Abstract
A new method is presented for synthesising a control algorithm for second-order nonlinear dynamic systems based on the concept of fixed-time stabilisation with output feedback. The study focuses on a broad class of planar nonlinear systems for which full access to state variables is not possible. The proposed methodology is based on a combination of the theory of bi-limit homogeneity and the principles of classical Lyapunov stability analysis. This approach has enabled the development of a continuous observer with a fixed convergence time, which reliably estimates the unmeasurable state of the system regardless of initial conditions and initial estimation errors. Based on this estimation, a continuous controller is constructed that ensures system stabilisation within a predetermined time. The method has a number of advantages: stability and convergence do not depend on the magnitude and sign of the initial conditions; control remains continuous, which eliminates oscillation of the actuators; high robustness to limited external disturbances and measurement noise is achieved. The algorithm can be implemented on microcontrollers without the need for high-frequency sampling, making it attractive for practical use. As an example, the dynamics of a microelectromechanical system (MEMS) mirror are considered, which is a striking example of a highly non-linear electromechanical object. Numerical simulations were carried out, the results of which confirm the effectiveness of the proposed control scheme. Compared to existing finite-time controllers, the transient response time is reduced by more than a factor of four, whilst the system error and energy consumption are reduced by almost half. The results obtained confirm the applicability of the developed method to high-precision control of micro- and macro-mechanical actuators, as well as in intelligent robotic and vibro-optical systems.