Design of a robust nonlinear observer for constrained systems

Abstract

In control applications, a full knowledge of the state variables is generally required for the computation of the control signals. This often translates into using an observer to estimate the state variables that are not readily available through measurements. The focus of this work is to develop a nonlinear robust observer for constrained systems whose dynamics are governed by a set of highly nonlinear differential-algebraic (D-A) equations. For fairly complicated and nonlinear constraint equations, the substitution method is not feasible to eliminate the superfluous coordinates. Therefore, the D-A form of the equations of motion of the system has to be dealt with in the design of the observer. The current study presents a general procedure for developing a robust nonlinear observer capable of accurately estimating all the state variables of a constrained system, including the superfluous ones. To assess the performance of the proposed observer, the multi-body dynamics of a piston/connecting-rod/crankshaft mechanism for a single cylinder internal combustion engine is considered. The equations of motion account for both the rigid and flexible motions of the crank-slider mechanism. The simulation results illustrate the capability of the proposed observer in accurately estimating all the state variables of the system. They demonstrate the robustness of the observer to modeling uncertainties and external disturbances. Moreover, the estimated state variables are shown to satisfy the nominal constraint equations.