Research on Advanced Control Strategies for Vehicle Active Seat Suspension Systems

Vehicle seat suspensions play a very important role in vibration reduction for vehicle drivers, especially for some heavy vehicles. Compared with small vehicles, these heavy vehicle drivers suffer much more from vibrations, which influence driving comfort and may cause health problems, so seat suspensions are necessary for those heavy vehicle drivers to reduce vibrations and improve driving comfort. Advanced control systems and control strategies are investigated for vehicle seat suspensions in this project. Firstly, for an active single-degree of freedom (single-DOF) seat suspension, a singular system-based approach for active vibration control of vehicle seat suspensions is proposed, where the drivers’ acceleration is augmented into the conventional seat suspension model together with seat suspension deflection and relative velocity as system states to make the suspen- sion model as a singular system. Then, an event-triggered H∞ controller is designed for an active seat suspension, where both the continuous and discrete-time event-triggered schemes are considered, respectively. The proposed control method can reduce the work- load of data transmission of the seat suspension system and work as a filter to remove the effect of noise, so it can decrease the precision requirement of the actuator, which can help to reduce the cost of the seat suspension. For complicated seat suspension systems, a singular active seat suspension system with a human body model is also established and an output-feedback event-triggered H∞ controller is designed. The accelerations of each part are considered as part of the system states, which makes the system a singular sys- tem. The seat suspension deflection, relative velocity, the accelerations of the seat frame, body torso, and head are defined as the system outputs. At last, to deal with whole-body vibration, a control system and a robust H∞ control strategy are designed for a 2-DOF seat suspension system. Two H∞ controllers are designed to reduce vertical and rotational vibrations simultaneously. All the proposed seat suspension systems and control methods are verified by simulations and some are also tested by experiments. These simulation and experimental results show their effectiveness and advantages of the proposed methods to improve the driving comfort and some can reduce the workload of data transmission

Balancing and model reduction for discrete-time nonlinear systems based on Hankel singular value analysis

This paper is concerned with balanced realization and model reduction for discrete-time nonlinear systems. Singular perturbation type balanced truncation method is proposed. In this procedure, the Hankel singular values and the related controllability and observability properties are preserved, which is a natural generalization of both the linear discrete-time case and the nonlinear continuous-time case.

Energy preserving model order reduction of the nonlinear Schr\"odinger equation

An energy preserving reduced order model is developed for two dimensional nonlinear Schr\"odinger equation (NLSE) with plane wave solutions and with an external potential. The NLSE is discretized in space by the symmetric interior penalty discontinuous Galerkin (SIPG) method. The resulting system of Hamiltonian ordinary differential equations are integrated in time by the energy preserving average vector field (AVF) method. The mass and energy preserving reduced order model (ROM) is constructed by proper orthogonal decomposition (POD) Galerkin projection. The nonlinearities are computed for the ROM efficiently by discrete empirical interpolation method (DEIM) and dynamic mode decomposition (DMD). Preservation of the semi-discrete energy and mass are shown for the full order model (FOM) and for the ROM which ensures the long term stability of the solutions. Numerical simulations illustrate the preservation of the energy and mass in the reduced order model for the two dimensional NLSE with and without the external potential. The POD-DMD makes a remarkable improvement in computational speed-up over the POD-DEIM. Both methods approximate accurately the FOM, whereas POD-DEIM is more accurate than the POD-DMD

Balanced truncation for linear switched systems

In this paper, we present a theoretical analysis of the model reduction algorithm for linear switched systems. This algorithm is a reminiscence of the balanced truncation method for linear parameter varying systems. Specifically in this paper, we provide a bound on the approximation error in L2 norm for continuous-time and l2 norm for discrete-time linear switched systems. We provide a system theoretic interpretation of grammians and their singular values. Furthermore, we show that the performance of bal- anced truncation depends only on the input-output map and not on the choice of the state-space representation. For a class of stable discrete-time linear switched systems (so called strongly stable systems), we define nice controllability and nice observability grammians, which are genuinely related to reachability and controllability of switched systems. In addition, we show that quadratic stability and LMI estimates of the L2 and l2 gains depend only on the input-output map.Comment: We have corrected a number of typos and inconsistencies. In addition, we added new results in Theorem

Model Reduction of Multi-Dimensional and Uncertain Systems

We present model reduction methods with guaranteed error bounds for systems represented by a Linear Fractional Transformation (LFT) on a repeated scalar uncertainty structure. These reduction methods can be interpreted either as doing state order reduction for multi-dimensionalsystems, or as uncertainty simplification in the case of uncertain systems, and are based on finding solutions to a pair of Linear Matrix Inequalities (LMIs). A related necessary and sufficient condition for the exact reducibility of stable uncertain systems is also presented