A novel terminal sliding mode control is introduced to control a class of nonlinear uncertain systems in finite time. Having command on the definition of the final time as an input control parameter is the goal of this work. Terminal sliding mode control is naturally a finite-time controller though the time cannot be set as input, and the convergence time is not exactly known to the user before execution of the control loop. The sliding surface of the introduced controller is equipped with a finite-time gain that finishes the control task in the desired predefined time. The gain is found by partitioning the state-dependent differential Riccati equation gain, then arranging the sub-blocks in a symmetric positive-definite structure. The state-dependent differential Riccati equation is a nonlinear optimal controller with a final boundary condition that penalizes the states at the final time. This guides the states to the desired condition by imposing extra force on the input control law. Here the gain is removed from standard state-dependent differential Riccati equation control law (partitioned and made symmetric positive-definite) and inserted into the nonlinear sliding surface to present a novel finite-time terminal sliding mode control. The stability of the proposed terminal sliding mode control is guaranteed by the definition of the adaptive gain of terminal sliding mode control, which is limited by the Lyapunov stability condition. The proposed approach was validated and compared with state-dependent differential Riccati equation and conventional terminal sliding mode control as independent controllers, applied on a van der Pol oscillator. The capability of the proposed approach of controlling complex systems was checked by simulating a flapping-wing flying robot. The flapping-wing flying robot possesses a highly nonlinear model with uncertainty and disturbance caused by flapping. The flight assumptions also limit the input law significantly. The proposed terminal sliding mode control successfully controlled the illustrative example and flapping-wing flying robot model and has been compared with state-dependent differential Riccati equation and conventional terminal sliding mode control.

https://zenodo.org/record/7410975/files/TSMC_40_without_nonsingular_Clean_Preprint.pdf

Combination of terminal sliding mode and finite-time state-dependent Riccati equation: Flapping-wing flying robot control

A review of bird-like flapping wing with high aspect ratio

The flight mechanism of a bird-like flapping wing robot at a low Reynolds number was studied in this study for improving the robot performances. Both the physical model and the kinematic model were first established. The dynamic model of the robot at a low Reynolds number was built with the RANS (Reynolds-averaged Navier-Stokes) equations and the Spalart-Allmaras turbulence model. The flight experiments were carried out and the results were discussed. Lift and drag coefficient curves show that it generates upward lift and forward thrust in the phase that the wing flaps downwards, the rate of the coefficient curves is the biggest when the flapping direction changes. Pressure contours indicate that small vortexes with high pressure values appear at the wing edges. There are four velocity vortex groups in total at the front and back of the wing in the velocity contours. Some methods for improving the robot flight efficiency and the robot strength as well as the stitching position of the robot skin have been obtained from the above results. The methods provide the important guidance for the stable flights of the flapping wing robot with the high efficiency.

/pdf/the-flight-mechanism-of-a-bird-like-flapping-wing-robot-at-a-34hdf9hx.pdf

The Flight Mechanism of a Bird-like Flapping Wing Robot at a Low Reynolds Number

The nonlinear dynamics of a bird-like flapping wing robot under randomly uncertain disturbances was studied in this study. The bird-like flapping wing robot was first simplified into a two-rod model with a spring connection. Then, the dynamic model of the robot under randomly uncertain disturbances was established according to the principle of moment equilibrium, and the disturbances were modeled in the form of bounded noise. Next, the energy model of the robot was established. Finally, numerical simulations and experiments were carried out based on the above models. The results show that the robot is more likely to deviate from its normal trajectory when the randomly uncertain disturbances are applied in a chaotic state than in a periodic state. With the increase of the spring stiffness under the randomly uncertain disturbances, the robot has a stronger ability to reject the disturbances. The mass center of the robot is vital to realize stable flights. The greater the amplitude of randomly uncertain disturbances, the more likely it is for the robot to be in a divergent state.

/pdf/dynamic-performances-of-a-bird-like-flapping-wing-robot-76rbxexpdm.pdf

Changtao Ding

Papers

Dynamic performances of a bird-like flapping wing robot under randomly uncertain disturbances.