Variable Structure Controller Design for Linear Systems with Bounded Inputs

Shengjian Bai,Pinhas Ben-Tzvi,Qingkun Zhou,Xinsheng Huang 제어·로봇·시스템학회 2011 International Journal of Control, Automation, and Vol.9 No.2

This paper studies the design of variable structure systems with saturation inputs. Sliding mode domain, reaching domain, and unescapable reaching domain of linear systems with variable structure are defined and investigated. When the state matrix of the linear system is Hurwitz, the stability of the variable structure systems is proven by using passivity theory. Moreover, variable structure systems with novel nonlinear switching surfaces are proposed for second order systems. Two strategies for designing variable structure control for high order linear systems are also proposed, such as step-by-step variable structure control and moving-surface variable structure control, which were found to guarantee that the reaching condition of the variable structure control is always satisfied. Finally, an il-lustrative example pertaining to the attitude control of a flexible spacecraft demonstrates the effectiveness of the proposed methods.

고속전자밸브를 사용한 서보인덱싱 시스템의 가변구조제어에 관한 연구

허준영,유태재 한국기술교육대학교 1999 論文集 Vol.6 No.1

This study describes the application of the various structure control(VSC) concept for the position control of a servo indexing system using high speed on-off valves. The basic philosophy of VSC is that the structure of the feedback control is altered as the state crosses discontinuity surfaces in the state space with the result that certain desirable properties are achieved. The switching of the control function yields total(or selective) invariance to system parameter variations and disturbances, closed loop eigen value placement in time-varing and uncertain systems. The control scheme is derived, implemented and tested in simulation program. The control system schematics are given and simple results are shown for illustration. And the results of variable structure system for the servo indexing system using high speed on-off valves were compared each other when system parameter variation exists.

비선형 시스템 계통에서 신경망에 근거한 가변구조 제어

김현호,이천희,Kim, Hyeon-Ho,Lee, Cheon-Hui 한국정보처리학회 2001 정보처리학회논문지 A Vol.8 No.1

This paper presents a neural network based variable structure control scheme for nonlinear systems. In this scheme, a set of local variable structure control laws are designed on the basis of the linear models about preselected representative points which cover the range of the system operation of interest. From the combination of the set of local variable structure control laws, neural networks infer the approximate control input in between the operating points. The neural network based variable structure control alleviates the effects of model uncertainties, which cannot be compensated by the control techniques using feedback linearization. It also relaxes the discontinuity in the system’s behavior that appears when the control schemes based on the family of the linear models are applied to nonlinear systems. Simulation results of a ball and beam system, to which feedback linearization cannot be applied, demonstrate the feasibility of the proposed method.

The Generator Excitation Control Based on the Quasi-sliding Mode Pseudo-variable Structure Control

Jian Hu,Lijun Fu 대한전기학회 2018 Journal of Electrical Engineering & Technology Vol.13 No.4

As an essential means of generator voltage regulation, excitation control plays an important role in controlling the stability of the power system. Therefore, the reasonable design of an excitation controller can help improve the system stability. In order to raise the robustness of the generator exciting system under outside interference and parametric perturbation and eliminate chattering in the sliding mode control, this paper presents a generator excitation control based on the quasi-sliding mode pseudo-variable structure control. A mathematical model of the synchronous generator is established by selecting its power, speed and voltage deviation as state variables. Then, according to the existing conditions of the quasi-sliding mode, a quasi-sliding mode pseudo-variable structure controller is designed, and the parameters of the controller are obtained with the method of pole configuration. Simulations show that compared with the existing methods, the proposed method is not only useful for accurate voltage regulation, but also beneficial to improving the robustness of the system at a time when perturbance happens in the system.

Robust Tracking Design Based on Adaptive Fuzzy Control of Uncertain Nonlinear MIMO Systems with Time Delayed States

Tzu-Sung Wu,Mansour Karkoub,Chien-Ting Chen,Wen-Shyong Yu,Ming-Guo Her,Jui-Yiao Su 제어·로봇·시스템학회 2013 International Journal of Control, Automation, and Vol.11 No.6

It is proposed here to use a robust tracking design based on adaptive fuzzy control technique to control a class of multi-input-multi-output (MIMO) nonlinear systems with time delayed uncertainty in which each uncertainty is assumed to be bounded by an unknown gain. This technique will overcome modeling inaccuracies, such as drag and friction losses, effect of time delayed uncertainty, as well as parameter uncertainties. The proposed control law is based on indirect adaptive fuzzy control. A fuzzy model is used to approximate the dynamics of the nonlinear MIMO system; then, two on-line estimation schemes are developed to overcome the nonlinearities and identify the gains of the delayed state uncertainties, simultaneously. The advantage of employing an adaptive fuzzy system is the use of linear analytical results instead of estimating nonlinear system functions with an online update law. The adaptive fuzzy scheme uses a Variable Structure (VS) scheme to resolve the system uncertainties, time delayed uncertainty and the external disturbances such that H∞ tracking performance is achieved. The control laws are derived based on a Lyapunov criterion and the Riccati-inequality such that all states of the system are uniformly ultimately bounded (UUB). Therefore, the effect can be reduced to any prescribed level to achieve H∞ tracking performance. A two-connected inverted pendulums system on carts and a two-degree-of-freedom mass-spring-damper system are used to validate the performance of the proposed fuzzy technique for the control of MIMO nonlinear systems.

