Abstract
Latest advances in road profile sensors make the implementation of preemptive suspension control a viable option for production vehicles. From the control side, model predictive control (MPC) in combination with preview is a powerful solution for this application. However, the significant computational load associated with conventional implicit model predictive controllers is one of the limiting factors to the widespread industrial adoption of MPC. As an alternative, this article proposes an explicit model predictive controller (e-MPC) for an active suspension system with preview. The MPC optimization is run offline, and the online controller is reduced to a function evaluation. To overcome the increased memory requirements, the controller uses the recently developed regionless e-MPC approach. The controller is assessed through simulations and experiments on a sport utility vehicle demonstrator with controllable hydraulic suspension actuators. For frequencies < 4 Hz, the experimental results with the regionless e-MPC without preview show a ∼10% reduction of the root-mean-square (RMS) value of the vertical acceleration of the sprung mass with respect to the same vehicle with a skyhook controller. In the same frequency range, the addition of preview improves the heave and pitch acceleration performance by a further 8 to 21%.
Highlights
T HE performance benefits of active suspension systems that account for the road profile ahead have been investigated and demonstrated by several authors ([1]–[4])
With simplified notations (4) can be rewritten as w (k + 1) = 0 Ar,d w (k) + Er,d yr (k) where w = [ w0 · · · wN ]T is the vector of the road system states, i.e., the road profile heights ahead of the tire, which consists of N points spaced according to the time step Δt of the internal model; Ar,d is the shift model matrix; yr (k) = wN (k + 1) is the disturbance input provided by the preview sensor measurement; and Er,d is the road system disturbance matrix
The simulations with the controllers were based on realistic data of next-generation suspension actuators with higher bandwidth than those installed on the real vehicle demonstrator, and under the hypothesis of perfect synchronization of the preview input with the actual road profile at the wheels
Summary
T HE performance benefits of active suspension systems that account for the road profile ahead have been investigated and demonstrated by several authors ([1]–[4]). Several authors, e.g., [22]–[31], proposed MPC implementations for preview suspension systems. To the best of our knowledge, the published work to date focused on conventional implicit model predictive control (i-MPC) implementations, in which the optimization is run online. To facilitate the industrial adoption of MPC for active suspension control with preview, this article proposes an e-MPC approach ([32], [33]). 2) The adoption of the regionless e-MPC approach for suspension control This facilitates the implementation at shorter time steps with respect to i-MPC, and reduces the memory requirements in comparison with the traditional region-based e-MPC. The proof-of-concept regionless e-MPC algorithm is assessed through vehicle simulations and preliminary experimental tests on a vehicle demonstrator equipped with four commercially available active suspension actuators
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