Vorsteuerungsentwurf für Arbeitspunktwechsel nichtlinearer Systeme mit Ein- und Ausgangsbeschränkungen

摘要

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 stability by the feedback part ("two-degree-of-freedom control"). However, compared to the broad spectrum of methods for designing the feedback control, only few systematic approaches are available for feedforward control design. This methodological gap is mainly caused by the required inversion of the input-output behavior and the respective difficulties arising with nonlinear systems.A particularly convenient feedforward design task is the transition between two stationary setpoints in a finite time interval. Practical applications are e.g. rest-to-rest motions in mechatronics or load changes in process control. For this common class of control problems, a new approach is presented for the feedforward control design of nonlinear systems. The inversion-based design treats the setpoint transition as a two-point boundary value problem (BVP) in the coordinates of the input/output normal form. In order to solve the overdetermined BVP of the internal dynamics, a sufficient number of free parameters is provided in the output trajectory. The resulting BVP with free parameters can be numerically solved e.g. with the Matlab function bvp4c.The approach also allows to directly incorporate constraints on the input, the output, and its time derivatives within the formulation of the BVP. Moreover, the feedforward control design can be directly extended to nonlinear multiple-input multiple-output (MIMO) systems.The design approach and the incorporation of the constraints are illustrated by the swing-up of the double pendulum and the side-stepping of the triple pendulum on a cart. The feedforward design for nonlinear MIMO systems is shown for a 3DOF laboratory helicopter with constraints on both inputs and the angle of attack. The experimental results for the considered examples reveal the high accuracy of the feedforward controls in combination with stabilizing feedback controls and moreover illustrate the applicability of the feedforward control design under input and output constraints to setpoint transitions of nonlinear systems.