Acceleration feedback via an algebraic state estimation method

In many mechanical systems, only accelerations are available for feedback purposes. For example, certain aerospace, positioning systems and force-position controllers in robotic systems, use accelerometers as the only sensing device. This paper presents initial steps towards an algebraic approach for the state estimation based feedback control problem in systems where the highest order derivative of the controlled variable is available. An illustrative case is presented dealing with the trajectory tracking problem for a second order position system on which only the acceleration is available for measurement. Based on an algebraic approach, an on-line algebraic estimator is developed for the unmeasured position and velocity variables. The obtained expressions depend solely on iterated integrals of the measured acceleration output and of the control input. The approach is robust to noisy measurement and it has the advantage to provide fast, on-line, non-asymptotic state estimations in the form of formulae requiring only the input and the output of the system. Based on these estimations, a linear feedback control law including estimated position error integrals is designed illustrating the possibilities of acceleration feedback via algebraic state estimation.