Explicit model predictive control of an active suspension system

Abstract

Model predictive control (MPC) is increasingly finding its way into industrial applications, due to its superior tracking performance and ability to formally handle system constraints. However, the real-time capability problems related to the conventional implicit model predictive control (i-MPC) framework are well known, especially when targeting low-cost electronic control units (ECUs) for high bandwidth systems, such as automotive active suspensions, which are the topic of this paper. In this context, to overcome the real-time implementation issues of i-MPC, this study proposes explicit model predictive control (e-MPC), which solves the optimization problem off-line, via multi-parametric quadratic programming (mp-QP). e-MPC reduces the on-line algorithm to a function evaluation, which replaces the computationally demanding on-line solution of the quadratic programming (QP) problem. An e-MPC based suspension controller is designed and experimentally validated for a case study Sport Utility Vehicle (SUV), equipped with the active ACOCAR suspension system from the Tenneco Monroe product family. The target is to improve ride comfort in the frequency range of primary ride (< 4 Hz), without affecting the performance at higher frequencies. The proposed e-MPC implementations reduce the root mean square (RMS) value of the sprung mass acceleration by > 40% compared to the passive vehicle set-up for frequencies < 4 Hz, and by up to 19% compared to the same vehicle with a skyhook controller on the 0-100 Hz frequency range.

Development of a model predictive controller for an active torsional vibration damper to suppress torsional vibrations in vehicle powertrains

“…A multivariable MPC-based vibration reduction system for a flexible link mechanism is investigated in Hassan et al, 14 an active control of engine-induced vibrations is presented in Bohn et al 15 , Kowalczyk et al 16 An extended LQG controller with an estimator to suppress the vibrations in the transmission of power-split vehicles is proposed in Zhang et al 17 The MPC suspension controller aiming at enhancing the ride comfort and the vehicle handling is evaluated by the acceleration at the center of gravity and the roll motion in the works. [18][19][20][21] The MPC is offered for the tip-in and tip-out cycles of the vehicles in Xiaohui et al 22 The article Taka´cs et al 23 presents an embedded active vibration suppression system featuring real-time explicit MPC implemented on a microcontroller. A robust hybrid control system to combine the passive electromagnetic shunt damper with an active control to improve the performance is investigated in Paknejad et al 24 The MPC is applied to the two-mass resonant system which has a motor and a load connected with a flexible shaft in Wang et al 25 The MPC is implemented on a low-cost hardware at high sampling rates using online quadratic programming methods for nontrivial models in the paper Wills et al 26 An MPC model is established based on experimental data to control electromagnetic actuator for a quarter vehicle suspension system in the article Huang et al 27 The research Caruntu et al 28 is related to a realtime implementation of a networked predictive controller to minimize driveline vibrations while compensating the time-varying delays.…”