Application of a novel linearization method to compare the on–off control strategies modeled by piecewise linear systems

In this study, a novel approach for linearization of piecewise linear systems is applied to approximate the root mean square output of a quarter car model with semiactive control. The on–off control strategies, balance logic, skyhook, groundhook, and hybrid are modeled by piecewise linear systems with variable friction. By the proposed method, one can attach, for each output of practical interest, a linear system with the same transmissibility factor. The obtained transmissibility factors are used to approximate the root mean square output of considered semiactive systems using the power spectral density input–output relationships for constant parameter linear systems with stationary random inputs. The method is applied for optimization of hybrid control strategy with respect to a performance index defined in terms of sprung mass acceleration, suspension travel, and dynamic contact force.