Design of a Takagi-Sugeno State and Disturbance Observer for a Torque-Controlled Hydrostatic Transmission

In this paper, a Takagi-Sugeno (TS) state and disturbance observer is designed. The corresponding estimates are employed in a decentralized control approach for the normalized tilt angle of the hydraulic motor as well as the motor torque of a hydrostatic transmission. For the observer design, a nonlinear state-space model is written in quasi-linear form and extended by two integrator disturbance models. The observer gain matrix is derived by an exact interpolation of optimal designs at the vertices of a polytopic description using corresponding membership functions. Asymptotic stability of the observer error dynamics is guaranteed by solving a set of linear matrix inequalities (LMIs) resulting in a joint Lyapunov function. For an accurate trajectory tracking, feedback control is extended by feedforward control. The estimated disturbances from the TS observer are used for a subsequent disturbance rejection. The performance of the observer-based control structure is shown by simulations based on a validated model of a dedicated test rig which is available at the Chair of Mechatronics, University of Rostock.