Unstable Poles Research Articles

Anomalous thresholds for the S-matrix of unstable particles

In this work, we study the analytic properties of S-matrix for unstable particles, which is defined as the residues on the unphysical sheets where unstable poles reside. We demonstrate that anomalous thresholds associated with UV physics are unavoidable for unstable particles. This is in contrast to stable particles, where the anomalous thresholds are due to IR physics, set by the scale of the external kinematics. As a result, any dispersive representation for the amplitude will involve contributions from these thresholds that are not computable from the IR theory, and thus invalidate the general positivity bound. Indeed using toy models, we explicitly demonstrate that the four-derivative couplings for unstable particles can become negative, violating positivity bounds even for non-gravitational theories. Along the way, we show that contributions from anomalous thresholds in a given channel can be captured by the double discontinuity of that channel.

A Simple modification to the Smith Predictor Structure for dealing with high-order delayed processes considering one unstable pole

The traditional Smith Predictor (SP) is restricted to dealing with stable plants. In this paper, a slight modification of the SP is proposed in order to control unstable plants: systems of any order but with one unstable pole are tackled. In fact, many modifications to the SP can be found in the literature dealing with this kind of system, but none, to our best knowledge, have the simplicity of the structure here proposed. Only one or two gains are added to the traditional SP structure to achieve the stabilization of this kind of unstable system. A simple relation states the necessary and sufficient condition guaranteeing the existence of stabilizing gains, in terms of the location of the unstable pole and the size of the delay term. The range of values for the gains solving the problem is characterized. In addition, the tracking of setpoints and disturbance rejections are analysed. Some numerical examples are presented to illustrate the effectiveness of the proposed strategy, as well as one real-time example.

A homotopy-based reinforcement learning scheme to optimal control for Markov switched interconnected systems

ABSTRACT In this paper, a homotopy-based reinforcement learning optimal control method is developed for Markov switched interconnected systems with unknown system dynamics. By utilising the subsystem decomposition method and parallel learning control method, the solution of the game coupled algebraic Riccati equations with jumping parameters is approximated. To dispense with the requirement of initial stability, a homotopy-based policy iteration is introduced, which can place unstable poles into a stable plane. In this regard, a model-free reinforcement learning method is presented to design the optimal controller for Markov switched interconnected systems. Finally, the effectiveness of the proposed method is verified by a numerical example and a practical example.

Design of MIMO PI-compensators without exponentially unstable poles

Abstract There is a class of systems that can only be stabilized by unstable compensators. However, for most practical systems suitable for use with linear regulators, this is possible with stable ones. To avoid exponentially unstable results in the design of pole placing PI-compensators it is of crucial importance to consider the position of the transmission zeros. This also has a favourable effect on the disturbance rejection. In multi-input multi-output (MIMO) systems, however, not only the zero position but also the zero direction is of importance. In this paper, a design method for multivariable PI-controllers in the time- and in the frequency-domains is presented which helps to avoid the occurrence of exponentially unstable controllers. A modified design method for multivariable PI-controllers, recently published in this journal, facilitates the procedure.

Differential Entropy-Based Fault-Detection Mechanism for Power-Constrained Networked Control Systems.

In this work, we consider the design of power-constrained networked control systems (NCSs) and a differential entropy-based fault-detection mechanism. For the NCS design of the control loop, we consider faults in the plant gain and unstable plant pole locations, either due to natural causes or malicious intent. Since the power-constrained approach utilized in the NCS design is a stationary approach, we then discuss the finite-time approximation of the power constraints for the relevant control loop signals. The network under study is formed by two additive white Gaussian noise (AWGN) channels located on the direct and feedback paths of the closed control loop. The finite-time approximation of the controller output signal allows us to estimate its differential entropy, which is used in our proposed fault-detection mechanism. After fault detection, we propose a fault-identification mechanism that is capable of correctly discriminating faults. Finally, we discuss the extension of the contributions developed here to future research directions, such as fault recovery and control resilience.

Tracking Performance of Feedback Systems Over a Fading Channel With Limited Bandwidth.

In this study, we investigated the optimal tracking performance (OTP) of feedback control systems with limited bandwidth and colored noise in a fading channel. For the steady state of the feedback control systems, an equivalent average channel (EAC) model was developed by retaining the effects of the first and second moments of the multiplicative channel output, and on the basis of the coprime decomposition, all-pass factorization, and Youla parameterization of controllers, exact expressions for the OTP were derived by designing two compensators. The expressions quantitatively show the relationship between the OTP and inherent features of the plant. Specifically, the directions and locations of unstable poles (UPs) and nonminimum phase (NMP) zeros adversely affect the tracking performance. Furthermore, the bandwidth limitation and the presence of colored noise also degrade the tracking performance. Finally, our conclusions were verified by considering a numerical arithmetic example.

