Naive approximate realization of noisy data

\u3cp\u3eThis paper presents suboptimal solutions to the problem of Approximate Partial Realization: given a multivariable formal power series of finite length, a state space description has to be constructed with limited dimension, in such a way that it approximates the available matrix sequence with respect to some specific criterion. The methods based on the Ho-Kalman algorithm and employing a Hankel matrix or an alternative to it, a Page matrix, fail theoretically but appear to be practically quite useful. Results of the simulations allow us to determine in which cases the Hankel or Page matrix approach would be more appropriate.\u3c/p\u3

Robust vibration isolation by frequency-shaped sliding surface control with geophone dynamics

The Frequency-Shaped Sliding Surface Control (FSSSC) has been recently applied to the Active Vibration Isolation System (AVIS) and the robust skyhook performance is experimentally validated. However, the performance of this approach is theoretically limited by the sensor dynamics. This paper generalizes the FSSSC approach as a two-step AVIS control design method. The first step is to design the sliding surface which determines the designed performances. The second step is to design the regulator which guarantees the convergence of the system dynamics. As long as this convergence is guaranteed, the designed performances would be realized. The vibration isolation of the original plant is therefore transformed to the regulation of a new system which is composed of the original plant and the sliding surface. As the regulator design has been well studied in the literature, this paper focuses on the sliding surface design. An example sliding surface design to achieve low-frequency vibration isolation is provided. The FSSSC of an example 1-DOF plant using both original and the improved sliding surface are compared. Theoretical calculations show that the improved sliding surface has no theoretical performance limit and achieves robust vibration isolation at much lower frequencies than the original design

On the interplay between model uncertainty and data disturbances

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Vibration control with optimized sliding surface for active suspension systems using geophone

The frequency shaped sliding surface approach has been proposed for control of a suspension system measured by a relative displacement sensor and an absolute velocity sensor (geophone). The vibration isolation performance (transmissibility) is determined by the sliding surface design. The direct disturbance-force rejection performance (compliance) is determined by the regulator design. The sliding surface was designed by the pole placement method in our previous work. But manual pole placement is difficult to achieve the optimal performance. This paper formulates the problem of sliding surface optimization taking into account the geophone dynamics and solves it using Matlab optimization toolbox. The vibration isolation performance designed by sliding surface optimization is much better than the manual pole placement. The regulator is designed to realize the designed performances and to reduce the compliance

A simple LPV identification and control scheme for an electromagnetic suspension system

A simple Linear Parameter Varying (LPV) identification and control sheme is applied to a single degree-of-freedom (DOF) noncontact and highly non-linear electromagnetic levitation system. The control requirements demand accurate positioning and robust performance in a working range of high nonlinearity. An LPV model and a simple LPV controller structure are introduced. Closed-loop stability can be verified by LMIs. Simulation results show that the proposed LPV controller stabilizes the electromagnetic system in a working range of high nonlinearity with robust performance