Estimation of MIMO closed loop systems using transfer function data
For the development of high tech systems such as lithographic positioning systems, throughput and accuracy are the main requirements. Nowadays, the trend to reach the demanded accuracy and throughput levels is designing lightweight and consequently more flexible systems. To control these systems with a more effective and less conservative way, control design should go beyond the traditional rigid control and cope with the flexibilities that limit achievable bandwidth and performance. Therefore conventional loop shaping methods are not sufficient to reach the performance criterions. Since obtaining an accurate parametric model is very complex and time-consuming for these high tech systems, using well-developed model-based controller synthesis methods is also not a superior option. To achieve desired performance criterions, one solution can be implemented is reducing the gap between model-based and data-based control synthesis methods. In previous research,, a method was developed to define the dynamic behavior of the system without a need for a parametric model. By this method transfer function data (TFD), which provides the information on the whole s-plane can be obtained from frequency response data (FRD) of the system. This innovation was a very important step to use data-based techniques for model-based controller synthesis methods.
In this project firstly the standard technique to obtain TFD defined in  is extended. This standard technique to obtain TFD is not compatible for systems with pure integrators. To extend the methodology also for those systems, two techniques, which are altering the contour and filtering the system, are proposed. Then, the accuracy of TFD is investigated in detail. It is shown that the accuracy of TFD depends on the quality of FRD obtained and the computation techniques used to calculate TFD. Then, a technique which enables to determine the closed-loop poles of a MIMO system using TFD is discussed. The validity of the technique is proven with the help of complex function theory and calculus. Also, the factors that prevent determination of the closed-loop poles are discussed. In addition, it is observed that the accuracy of the closed-loop determination method depends on the quality of the obtained TFD and the computation techniques. The proposed theory to obtain TFD and determination of closed-loop poles is validated with experiments conducted on a prototype lightweight system. Also, using experimental frequency response data of NXT-A7 test rig, the success of the proposed methodology is validated also for complex systems. Through these experimental results, it can be concluded that this new technique could be very advantageous in terms of ease of use and accuracy to determine the closed-loop poles of a MIMO lightly damped system.
People: Yasemin Vardar, Niels van Dijk, Marteen Steinbuch
See publication here.