Dual-locus Diagram Research Articles

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

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.

Application of LADRC with stability region for a hydrotreating back-flushing process

Control of liquid level is an important factor in diesel catalytic cracking. Because there may be many unexpected situations during operation, we should not only consider the deviation control of the liquid level, but also consider the sudden change of liquid level caused by sudden feeding. Therefore, it is necessary to design a controller to guarantee the stability control effect in both cases. Taking advantages of the dual-locus diagram method, a stability region determination method for linear active disturbance reject controller (LADRC) is proposed to determine the stability region of controller to ease engineering applications. Hence, this theorem is applied to solve the LADRC stabilization problem of 1.2 million tons hydrotreating back-flushing process. Numerical examples and experiment results demonstrate the validity of the proposed method.

Design and Implementation of Stable PID Controller for Interacting Level Control System

In this present study a Stability Region Analysis method for designing PID controller for time delay system is validated with real time experimentation with Interacting process. The higher order system is reduced into first order plus time delay (FOPDT) model. A polyhedral sets in the 3D (three dimensional) search band parameter space Kp Ki Kd is resulted from set of stable PID controllers for a fixed value of Kd, and it is faster and simple to identify these regions. The stability region verification is done with dual locus diagram. An approach presented works satisfactorily without sweeping over the parameters, and without any complicated mathematics. While designing optimization method based advanced PID controllers it is beneficial and reliable to determine range of variables. We have presented one simulation example and experimental validation on Interacting Level Control System.

Nominal and robust stability regions of optimization-based PID controllers

Abstract In recent decades, several optimization-based methods have been developed for the proportional-integral-derivative (PID) controller design, and the common feature of these methods is that the controller has only one adjustable parameter. To keep the closed-loop systems stable is an essential requirement for the optimization-based PID controllers. In almost all these methods, however, no exact stability region for the single adjustable parameter was sketched. In this paper, using the proposed analytical procedure based on the dual-locus diagram technique, explicit stability regions of the optimization-based PID controllers are derived for stable, integrating, and unstable processes with time delay in the nominal and perturbed cases, respectively. It is revealed that the proposed analytical procedure is effective for the determination of the nominal and robust stability regions and it offers simplicity and ease of mathematical calculations over other available stability analysis methods. The results in this paper provide some insight into the tuning of the optimization-based PID controllers.

Robust stability analysis of simple systems controlled over communication networks

There is increasing interest in controlling systems over communication networks. Using a simple method called dual-locus diagram, this communique proposes complete stability criteria for a mass-spring-damper system controlled over the network. The stability region is divided into a delay-dependent stability region and a delay-independent stability region, which offers a nice graphical view on the conservativeness of the delay-independent stability criteria.

Stability Determination of Retarded Linear Control System Using Dual-Locus-Diagram Technique

This paper first reviews in brief, the different methods presented in the last ten years and then outlines the Nyquist stability criterion for linear control systems with time-delay, using dual-locus diagram technique. The variation of the loopgain and time-delay are investigated when the time-delay occurs in the forward loop or the feedback-loop or both. The criterion employs a delay chart prepared beforehand and only requires the plotting of a simple curve derived from the open-loop transfer function. The stability condition of a simple control system is used to illustrate the method.

Comments on "An extension of Oppelt́s stability criterion based on the method of two hodographs" and "Relative stability from the dual-locus diagram"

Comments on "An extension of Oppelt́s stability criterion based on the method of two hodographs" and "Relative stability from the dual-locus diagram"

Dual-locus Stability Analysis†

ABSTRACT A graphical procedure is described for determining the stability of a linear control system whose characteristic equation is the sum of two frequency dependent functions. This procedure uses a dual-locus diagram. One locus is the polar plot of one of the frequency dependent functions; the second locus is the negative of the polar plot of the other function. The frequency distribution that exists along these two loci and their intersection determines the stability of the system. In comparison to the regular Nyquist method of stability analysis a number of specific advantages are associated with this procedure, A geometric justification and an illustrative example are included.

Relative stability from the dual-locus diagram

Relative stability from the dual-locus diagram