A Poof of Utkin’s Theorem for ISMC of Uncertain Nonlinear Plants

Jung-Hoon Lee(이정훈) 대한전기학회 2019 전기학회논문지 Vol.68 No.3

Nowadays the integral action has been augmented to the VSS(variable structure system) or SMC(sliding mode control) to improve the control performance. In this note, for the integral sliding mode control(ISMC) of SI(single input) uncertain nonlinear systems, a complete proof of Utkin"s theorem is presented. The Utkin’s invariance theorem with respect to the two nonlinear transformation methods so called the two diagonalization methods is proved clearly, comparatively, and completely for the ISMC of SI uncertain nonlinear systems. With respect to the sliding surface and control input transformations, the equation of the sliding mode i.e., the integral sliding surface is invariant, which is proved completely. During the proof, the guideline for obtaining the ideal sliding dynamics of the integral sliding surface is provided and by using the solution of the ideal sliding dynamics the controlled output is predictable, which is shown in the design example and simulation study, and the design rule of the nonlinear feedback gains of the ISMC are proposed. Through an illustrative example and simulation study, the usefulness of the main results is verified. By means of the two nonlinear transformation methods, the same results can be obtained.

An Improved Continuous Integral Variable Structure Systems with Prescribed Control Performance for Regulation Controls of Uncertain General Linear Systems

Jung-Hoon Lee(이정훈) 대한전기학회 2017 전기학회논문지 Vol.66 No.12

In this paper, an improved continuous integral variable structure systems(ICIVSS) with the prescribed control performance is designed for simple regulation controls of uncertain general linear systems. An integral sliding surface with an integral state having a special initial condition is adopted for removing the reaching phase and predetermining the ideal sliding trajectory from a given initial state to the origin in the state space. The ideal sliding dynamics of the integral sliding surface is analytically obtained and the solution of the ideal sliding dynamics can predetermine the ideal sliding trajectory(integral sliding surface) from the given initial state to the origin. Provided that the value of the integral sliding surface is bounded by certain value by means of the continuous input, the norm of the state error to the ideal sliding trajectory is analyzed and obtained in Theorem 1. A corresponding discontinuous control input with the exponential stability is proposed to generate the perfect sliding mode on the every point of the pre-selected sliding surface. For practical applications, the discontinuity of the VSS control input is approximated to be continuous based on the proposed modified fixed boundary layer method. The bounded stability by the continuous input is investigated in Theorem 3. With combining the results of Theorem 1 and Theorem 3, as the prescribed control performance, the pre specification on the error to the ideal sliding trajectory is possible by means of the boundary layer continuous input with the integral sliding surface. The suggested algorithm with the continuous input can provide the effective method to increase the control accuracy within the boundary layer by means of the increase of the G₁ gain. Through an illustrative design example and simulation study, the usefulness of the main results is verified.

RELSYS: A computer program for structural system reliability

Estes, Allen C.,Frangopol, Dan M. Techno-Press 1998 Structural Engineering and Mechanics, An Int'l Jou Vol.6 No.8

Most reliability-based analyses focus on the reliability of the individual components of a structure. There are many advantages to examining the components in combination as an entire structural system. This paper illustrates an algorithm used in the computer program RELSYS (RELiability of SYStems) which computes the system reliability of any structure which can be modeled as a series-parallel combination of its components. A first-order method is used to initially compute the reliability of each individual component. The system reliability is computed by successively reducing the series and parallel systems until the system has been simplified to a single equivalent component. Equivalent alpha vectors are used to account for the correlation between failure modes during the system reduction process.

가변속 냉동시스템의 견실 온도 제어를 위한 구조화 불확실성 기반의 μ-Synthesis 제어기 설계

김인아(In A Kim),정석권(Seok Kwon Jeong) 대한설비공학회 2021 설비공학 논문집 Vol.33 No.12

This paper investigates μ-synthesis robust control for a variable speed refrigeration system to enhance robustness against model uncertainty and external disturbance. As the practical transfer function model obtained by experiments to design a controller inevitably contains model uncertainties such as unmodeled dynamics and modeling errors, a robust controller is necessary to track references in the system. Target temperature and superheat were simultaneously controlled in the system by adjusting rotating speed of compressor and opening angle of an electronic expansion valve respectively. Moreover, the μ-synthesis controller treats model uncertainty as structured perturbation; it is designed using structured singular value. It is shown that the μ-synthesis approach which takes structured uncertainties into account provides robust control performance against both dynamic perturbations including modeling errors and external disturbances. The validity of the proposed method was demonstrated by simulations and experiments.

RELTSYS: A computer program for life prediction of deteriorating systems

Enright, Michael P.,Frangopol, Dan M. Techno-Press 2000 Structural Engineering and Mechanics, An Int'l Jou Vol.9 No.6

As time-variant reliability approaches become increasingly used for service life prediction of the aging infrastructure, the demand for computer solution methods continues to increase. Effcient computer techniques have become well established for the reliability analysis of structural systems. Thus far, however, this is largely limited to time-invariant reliability problems. Therefore, the requirements for time-variant reliability prediction of deteriorating structural systems under time-variant loads have remained incomplete. This study presents a computer program for $\underline{REL}$iability of $\underline{T}$ime-Variant $\underline{SYS}$tems, RELTSYS. This program uses a combined technique of adaptive importance sampling, numerical integration, and fault tree analysis to compute time-variant reliabilities of individual components and systems. Time-invariant quantities are generated using Monte Carlo simulation, whereas time-variant quantities are evaluated using numerical integration. Load distribution and post-failure redistribution are considered using fault tree analysis. The strengths and limitations of RELTSYS are presented via a numerical example.