An Output Feedback Controller for a Second-Order System Subject to Asymmetric Output Constraint Based on Lyapunov Function with Unlimited Domain

Abstract

In this work, a new robust controller is designed for a second-order plant model, considering asymmetric output constraints. The tracking error convergence and output constraint are achieved by using a control law whose output feedback term is user-defined and bounded: it takes on large but finite and user-defined values for tracking error values equal to or higher than the constraint boundary, and it comprises a previously known user-defined function for tracking error values far from the constraint boundary. This is a significant contribution that remedies two important limitations of common output constraint control designs: the infinite control effort for tracking error equal to or higher than the constraint boundary, and the impossibility of using previously known user-defined functions in the output feedback function for tracking error values far from the constraint boundary. As another contribution, the control design is based on the dead-zone Lyapunov function, which facilitates the achievement of convergence to a compact set with user-defined size, avoidance of discontinuous signals in the controller, and robustness to model uncertainty or disturbances. The proposed output feedback term consists of the product between two functions of the tracking error, an increasing function and a sigmoid function, whose exact expressions are user-defined. Finally, the effectiveness of the developed controller is illustrated by the simulation of substrate concentration tracking in a continuous flow stirred bioreactor.