Moving force identification based on the frequency-time domain method

This paper develops a data-driven decoupling feedforward control scheme with iterative tuning to meet the challenge of the crosstalk problem in multiple-input multiple-output (MIMO) motion control systems. In contrast to model-based approaches, iterative tuning fully utilizes the available data to address the practical difficulty in obtaining an accurate dynamic model. The MIMO feedforward signal is iteratively updated by minimizing the developed crosstalk criterion. Specifically, to make the optimal problem convex, the MIMO feedforward controller is structuralized with a finite impulse response (FIR) filter and is parameterized by corresponding coefficients. A data-driven unbiased gradient approximation based on the Toeplitz matrix is then developed for updating the parameter vector. Furthermore, to deal with the Hessian inverse problem encountered in the numerical calculation of the update law, a stable inversion method combined with singular value decomposition is employed. The basic characteristics of the proposed scheme, including convergence accuracy and convergence rate, are illustrated through simulation. Finally, the proposed data-driven decoupling control scheme is applied to a developed ultraprecision motion stage, and the results show that the approach can significantly attenuate the servo error caused by the crosstalk problem. This simplicity and accuracy oriented control method without need of dynamic modeling is definitely suitable for industrial applications.

A Data-Driven Iterative Decoupling Feedforward Control Strategy With Application to an Ultraprecision Motion Stage

This paper addresses the problem on the identification of moving vehicle axle loads based on measured bridge responses using a frequency-time domain method. The focus is on the evaluation of two solutions to the overdetermined set of equations established as part of the identification method. The two solutions are (i) direct calculation of the pseudo-inverse and (ii) calculation of the pseudo-inverse via the singular value decomposition (SVD) technique. For this purpose, a bridge-vehicle system model was fabricated in the laboratory and the bending moment responses of bridge model were measured as a two-axle vehicle model moved across the bridge deck. The moving axle loads are then calculated from the measured responses via the two solutions to the over-determined set of equations. The effects of changes in the bridge-vehicle system, measurement and algorithm parameters on the two solutions are evaluated. Case studies show that the moving force identification is more feasible and its accuracy acceptable with the use of the SVD technique. This technique can effectively enhance the identification method and improve the identification accuracy over that of the direct pseudo-inverse solution.

Moving Force Identification based on the Frequency-Time Domain Method

This paper presents experimental results of source identification for a non-minimum phase system. Generally, a causal linear system may be described by matrix form. The inverse problem is considered as a matrix inversion. Direct inverse method cannot be applied for a non-minimum phase system, because the system has ill-conditioning. Therefore, in this study the SVD inverse technique is introduced to execute an effective inversion. In a non-minimum phase system, its system matrix may be singular or near-singular and has very small singular values. These very small singular values have information about a phase of the system and ill-conditioning. Using this property, we could solve the ill-conditioned problem of the system and then verify it for the practical system (cantilever beam). The experimental results show that the SVD inverse technique works well for a non-minimum phase system. This inverse technique can be applied to the estimation of the magnitude of impact force, which becomes often a cause of damage to a mechanical system.

S. Hashemi

Papers

The Interpretation of Singular Values in the Inversion of Minimum and Non-Minimum Phase Systems