Feedforward Control Design for Finite-Time Transition Problems of Nonlinear Systems with Input and Output Constraints

Feedforward controls are used in many practical control applications as an extension of the feedback control loop to separately design the tracking performance by the feedforward part and the robustness and closed-loop dynamics by the feedback part ("two-degree-of-freedom control"). However, only few systematic approaches are available for the feedforward control design due to the required inversion of the input-output behavior and the respective difficulties arising with nonlinear systems. Moreover, if the considered system is nonminimum-phase, the numerical solution of the unstable internal dynamics can lead to a noncausal feedforward control. The feedforward design is further complicated if input and output constraints have to be satisfied, e.g. to account for actuator constraints or to impose bounds on the output trajectory.

The offline feedforward design presented in this thesis considers the transition between two stationary setpoints in a finite time interval, which represents a particularly convenient feedforward design task. Practical applications are e.g. rest-to-rest motions in mechatronics or load changes in process control. The finite-time transition problem between stationary setpoints is treated as a twopoint boundary value problem (BVP) in the coordinates of the input-output normal form. In order to solve the overdetermined BVP of the internal dynamics and to ensure the causality of the feedforward control, a sufficient number of free parameters is provided in the setup function of the output trajectory. The resulting BVP with free parameters can be solved with standard numerical methods, e.g. with the Matlab function bvp4c. Thereby, the free parameters determine the shape of the output trajectory.