Unstable Poles Research Articles

Optimal performance of networked control systems over limited communication channels

The optimal tracking performance of single-input-single-output networked control systems over limited communication channels is proposed in this paper. The signal-to-noise ratio (SNR) constrained of communication channel is considered. The tracking performance is measured by the energy of the error variance response between the output of the plant and the reference signal. The optimal tracking performance is obtained by applying the [Formula: see text] square error criterion and the spectral factorization technique. It is shown that the optimal tracking performance is constrained by the non-minimum phase zeros, the unstable poles of a given plant, the power spectral density of a given reference signal, and the SNR of a communication channel. The results obtained in this work explicitly show how the optimal tracking performance is limited by the communication parameters (SNR in this paper). Finally, computer simulations are performed to verify the analytical results.

Stabilization of projection-based reduced order models for linear time-invariant systems via optimization-based eigenvalue reassignment

A new approach for stabilizing unstable reduced order models (ROMs) for linear time-invariant (LTI) systems through an a posteriori post-processing step applied to the algebraic ROM system is developed. The key idea is to modify the unstable eigenvalues of the ROM system by moving these eigenvalues into the stable half of the complex plane. It is demonstrated that this modification to the ROM system eigenvalues can be accomplished using full state feedback (a.k.a. pole placement) algorithms from control theory. This approach ensures that the modified ROM is stable provided the system’s unstable poles are controllable and observable; however, the accuracy of the stabilized ROM is not guaranteed. To remedy this difficulty and guarantee an accurate stabilized ROM, a constrained nonlinear least-squares optimization problem for the stabilized ROM eigenvalues in which the error in the ROM output is minimized is formulated. This optimization problem is small and therefore computationally inexpensive to solve. Performance of the proposed algorithms is evaluated on two test cases for which ROMs constructed via the proper orthogonal decomposition (POD)/Galerkin method suffer from instabilities.

Transient management of a supervisory fault‐tolerant control scheme based on dwell‐time conditions

SUMMARYThe paper deals with the design of an active fault‐tolerant control strategy based on the supervisory control approach technique for linear time invariant MIMO systems affected by disturbances, measurement noise, and faults. From a bank of Luenberger observers that plays the role of a fault detection and isolation scheme, the supervisory algorithm aims at selecting the suitable fault‐tolerant controller by means of a hysteresis‐based switching mechanism. Based on dwell‐time conditions, Lyapunov global exponential stability is addressed, and it is shown how transient behaviors due to the inherent interactions between fault detection and isolation, fault‐tolerant control, and the reconfiguration mechanism can be improved. The main advantage with respect to existing solutions of open literature is relative to a simple parameterization of all controllers (possibly having different state dimensions, integral action, and/or unstable poles) in order to cope with bumps and undesirable transients when (possible multiple) switches occur. Moreover, it is shown that it is possible to improve (reduce) the dwell‐time value in some cases. The efficiency of the approach is demonstrated on the academic highly maneuverable technology benchmark. Copyright © 2014 John Wiley & Sons, Ltd.

Vishamanava-The Myth Broken: A Case Report

A nineteen year old male presented to the casualty department of our tertiary care hospital with a history of snake venom addiction. The case coloured on a background of emotionally unstable personality disorder and poly substance abuse {as per criteria coinciding with ICD-10}. Behavioural traits were characterized typically by impulsivity, mood swings and marked interpersonal dysfunction. The hallmark of the case was however an absence of severe and evident withdrawal symptoms caused due to venom intoxication.

Performance limitations in the tracking and regulation problem for discrete-time systems

In this paper, the optimal tracking and regulation performance of discrete-time, multi-input multi-output, linear time-invariant systems is investigated. The control signal is influenced by the external disturbance, and the output feedback is subjected to an additive white Gaussian noise (AWGN) corruption. The tracking error with channel input power constraint and the output regulation with control energy constraint are adopted as the measure of tracking and regulation performance respectively, which can be obtained by searching through all stabilizing two-parameter controllers. Both results demonstrate that the performance is closely related to locations and directions of the nonminimum phase zeros, unstable poles of the plant and may be badly degraded by external disturbance and AWGN.

