On Parameter Stability Region of LADRC for Time-Delay Analysis with a Coupled Tank Application

Abstract

The control of time-delay systems is a hot research topic. Ever since the theory of linear active disturbance rejection control (LADRC) was put forward, considerable progress has been made. LADRC shows a good control effect on the control of time-delay systems. The problem about the parameter stability region of LADRC controllers has been seldom discussed, which is very important for practical application. In this study, the dual-locus diagram method, which is used to solve the upper limit of the LADRC controller bandwidth, is studied for both first-order time-delay systems and second-order time-delay systems. The characteristic equation roots distribution is firstly transformed into the problem of finding the frequency of the dual-locus diagram intersection point. To solve the problem for second-order time-delay system LADRC controllers, which is a dual 10-order nonlinear equation, a transformation has been made through Euler’s formula and genetic algorithm (GA) has been adopted to search for the optimal parameters. Simulation results and experimental results on coupled tanks show the effectivity of the proposed method.

Tuning Rules for Active Disturbance Rejection Controllers via Multiobjective Optimization—A Guide for Parameters Computation Based on Robustness

“…which indicates that LADRC parameters meeting the relation ω c < ω o are preferred. This additional scaling is commonly suggested in literature (e.g., in [4,11,12]). The transfer function (40) is obtained by substituting (39) in (32).…”

“…High-order plants can be used as approximations for some industrial processes. Nevertheless, the First Order Plus Dead Time (FOPDT) model is also a very common approximation which takes into account delays due to mass or energy transport, or limitations related to measuring and energy conversion devices [12]. The interest in the control of the FOPDT processes has inspired control strategies as the fractional order internal model controller (FO-IMC) from [13], where phase margin and gain crossover frequency specifications are employed to formulate a system of nonlinear equations which needs to be solved for the controller design.…”

Adaptive LADRC Parameter Optimization in Magnetic Levitation

“…10mm k ≤ t ≤ k + 1(k = 1, 3, 5......) (28) Tracking effects of SMC, LADRC, and A-LADRC are illustrated in Fig. 10(a).…”

“…the number of tuning parameters of LADRC was also reduced to two by a pole placement design. However, the remaining parameter tuning task of ALADRC was still very arduous.Li et al [28] (2020) investigated a method for the stable area of LADRC controller parameters and introduced a genetic algorithm to optimize controller parameters and obtain acceptable results.However, this method fails to solve and determine the upper limit of position maps. These studies demonstrate the importance of parameter optimization in LADRC.…”

Control por rechazo activo de perturbaciones: guía de diseño y aplicación

“…Por ejemplo, para un valor determinado de b 0 , existe un conjunto de valores de ω c y ω o que representan la región de estabilidad y que pueden ofrecer diferente desempeño si se analiza ya sea el problema del rechazo de perturbaciones o el de seguimiento de trayectoria. Recientemente, en (Li et al, 2020) se aborda el estudio de la región de estabilidad del LADRC para el control de sistemas con retardo y la utilidad de la misma en la selección de los parámetros de sintonía.…”