Asymptotic Output Tracking Control of a Class of Linear Systems by Finite-and-Quantized Output Feedback

This paper presents a novel finite-and-quantized output feedback asymptotic tracking control method for a general class of continuous-time linear time-invariant systems. First, we construct a finite quantizer with time-varying thresholds and design a pole placement control law that exclusively utilizes the finite-and-quantized output signal and an external reference signal. Then, we establish the boundedness of all closed-loop signals and prove the asymptotic convergence of the output tracking error to zero. The proposed method combines the advantages of classical pole placement control technique and finite quantization feedback technique. It not only reduces the requirement for feedback information compared with existing tracking control methods but also effectively handles unstable poles and zeros in controlled systems, thereby achieving asymptotic output tracking. Finally, we provide a representative example to validate the effectiveness and new features of our proposed method.

Output consensus robustness and performance of first‐order agents

AbstractIn this article, we study consensus robustness and performance problems for continuous‐time multi‐agent systems. We consider first‐order unstable agents coordinated by an output feedback protocol over a network subject to an unknown, uncertain constant delay. Our objectives are twofold. First, we seek to determine the largest range of delay permissible so that the agents may achieve robustly consensus despite variation of the delay length, herein referred to as the delay consensus margin. Second, we attempt to determine consensus error performance quantified under an norm criterion, which measures the disruptive effect of random nodal noises on consensus. We consider both undirected and directed graphs. For undirected graphs, we obtain analytical results for the delay consensus margin and the consensus error performance, while for directed graphs, we develop computational results and analytical bounds. The results provide conceptual insights and exhibit how the agents' unstable pole, nonminimum phase zero, as well as the network topology and network delay may limit fundamentally the consensus robustness and performance of first‐order agents.

Relationship between DOB and MEC for Second-order Systems without Zeros and Unstable Poles

Relationship between DOB and MEC for Second-order Systems without Zeros and Unstable Poles

Detection and Elimination of the Causes of Unstable System Operation

Small-signal stability, which is also called static stability or modal analysis, deals with system stability in case of small disturbances such as consumption and production variations on hourly and daily basis. Advantage of this type of analysis is its global character because it provides all system state matrix eigenvalues, i.e. system poles, within single system calculation. Existence of single system pole with positive real part indicates unstable system. Measure of relative participation of a particular state variable, which is correlated to particular generator, and particular system pole is provided by calculating participation factors. Sorting of participation factors for all system poles in descending order and establishing a correlation to certain state variable of particular generator provides feedback to generators that are dominant causes of existence of system poles with positive real part. The paper presents calculation of system eigenvalues and establishment of user feedback to generator causing appearance of unstable pole. The establishment of this feedback and elimination of unstable system pole by changing generator parameters is demonstrated on the example of the real distribution system of Leskovac branch with over 2500 nodes and more than 40 synchronous generators connected.

Modeling and Hover Flight Control of a Micromechanical Flapping-Wing Aircraft Inspired by Wing–Tail Interaction

This article intends to give a comprehensive model to a brand new micromechanical flapping-wing aircraft inspired by wing–tail interaction. In this aircraft, the flapping-wing induced flow contributes to the tail control torque generation. However, this also makes the wing–tail interaction nonnegligible, and this flow would be disturbed by the relative flow produced by the body motion. The dominant unsteady aerodynamic effects of the flapping wing are considered. The flapping-wing induced flow over the tail is included when analyzing the tail aerodynamics. Especially, the aerodynamic–dynamic coupling effect of both the wing and the tail is considered to account for the force due to the body motion. A nonlinear and time-periodic simulation model of the aircraft is, thus, established. The model is averaged and linearized around hover status. Because of the combination of the wing–tail interaction with the aerodynamic–dynamic coupling, the state and control matrixes, including both the induced flow effect and the body motion effect, can be obtained. The pitch dynamics are analyzed, and it is found that the tail can push the two unstable oscillatory poles closer to the imaginary axis. The role of the tail is fully demonstrated by considering the induced flow. Cascade controllers are also designed according to the root-locus plot based on the built model. Due to the inclusion of the wing–tail interaction and the aerodynamic–dynamic coupling, the controllers are proved to be efficient in the attitude stabilization during statistic hover, descent, and ascent flights. Our proposed model can be easily applied to the modeling of other flapping-wing aircraft with similar structures, and it makes the controller design process more efficient and targeted.

Optimal tracking performance of networked control systems under communication constraints

This paper investigates the optimal tracking performance (OTP) of multiple-input multiple-output discrete-time communication-constrained systems by thinking about Denial of Service (DoS) attacks, codecs and additive Gaussian white noise under energy constraints. The non-cooperative relationship between DoS attacks and intrusion detection systems (IDS) is analyzed using repeated game theory. A penalty mechanism is constructed to force the attackers to adopt a cooperative strategy, thus improving the system performance. Partial factorization and spectrum decomposition are used to provide the OTP for systems. The results demonstrate that the systems’ OTP are linked to intrinsic characteristics like non-minimum phase zeros and unstable poles. Finally, concrete examples are shown that the results are accurate.