Best Tracking Performance of Networked Control Systems Based on Communication Constraints

ABSTRACTThe best tracking problem for a single‐input‐single‐output (SISO) networked control system with communication constraints is studied in this paper. The tracking performance is measured by the energy of the error signal between the output of the plant and the reference signal. The communication constraints under consideration are finite bandwidth and networked induced‐delay. Explicit expressions of the minimal tracking error have been obtained for networked control systems with or without communication constraints. It is shown that the best tracking performance dependents on the nonminimum phase zeros, and unstable poles of the given plant, as well as the bandwidth and networked induced‐delay. It is also shown that, if the constraints of the communication channel do not exist, the best tracking performance reduces to the existing tracking performance of the control system without communication constraints. The result shows how the bandwidth and networked induced‐delay of a communication channel may fundamentally constrain a control system's tracking capability. Some typical examples are given to illustrate the theoretical results.

Observer‐based scheme for the control of high order systems with two unstable poles plus time delay

ABSTRACTThis paper deals with the problem of the stabilization and control of linear time invariant high order systems with two unstable real poles plus time delay. A simple observer‐based controller is designed in order to achieve a stable behavior of the closed‐loop system. Necessary and sufficient conditions for the existence of the proposed control structure are stated. Hence, only four proportional gains and the model of the plant are enough to obtain a stable response of the delayed system. Moreover, a robustness analysis is presented in order to compute the maximal uncertainty bound accepted for the delay term. In addition, a two degree of freedom proportional‐integral control action is implemented in order to track step references and to reject step disturbances. The achieved performance of the proposed control strategy is illustrated by mean of numerical simulations. © 2013 Curtin University of Technology and John Wiley & Sons, Ltd.

On the instability of time-domain acoustic boundary element method due to the static mode in interior problems

In the analysis of interior acoustic problems, the time domain boundary element method (TBEM) suffers the monotonically increasing instability when using the direct Kirchhoff integral. This instability is related to the non-oscillatory static acoustic mode describing the constant spatial response in an enclosure. In this work, nonphysical natures of non-oscillatory static mode influencing the instability of TBEM calculation are investigated, and a method for stabilization is studied. In TBEM calculation, the static mode is represented by two non-oscillatory eigenmodes with different eigenvalues. The monotonically increasing instability is caused by the unstable poles of non-oscillatory eigenmodes as well as very small, very low frequency noise of an input signal. Interior problems with impedance boundary condition also exhibit the monotonically increasing instability stemming from its pseudo non-oscillatory static mode due to the lack of dissipation at very low frequencies. Calculation of transient sound fields within rigid and lined boxes provides numerical evidences. It is noted that the stabilization effort by modifying the coefficient matrix based on the spectral decomposition can be used only for correcting the unstable pole. The filtering method based on the eigen-analysis must be additionally used to avoid the remaining instability caused by very low frequency noise of input signal.

Stabilizing a first order system with an arbitrarily large time varying delay and an uncertain gain

Handling delays and uncertain parameters in control systems is difficult and of long-standing interest. In this paper, we consider the problem of stabilizing (in a bounded-input–bounded-output sense) a first order linear time invariant plant with an arbitrarily large time varying delay and an arbitrarily large uncertain gain; we propose the use of a mildly non-linear, periodic controller, which is simple to implement. We will derive a clear, simple formula relating the maximum delay duration, the location of the unstable plant pole and the bounds on the derivative of the delay for which our controller stabilizes the system.

Optimal tracking performance and design of networked control systems with packet dropouts

The optimal tracking problem for single-input–single-output (SISO) networked control system over a communication channel with packet dropouts is studied in this paper. The tracking performance is measured by the energy of the error signal between the output of the plant and the reference signal. It is shown that the optimal tracking performance is constrained by nonminimum phase zeros, unstable poles, the characteristics of the reference signal and packet dropout probability, and the optimal controller is obtained. It is also shown that when the communication constraint does not exist, the optimal tracking performance reduces to the existing normal tracking performance of the control system without a communication channel. The result shows how the packet dropouts probability of a communication channel may fundamentally constrain a control system's tracking ability. Some typical examples and simulations are given to illustrate the theoretical results.

