An L Disturbance Attenuation Approach to the Nonlinear Benchmark Problem

In this paper we use the theory of L disturbance at tenuation for linear H and nonlinear systems to obtain solutions to the Nonlinear Benchmark Problem NLBP proposed in the companion paper by Bupp et al By considering a series expansion solution to the Hamilton Jacobi Isaacs Equation associated with the nonlinear disturbance attenuation problem we obtain a series expansion solution for a nonlinear controller Numerical simulations compare the performance of the third order approximation of the nonlinear controller with its rst order approximation which is the same as a linear H controller obtained from the linearized problem Introduction The control of nonlinear systems has received much attention in recent years and many nonlinear control design methodologies have been developed It is im portant to determine the advantages and limitations of the di erent nonlinear control design methodologies The Nonlinear Benchmark Problem NLBP proposed by Bupp et al is an initial attempt to achieve this objective The NLBP involves a cart of mass M whose mass center is constrained to move along a straight horizontal line see Figure Attached to the cart is a proof body actuator of mass m and moment of inertia I Relative to the cart the proof body rotates about a vertical line passing through the cart mass center The nonlinearity of the problem comes from the interaction between the translational motion of the cart and the rotational motion of the eccentric proof mass