Flatness based control and tracking control based on nonlinearity measures

摘要

This paper deals with the derivation and the simulation of flatness based control and tracking control for a ball in tube system. Flatness based control is a control loop with a two-degree-of-freedom structure in terms of a feedforward (precontrol) and a feedback control path. Tracking control is characterized as a control loop in terms of a feedback control path only where the state vector needs to be measured or estimated. The control laws for both methods are computed for the nonlinear and the linearized system. The reference trajectory for the flat system output, the ball position, is defined as a polynomial transition between two stationary setpoints. The control quality of the closed-loop system is evaluated with the given reference trajectory in a simulation study. The disturbance rejection of the ball in tube system is examined by an external force impulse. In the literature nonlinearity measures are defined in order to answer the question how nonlinear a nonlinear system is. The nonlinearity measure gives therefore a decision if it is a mildly or a highly nonlinear system. The introduced nonlinearity measure is valid for nonlinear input-affine systems represented as a state space model and is calculated for the ball in tube system.