State estimation in a magnetic levitation system using higher order implicit numerical methods

When digital control systems are operated at relatively large sampling times, the use of higher order numerical control models improves the quality of state estimation and the robustness of feedback control. In this article we show how implicit one-step integration methods, such as the second order implicit midpoint rule and higher order Gauss collocation schemes, can be exploited for highly accurate state estimation at very large sampling times. We first introduce discrete-time variants of the nonlinear Luenberger observer based on the implicit midpoint rule, and then extend the concept of Newton observers to higher order implicit discrete-time system models. This simple type of a moving horizon estimator allows to easily include the estimation of uncertain control inputs. In a series of experiments with nonlinear backstepping control of the magnetic levitation system, we prove the drastically increased performance of the proposed estimators at slow sampling rates. Detailed error analyses illustrate the limits of the sampling times for the different estimators, and prove that the higher order estimation does not affect the theoretical error of order O(h²) of the second order control implementation.     «

When digital control systems are operated at relatively large sampling times, the use of higher order numerical control models improves the quality of state estimation and the robustness of feedback control. In this article we show how implicit one-step integration methods, such as the second order implicit midpoint rule and higher order Gauss collocation schemes, can be exploited for highly accurate state estimation at very large sampling times. We first introduce discrete-time variants of the...     »