Optimal tracking over noisy channels in the presence of data dropouts

This study investigates the optimal tracking performance of multiple-input multiple-output linear time-invariant systems over a noisy channel in the feedback path. The communication channel is also subject to data dropouts, which was modelled as a binary stochastic process. The problem under consideration amounts to determining the minimal error in tracking a Brownian motion random process, which emulates a step reference signal in the deterministic setting. With the unity feedback and two-parameter control structure, a lower bound and an exact expression of optimal tracking performance are obtained respectively. It is shown how the noise may degenerate the tracking performance and how the data dropouts effect may intertwine with unstable poles and non-minimum phase zeros, including the location and direction, which are intrinsic characteristics of the plant. Finally, computer simulations are provided to illustrate the analytical results obtained.

EDITORIAL FOREWORD

The first two articles in this issue, reflecting growing scholarly interest in the global era of decolonization in the two decades after World War II, track multilayered local, regional, and global forces that shaped particular historical shifts during these pivotal years. Cyrus Schayegh, in “1958 Reconsidered: State Formation and the Cold War in the Early Postcolonial Arab Middle East,” revisits the political crises that tore rapidly through the central Arab states in 1958, focusing on Syria, Lebanon, and Jordan, all of which were “sandwiched between the unstable poles of the Arab state system, Iraq and Egypt.” While Schayegh concurs with previous scholarship that the convulsions of that year did not lead to the deep sociopolitical and ideological transformations in the region that many contemporaries either hoped or feared, he argues that they can now be read as marking a historical milestone of a different sort. In all three countries, the events of 1958 sparked immediate, dramatic, and persistent “state-formation surges,” particularly through the rapid implementation of development plans aimed at defusing both socioeconomic discontent and the political aspirations fueled by Nasirist Arab nationalism on one side and Arab communist movements on the other. Schayegh suggests that these state-formation surges in turn shaped similarities in the three countries’ subsequent historical development in spite of stark differences in their political systems of governance.

1958 RECONSIDERED: STATE FORMATION AND THE COLD WAR IN THE EARLY POSTCOLONIAL ARAB MIDDLE EAST

AbstractUsing Arabic, English, and French sources, and engaging Middle East and Cold War historians, this article makes a threefold argument. First, in United Arab Republic (UAR)–Syria, Jordan, and Lebanon, the 1958–59 explosion of domestic and regional tensions triggered state-formation surges. Second, these formed one process, which made those states more alike, with state-led socioeconomic planning playing a key role. Third, that process partook of a global Third World trend intersecting with the early Cold War. I draw three conclusions. Although existing scholarly readings that the events of 1958–59 in the Arab Middle East formed a crisis but not an ideological or political watershed are correct, from the viewpoint of state formation this crisis was a milestone. Moreover, UAR–Syria, Jordan, and Lebanon had persisting affinities and shared regional positions—notably, the fact that all were sandwiched between the unstable poles of the Arab state system, Iraq and Egypt—that shaped their individual postindependence histories of state formation. Last, Washington's low-profile involvement in this state-formation surge illustrates how domestic sociopolitics and regional geopolitics—including the UAR's peaking popularity and influence in 1958–59—affected U.S. policy in the Cold War postcolonial world.

Truncated predictor feedback control for exponentially unstable linear systems with time-varying input delay

The stabilization of exponentially unstable linear systems with time-varying input delay is considered in this paper. We extend the truncated predictor feedback (TPF) design method, which was recently developed for systems with all poles on the closed left-half plane, to be applicable to exponentially unstable linear systems. Assuming that the time-varying delay is known and bounded, the design approach of a time-varying state feedback controller is developed based on the solution of a parametric Lyapunov equation. An explicit condition is derived for which the stability of the closed-loop system with the proposed controller is guaranteed. It is shown that, for the stability of the closed-loop system, the maximum allowable time-delay in the input is inversely proportional to the sum of the unstable poles in the plant. The effectiveness of the proposed method is demonstrated through numerical examples.

