This technical note presents a solution to the problem of stabilizing a given fractional-order system with time delay using fractional-order PllambdaDmu controllers. It is based on determining a set of global stability regions in the (kp, Ki, Kd)-space corresponding to the fractional orders lambda and mu in the range of (0, 2) and then choosing the biggest global stability region in this set. This method can be also used to find the set of stabilizing controllers that guarantees prespecified gain and phase margin requirements. The algorithm is simple and has reliable result which is illustrated by an example, and, hence, is practically useful in the analysis and design of fractional-order control systems.

An Algorithm for Stabilization of Fractional-Order Time Delay Systems Using Fractional-Order PID Controllers

Stabilizing and robust fractional order PI controller synthesis for first order plus time delay systems

In this paper, the Kharitonov theorem for interval plants is exploited for the purpose of synthesizing a stabilizing controller. The aim here is to develop a controller to simultaneously stabilize the four Kharitonov-defined vortex polynomials. Different from the prevailing works, the controller is designed systematically and graphically through the search of a non-conservative Kharitonov region in the controller coefficient parameter plane. The region characterizes all stabilizing PID controllers that stabilize an uncertain plant. Thus the relationship between the Kharitonov region and the stabilizing controller parameters is manifest. Extensively, to further guarantee the system with certain robust safety margins, a virtual gain phase margin tester compensator is added. Stability analysis is carried out. The control system is proved to maintain robustness at least to the pre-specified margins. The synthesized controller with coefficients selected from the obtained non-conservative Kharitonov region can stabilize the concerned uncertain plants and fulfill system specifications in terms of gain margins and phase margins.

Robust PID tuning strategy for uncertain plants based on the Kharitonov theorem

In recent decades, increasingly intensive research attention has been given to dynamical systems containing delays and those affected by the after-effect phenomenon. Such research covers a wide range of human activities and the solutions of related engineering problems often require interdisciplinary cooperation. The knowledge of the spectrum of these so-called time-delay systems (TDSs) is very crucial for the analysis of their dynamical properties, especially stability, periodicity, and dumping effect. A great volume of mathematical methods and techniques to analyze the spectrum of the TDSs have been developed and further applied in the most recent times. Although a broad family of nonlinear, stochastic, sampled-data, time-variant or time-varying-delay systems has been considered, the study of the most fundamental continuous linear time-invariant (LTI) TDSs with fixed delays is still the dominant research direction with ever-increasing new results and novel applications. This paper is primarily aimed at a (systematic) literature overview of recent (mostly published between 2013 to 2017) advances regarding the spectrum analysis of the LTI-TDSs. Specifically, a total of 137 collected articles–which are most closely related to the research area–are eventually reviewed. There are two main objectives of this review paper: First, to provide the reader with a detailed literature survey on the selected recent results on the topic and Second, to suggest possible future research directions to be tackled by scientists and engineers in the field.

Spectrum Analysis of LTI Continuous-Time Systems With Constant Delays: A Literature Overview of Some Recent Results

Friction compensation is usually realized based on a friction model; however, the induced undercompensation or overcompensation, which can lead to steady-error or limit-cycle phenomenon, respectively, is inevitable. A novel straightforward reference compensation scheme for the brushless dc servo system independent of the friction model is presented to reject the aftereffect caused by the friction instead of its original mechanics. Neither the accurate friction model nor any estimation of some specific characteristic parameters is needed in this design. Moreover, the inexact velocity estimation information is not as crucial as it is in the traditional compensation methods. A linear control law is proposed based on a reduced-order observer, which could be readily implemented in low-cost embedded fixed-point chips. Two guidelines for the selection of control parameters are presented in terms of delay sensitivity and limit-cycle avoidance. The approach can be applied to the cases with multiple disturbance torque sources except the friction one, where the friction-model-based strategy is difficult to take effect. Finally, comparative mathematical simulation and practical experiment results are used to validate the effectiveness of the proposed method. Substantial low-velocity performance improvements are achieved in the hardware experiments.

On Low-Velocity Compensation of Brushless DC Servo in the Absence of Friction Model

This paper presents a method for finding the gain margins and phase margins of control systems with adjustable parameters. The considered systems are first modified by adding an analytical gain-phase margin tester. Then, the characteristic equations are formulated. Finally, the stability equations are used to find the boundaries of constant gain margins and phase margins. The main advantage of the proposed method is to obtain complete information about the effects of adjustable parameters on gain margins and phase margins. As an example, the method is applied to a pitch-rate control system for a re-entry vehicle, and comparisons with the results in current literature are made.

Gain margins and phase margins for control systems with adjustable parameters

A method for finding the boundaries of the constant gain margin and phase margin of control systems with transport lags and adjustable parameters is presented. The systems are first modified by adding a gain-phase margin tester, then the characteristic equations are formulated, and finally the stability equations are used to find the boundaries of the constant gain margin and phase margin. The main advantage of the proposed method is that it makes it possible to obtain complete information about the effects of adjustable parameters on the gain margin and phase margin and their corresponding crossover frequencies. In order to show the usefulness of the proposed method, a nuclear reactor control system with multiple transport lags is discussed as an example. >

https://ir.nctu.edu.tw/bitstream/11536/4315/1/A1989AP57800008.pdf

Gain margin and phase margin analysis of a nuclear reactor control system with multiple transport lags

A method for finding the grain margins and phase margins of nonlinear control systems for asymptotic stability is presented. The effects of adjustable parameters are analyzed. The systems considered are first linearized by the describing function method and modified by adding a gain-phase margin tester. Then the characteristic equations are formulated and factored into stability equations, and the parameter-plane method is used to find the boundaries of constant gain margin and phase margin. From these boundaries useful information about the effects of adjustable parameters on gain margins and phase margins can be obtained. >

Gain margins and phase margins for nonlinear control systems with adjustable parameters

Presents a method for finding the boundaries of constant gain margin and phase margin of sampled-data control systems. The considered systems are first modified by adding a gain-phase margin tester, then the characteristic equations are formulated and factored into stability equations, and finally the parameter-plane method is used to find the boundaries of constant gain margin and phase margin. The main advantage of the presented method is to obtain complete information about the effects of adjustable and/or variable parameters on gain margins and phase margins.

https://ir.nctu.edu.tw:443/bitstream/11536/3794/1/A1991FL50600014.pdf

Gain margins and phase margins for sampled-data control systems with adjustable parameters

This paper presents a method for finding the boundaries of gain margins and phase margins of multivariable control systems with adjustable parameters. The considered systems are first decomposed into the augmented open-loop transfer functions modified by adding an analytical gain-phase margin tester, then the characteristic equations are formulated, and finally the stability equations are used to find the boundaries of constant gain margins and phase margins. The main advantage of the proposed method is to obtain complete information about the effects of adjustable parameters on gain margins and phase margins; thus it is a useful tool for analysis and design of robust control systems,

C.-H. Chang

Papers

Gain margins and phase margins for control systems with adjustable parameters

Gain margin and phase margin analysis of a nuclear reactor control system with multiple transport lags

Gain margins and phase margins for nonlinear control systems with adjustable parameters

Gain margins and phase margins for sampled-data control systems with adjustable parameters

Gain margins and phase margins for multivariable control-systems with adjustable-parameters