Observer-predictor based on a PD controller for high-order delayed systems with one unstable pole and n pairs of complex conjugate poles

This paper considers the stability of continuous linear systems with time delay. In particular, systems with one unstable pole and n pairs of complex conjugate and/or real poles are analyzed. The proposed solution consists of using an estimated state observer with a closed-loop PD type controller to access to the internal variables of the system. A partition of the time delay is proposed in the observer to addmit the double of the maximum size that when a simple PD controller is considered. The necessary and sufficient conditions for the stability of the proposed control scheme are presented and an example is presented with simulations to demostrate the usefulness of the proposed control strategy.

Control for a Delayed System with Two Unstable Poles

This paper deals with the stabilization problem for unstable second order systems with time delay. The implementation of an observer scheme that makes use of a static gain parameter and a proportional-derivative (PD) controller is proposed. The necessary and sufficient conditions for the control scheme proposed are obtained. The performance of the proposed method is showed through numeric examples on simulations.

Model based predictive control (MPC) with constraints applied to a multi-predictor scheme for linear delayed systems with an unstable pole

In the present work, a model based predictive control (MPC) strategy using a multi-predictor scheme for unstable high-order linear systems with delay is proposed. The stability analysis of this type of systems is difficult due to two main reasons, the appearance of an infinite number of poles when the feedback of the controller is considered and the second reason, is the delay size considered. In this work the use of a digital multi-predictor scheme is proposed, this device allows to estimate the internal variables of the process, which will be used for the design of the MPC to stabilize the plant. The present proposal considers an MPC with constraints in the control and output variables, which it is one of the most attractive features of this strategy. Numerical simulations are presented to illustrate how the efficiency of the system is increased due to the proposed control approach.

Optimal tracking performance of network time‐delay systems with multiple constraints

AbstractThis paper investigates the optimal tracking performance based on the codec, colored noise, and bandwidth constraints in the network time‐delay systems. Choosing the optimal two‐degree‐of‐freedom compensator and the dominant expression of the system optimal tracking performance is obtained after Youla parameterization by using the coprime factorizations method and spectral decomposition technology. The result shows that the tracking performance of the system is determined by the nonminimum phase zero and unstable pole of the controlled plant. Moreover, codec, colored noise, and bandwidth constraints can also significantly impact the performance. Finally, two simulation examples prove the accuracy of the theory.

Stabilization of Linear Delay Systems With Two Unstable Poles by Modified PI Controller

Stabilization of Linear Delay Systems With Two Unstable Poles by Modified PI Controller

Stability analysis of time-delay systems in the parametric space

This paper presents a novel method for stability analysis of a wide class of linear, time-delay systems (TDS), including retarded, incommensurate and distributed delays. The proposed method is based on frequency domain analysis and application of Rouché’s theorem. Given a parametrized TDS and an arbitrary parametric point, the proposed method is capable of identifying the surrounding region in the parametric space for which the number of unstable poles remains invariant. First, a procedure for investigating stability along a line is developed. Then, the results are extended by application of Hölder’s inequality to investigate stability within a region. The proposed method is uniformly applicable to parameters of different types (simple delays, distributed delay limits, time constants, etc.), as illustrated by examples.

Limitations of energy SNR in control over channels with and without feedback

This paper presents limitations of energy signal-to-noise ratio (SNR) in control of discrete-time linear systems over noisy channels with and without feedback. The minimum SNR required for stabilization is shown to be the modulus of the product of unstable poles of the plants. Two types of optimal control laws that achieve this minimum are constructed based on the gains for expensive control, that is, LQ optimal control without input weight. It is observed that channel feedback does not improve the SNR limitation, which means feedback for control is efficient enough for communication.

Autocatalytic one-step high-temperature synthesis of carboxylated polyimides for in-situ high performance applications

Carboxylated polyimides (CxPIs) represent a great potential for gas separation membranes, highly thermostable coatings and fibers, ion-conducting materials, aerogels, (nano)composites, etc. However a prolonged and expensive two-stage method proceeding through the formation of an unstable poly(amic acid) and subsequent thermal or chemical imidization is traditionally used for the synthesis of CxPIs. Herein a new strategy consisting in one-step high-temperature synthesis of CxPIs based on 3,5-diaminobenzoic acid (DABA), the carboxyl groups of which provide an autocatalytic effect, in N-methyl-2-pyrrolidone (NMP) is presented. The effect of DABA content on the formation and properties of CxPIs is studied. It is established that high-molecular-weight CxPIs (Mw = 158–356 kDa) with five- and more stable six-membered imide rings from various dianhydrides of aromatic tetracarboxylic acids and diamines as comonomers are synthesized within 1–4 h of the reaction even with 25 mol% of DABA content. Additional catalyst-free synthesis of CxPIs in NMP allows to use the solutions obtained in situ for the production of various materials. In particular, CxPI-varnishes form the primary protective coating of the optical fiber superior to the commercial analogue in terms of its manufacturing technology, thermal and hydrolytic stability, which provides more reliable and long-term operation.