Lower bound of tracking performance with finite control energy and channel energy constraint

This paper studies the tracking performance of the single-input single-output (SISO), finite dimensional, linear and time-invariant (LTI) system over an additive white Gaussian noise (AWGN) channel with finite control energy and channel input energy constraint. A new performance index is proposed which is minimized over all stabilizing two-degree-of-freedom controllers. The explicit expressions of the lower bound of the tracking performance and the minimum of signal-to-noise required are obtained. The results show that the lower bound is correlated to the unstable pole, non-minimum phase zero and the channel scaling factor. Finally, one example is given to validate the conclusions by adopting the special inner-outer factorization.

Fractional-order unstable pole-zero cancellation in linear feedback systems

As a very well-known classical fact, non-minimum phase zeros of the process put some limitations on the performance of the feedback system. The source of these limitations is that non-minimum phase zeros cannot be cancelled by unstable poles of the controller since such a cancellation leads to internal instability. The aim of this paper is to propose a method for fractional-order cancellation of non-minimum phase zeros of the process and studying its properties. It is specially shown that the proposed cancellation strategy increases the phase and gain margin without leading to internal instability. Since the systems with higher gain and phase margin are easier to control, the proposed method can be used to arrive at more effective controls, which is also verified by the simulation results.

Stable controllers for robust stabilization of systems with infinitely many unstable poles

This paper studies the problem of robust stabilization by a stable controller for a linear time-invariant single-input single-output infinite dimensional system. We consider a class of plants having finitely many simple unstable zeros but possibly infinitely many unstable poles. First we show that the problem can be reduced to an interpolation–minimization by a unit element. Next, by the modified Nevanlinna–Pick interpolation, we obtain both lower and upper bounds on the multiplicative perturbation under which the plant can be stabilized by a stable controller. In addition, we find stable controllers to provide robust stability. We also present a numerical example to illustrate the results and apply the proposed method to a repetitive control system.

Optimal tracking performance of MIMO control systems with communication constraints and a code scheme

This paper investigates the issue of the optimal tracking performance for multiple-input multiple-output linear time-invariant continuous-time systems with power constrained. An H2 criterion of the error signal and the signal of the input channel are used as a measure for the tracking performance. A code scheme is introduced as a means of integrating controller and channel design to obtain the optimal tracking performance. It is shown that the optimal tracking performance index consists of two parts, one depends on the non-minimum phase zeros and zero direction of the given plant, as well as the reference input signal, while the other depends on the unstable poles and pole direction of the given plant, as well as on the bandwidth and additive white noise of a communication channel. It is also shown that when the communication does not exist, the optimal tracking performance reduces to the existing normal tracking performance of the control system. The results show how the optimal tracking performance is limited by the bandwidth and additive white noise of the communication channel. A typical example is given to illustrate the theoretical results.

Input delay margin for consensusability of multi-agent systems

In this paper, we are concerned with the consensus of multi-agent systems with input delay. Among all standard static protocols that achieve the consensus for the multi-agent system under no input delay, we aim to find the maximum input delay such that the system remains consensusable under the same protocols. In the case of continuous-time systems, in view of the continuity of stability with respect to the time delay, the maximum delay margin for consensusability is given for scalar systems and vector systems with a single unstable open-loop pole. For scalar discrete-time systems, we show that the maximum delay margin for consensusability is strictly greater than zero if and only if the open-loop pole of the system is located in a specified interval.

Stabilisability analysis of high-order unstable processes by fractional-order controllers

In this article, the sufficient stabilisability criteria for unstable time-delay processes by fractional-order controllers are investigated. The process is a high-order system with a single unstable pole, which also has a stable zero. The adopted approach to derive the sufficient conditions for stability is based on the well-known Nyquist stability criterion. Stabilisability is studied by applying fractional-order proportional integral and proportional derivative controllers and the results are given in terms of the maximum allowable value of time delay. Additionally, limitations on the parameters of the controllers which must be taken into account in the controller design are proposed.