A new concept on flatness-based control of nonlinear dynamical systems

Abstract

The paper proposes a new method for the control of nonlinear dynamical systems which is based on differential flatness theory. The method assumes that the system is already found or can be transformed to the so-called triangular form. The controller design proceeds by showing that each row of the statespace model of the nonlinear system stands for a differentially flat system, where the flat output is chosen to be the associated state variable. Next, for each subsystem which is linked with a row of the state-space model a virtual control input is computed, that can invert the subsystem's dynamics and can eliminate the subsystem's tracking error. From the last row of the state-space description, the control input that is actually applied to the nonlinear system is found. This control input contains recursively all virtual control inputs which were computed for the individual subsystems associated with the previous rows of the state-space equation. Thus, by tracing the rows of the state-space model backwards, at each iteration of the control algorithm, one can finally obtain the control input that should be applied to the nonlinear system so as to assure that all its state vector elements will converge to the desirable setpoints. The proposed flatness-based control method can solve efficiently several nonlinear control problems. Indicative evaluation results are presented in the manuscript in the form of simulation experiments. These confirm also the potential application of the proposed control method to electric power generators and to renewable power generation systems.