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Recent years, a new control method, ADRC (Active Disturbance Rejection Control), which can actively estimate and reject disturbance, is attracting a lot of attention from researchers and engineers. One of the important issues in ADRC design is to tune its parameters. ADRC consists of TD (tracking differentiator), ESO (extended state observer), ESO-based state feedback controller
We proposed a novel method to design ESO-based state feedback controller by using LQ method and Lyapunov stability theory.
ESO-based state feedback controller consists of state feedback controller that only feedbacks system states and disturbance compensator that compensates disturbance.
Because a state feedback controller could be designed easily by using LQ method, we focused on the design of disturbance compensator.
In conventional ADRC, after the disturbances are estimated, they are fully cancelled by compensator. But not all disturbances are harmful, and some disturbances may have good effects to the system dynamics.
Based on this, we proposed a novel method of disturbance compensator design by using Lyapunov stability theory.
The magnitude of the derivative of Lyapunov function determines the decay rate of Lyapunov function. That is, the smaller the derivative of Lyapunov function is, the quicker the Lyapunov function decreases. In general, Lyapunov function is quadratic with respect to the state, so the rapid decay of the Lyapunov function will accelerate the convergence of the state to zero, that is, a higher convergence rate is obtained.
In conventional ADRC, a disturbance was rejected by making the disturbance term in the derivative of Lyapunov function to be zero. Since the estimate of disturbance is available, the disturbance term in the derivative of Lyapunov function can also be made to be negative definite one. In this case, the derivative of Lyapunov function can be made smaller than that of conventional ADRC, so higher convergence rate is obtained.
Our work has been published in "Journal of the Brazilian Society of Mechanical Sciences and Engineering" (Vol. 44, Article number. 477) in 2022 under the title of "A Design of Active Disturbance Rejection Control with Higher Convergence Rate and Its Application in Inertia Wheel Pendulum Stabilization" (https://doi.org/10.1007/s40430-022-03771-w).