  Simultaneous vibration control and energy harvesting of vehicle suspensions
have attracted significant research attention over the past decades. However,
existing energy harvesting shock absorbers (EHSAs) are mainly designed based on
the principle of linear resonance, thereby compromising suspension performance
for high-efficiency energy harvesting and being only responsive to narrow
bandwidth vibrations. In this paper, we propose a new EHSA design -- inerter
pendulum vibration absorber (IPVA) -- that integrates an electromagnetic rotary
EHSA with a nonlinear pendulum vibration absorber. We show that this design
simultaneously improves ride comfort and energy harvesting efficiency by
exploiting the nonlinear effects of pendulum inertia. To further improve the
performance, we develop a novel stochastic linearization model predictive
control (SL-MPC) approach in which we employ stochastic linearization to
approximate the nonlinear dynamics of EHSA that has superior accuracy compared
to standard linearization. In particular, we develop a new stochastic
linearization method with guaranteed stabilizability, which is a prerequisite
for control designs. This leads to an MPC problem that is much more
computationally efficient than the nonlinear MPC counterpart with no major
performance degradation. Extensive simulations are performed to show the
superiority of the proposed new nonlinear EHSA and to demonstrate the efficacy
of the proposed SL-MPC.
