Direct data-driven filter design for automotive controlled suspensions

This paper investigates the filter design problem for automotive controlled suspensions when no mathematical model of the system is available, but a set of initial experiments can be performed, where also the variable to be estimated is measured. The problem of designing suitable linear time-invariant filters is here investigated, focusing the attention on the estimation of the relative vertical speed between chassis and wheel, using the data provided by two accelerometers measuring the chassis and wheel accelerations. Disturbances and noises are supposed to be norm-bounded and optimality refers to the minimization of the induced norm from disturbances to the estimation error. A Set Membership formulation is followed and, for classes of filters with exponentially decaying impulse response, an approximating set is determined guaranteed to contain all the solutions to the optimal filtering problem. A method is proposed for designing almost-optimal filters with finite impulse response, whose worst-case estimation error is at most twice the lowest achievable one. Numerical simulations using standard "benchmark" road profiles illustrate the effectiveness of the proposed solutions.