Model based reduced-order observers for a class of mechatronic systems with mitigation of disturbances effects using the Attractive Ellipsoid Method

State-estimation of mechatronic systems is essential because, in addition to position and velocity, there are electric and magnetic signals that must be measured, and can lead to sophisticated and expensive instrumentation systems. This paper addresses the problem of state-estimation for underactuated mechanical systems whose active joints are driven by permanent magnet dc-motors. Luenberger-type structures are designed, where the measured state variables and the dynamic model are used to construct the unavailable ones, in presence of uncertainties and disturbances as inputs. To avoid the peaking phenomenon is one of the main challenges on state observation for nonlinear systems. Underactuated mechatronic systems are not immune to this problem, which is exacerbated when external disturbances are taken into account. The major purpose here is to use a robust reduced observer to estimate the unmeasured state variables. The Attractive Ellipsoid Method provides reliable estimation of unmeasured state signals because it reduces the influence of external disturbances on the estimate error signals. This ensures that the estimated signals converge to an invariant set of minimal size around the real ones. The first design is based on the quasi-linear representation that meets the observability condition. The second considers the entire nonlinear model, which necessitates the availability of the entire position vector. The major findings are demonstrated experimentally on a non-traditional mechatronic system: the linear double pendulum system whose last joint is constrained by two linear springs. This shows a significant improvement of the estimation response, concerning robust techniques based on the linear approximation, towards its application in designing an adaptive observer to provide state and parameters estimation simultaneously, which is essential in robust and adaptive control systems.