1,713
Views
133
CrossRef citations to date
0
Altmetric
Original Articles

Hybrid model predictive control application towards optimal semi-active suspension

, , &
Pages 521-533 | Received 30 Jun 2005, Accepted 16 Nov 2005, Published online: 20 Feb 2007
 

Abstract

The optimal control problem of a quarter-car semi-active suspension has been studied in the past. Considering that a quarter-car semi-active suspension can either be modelled as a linear system with state dependent constraint on control (of actuator force) input, or a bi-linear system with a control (of variable damping coefficient) saturation, the seemingly simple problem poses several interesting questions and challenges. Does the saturated version of the optimal control law derived from the corresponding un-constrained system, i.e. “clipped-optimal”, remain optimal for the constrained case as suggested in some previous publications? Or should the optimal deviate from the “clipped-optimal” as suggested in other publications? If the optimal control law of the constrained system does deviate from its unconstrained counter-part, how different are they? What is the structure of the optimal control law? Does it retain the linear state feedback form (as the unconstrained case)? In this paper, we attempt to answer some of the above questions by utilizing the recent development in model predictive control (MPC) of hybrid dynamical systems.

The constrained quarter-car semi-active suspension is modelled as a switching affine system, where the switching is determined by the activation of passivity constraints, force saturation, and maximum power dissipation limits. Theoretically, over an infinite prediction horizon the MPC controller corresponds to the exact optimal controller. The performance of different finite-horizon hybrid MPC controllers is tested in simulation using mixed-integer quadratic programming. Then, for short-horizon MPC controllers, we derive the explicit optimal control law and show that the optimal control is piecewise affine in state. In the process, we show that for horizon equal to one the explicit MPC control law corresponds to clipped LQR as expected. We also compare the derived optimal control law to various semi-active control laws in the literature including the well-known “clipped-optimal”. We evaluate their corresponding performances for both a deterministic shock input case and a stochastic random disturbances case through simulations.

Acknowledgement

This work was partially supported by the HYCON Network of Excellence, contract number FP6-IST-511368.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.