though the stability of the closed-loop system is not guaranteed, the system performance is not satisfied. Therefore, new methods to design the feedback-matrix gain and unity-feedback matrix gains are introduced. With the use of the linear matrix inequality (LMI) technique, the derived solutions provide optimal control matrices to fulfill both decoupling and stability requirements. The efficiency of the proposed control strategy was evaluated through two simulation scenarios: platform positioning and vibration isolation. This paper is structured as follows: Section 2 presents the system modeling of the 6-DoF AVIS. In Section 3, the noninteracting control design is described in detail. Then, simulation results are presented in Section 4. Finally, the conclusions of this study are summarized in Section 5.