Nonlinear State Estimation in Suspension Control Based on Takagi-Sugeno Model

Abstract

We present a new nonlinear state estimation approach based on Kalman filter theory and Takagi-Sugeno (TS) modeling for an active vehicle suspension application in this paper. The nonlinear state equations of a so-called hybrid suspension configuration, which result from nonlinear spring and damping characteristics, are exactly represented by means of a continuoustime TS system, i. e. a convex combination of local linear state space models. We derive observer gain matrices for each linear subsystem on the basis of standard Kalman filter theory, before we construct the global observer for the overall nonlinear system. Convergence of the global observer is ensured in terms of linear matrix inequality conditions. We then study the estimation performance of the TS Kalman filter in simulations and experiments on a hybrid quarter-car test rig using a measured road profile as disturbance input. The approach achieves a high estimation accuracy of well above 90 % in the simulation and 70 − 90 % in the experiments.

Feasibility of Neural Network Based Virtual Sensor for Vehicle Unsprung Mass Relative Velocity Estimation

“…During hyperparameter optimisation of the selected NN model, the predefined window size was used for data samples and selectable unit counts in BiLSTM and FC layers. The window sizes of 3,7,11,17,19,21,25,31 and 51 have been used. The bigger the window size, the more features can be extracted from the signals, especially the lower frequency and more complex features.…”

“…For the task, the Direct Virtual Sensor design technique has been proposed. In 2014, Pletschen and Badur [21] presented a new nonlinear suspension state estimation approach based on Kalman Filter theory and Takagi-Sugeno modelling. Wang et al [22] proposed the Adaptive Kalman Filter for the purpose to obtain accurate state estimation of a vehicle's suspension system under different road conditions.…”

Nonlinear state estimation for suspension control applications: a Takagi-Sugeno Kalman filtering approach

“…This paper builds on the preliminary results presented in Pletschen and Badur (2014). In particular, the TS Kalman filtering approach is further developed with respect to the local nature of LMI-based stability proofs when applied to TS systems.…”

“…Simon (2003) describes a similar approach for fuzzy discrete-time systems, where optimality properties and simulation results for a vehicle tracking problem and a backing up truck-trailer are discussed. However, in Pletschen and Badur (2014) and also in the work at hand, the continuoustime case of state estimation is studied, since an exact transformation of the given nonlinear plant model into the discrete-time TS representation via the sector nonlinearity approach is not possible without inducing discretization errors. Moreover, it is noteworthy that nonlinear functions involved in the modeling of the vehicle suspension studied here are rather given in terms of identified nonlinear force characteristics, i.e.…”

“…Taking the benefits of linear Kalman filter theory and exact TS modeling together, a TS Kalman filtering approach has been presented in Pletschen and Badur (2014), which allows for state feedback in vertical suspension control. Therefore, the given nonlinear model of a hybrid suspension system in a quarter-car framework is represented as a family of linear state space models.…”