Nonlinear model predictive control of a linear axis based on pneumatic muscles

This paper presents a nonlinear optimal control scheme for a mechatronic system that consists of a guided carriage and an antagonistic pair of pneumatic muscles as actuators. Modelling leads to a system of nonlinear differential equations including polynomial approximations of the volume characteristic as well as the force characteristic of the pneumatic muscles. The proposed control has a cascade structure: the nonlinear normoptimal control of both pneumatic muscle pressures is based on an approximative solution of the corresponding HJB-equation, whereas the outer control loop involves a multivariable NMPC of the carriage position and the mean internal pressure of the pneumatic muscles. To improve the tracking behaviour, the feedback control loops are extended with nonlinear feedforward control based on differential flatness. Remaining model uncertainties as well as nonlinear friction can be counteracted by an observer-based disturbance compensation. Experimental results from an implementation on a test rig show an excellent control performance.