Unstable Poles Research Articles

Smith Predictor Controller Design Using the Direct Synthesis Method for Unstable Second-Order and Time-Delay Systems

Industrial processes often involve a long time delay, which adversely affects the stability of closed-loop control systems. The traditional Smith Predictor (SP) is a model-based controller used in processes with large time delays. The variation of system parameters and load disturbance situations are disadvantages of the traditional SP, and researchers have, therefore, proposed modified SP structures. In this paper, a design method based on the direct synthesis approach on a modified SP structure is discussed. In the design, an I-PD controller structure is used on the set-point tracking side of the SP, and a cascading PD lead–lag controller is used on the disturbance rejection side. In contrast with other studies in the literature, the use of simpler controllers enables the mathematical expressions that arise in the direct synthesis method to be significantly reduced. The proposed method is examined under the disturbance input effects for normal and parameter-changing conditions on system models with unstable second-order plus time-delay processes. The first plant model has two unstable poles, the second has one stable and one unstable pole, and the third has one unstable and one zero pole. When the results obtained using the proposed method were compared with other methods, significant improvements were achieved in terms of set-point tracking, disturbance rejection, and robustness conditions.

Optimal regulation performance of discrete time‐delay systems based on quantization and input energy constraints

AbstractIn this paper, we study the optimal regulation problem of networked control systems and propose a new performance index for a given discrete time‐delay system. The regulation performance of the controlled plant is investigated by considering the effects of various constraints on the communication channel such as quantization, bandwidth, and packet dropouts using frequency domain methods and two‐degree‐of‐freedom control techniques. The results show that the regulation performance is not only related to the location and direction of the non‐minimum phase zeros and unstable poles of a given system but also related to the internal time delay of the controlled plant. Packet dropouts, quantization, and bandwidth limitations can also negatively affect the optimal performance. In addition, the trade‐off of the input energy constraint can also make the optimal regulation performance suffer. Finally, the reliability of this innovative result is illustrated by some simulation examples.

Novel Active Damping Design Based on a Biquad Filter for an LLCL Grid-Tied Inverter

LLCL filters for grid-tied inverters have been adopted to get better performance for the harmonics near the switching frequency than commonly used LCL filters. However, the resonant peak caused by a pair of unstable resonance poles of the LLCL filters is introduced and makes the system become unstable. In this paper, a biquad filter composed of a notch filter and a resonator is introduced to restrain the resonant peak. In this method, the resonance point and the notch point of the biquad filter are placed at the appointed frequency, and the resonant peak is transferred to the stable area by phase transformation, so that the system does not cross −180° at the resonant peak. This method makes the system have higher control bandwidth and stronger robustness even in a weak power grid. Meanwhile, a proportional-integral multiresonant repetitive controller is used to restrain low-frequency current harmonics and improve the steady-state and dynamic performance of the control system. Furthermore, based on the active damping of the biquad filter, the stability criterion of the control system under a weak power grid is given. Finally, the accuracy of the analysis and the effectiveness of the method is verified by simulations.

Remote State Estimation With Enhanced Robustness in the Presence of Data Packet Dropouts

This article discusses the remote state estimation over unreliable links, where the packet dropouts occur from the sensor side to the filter, for discrete-time systems with both bounded-power disturbances and white Gaussian noises. A cascaded estimation scheme with enhanced robustness is proposed, driven by the residual signal related to the modeling mismatch. The estimation gains are characterized by two modified algebraic Riccati equations (MAREs), together with a complete and rigorous stability analysis in the mean square (MS) sense. Necessary and sufficient conditions for the MS stability of the corresponding error dynamics are then given in terms of the data arrival rate and unstable poles of the plant, i.e., the Mahler measure of the plant. Moreover, the filtering strategy is expanded into the case of distributed estimation over lossy sensor networks, where each sensor locally constructs an estimate based on its own observation and on those collected from its neighbors, and the solution is again derived by MAREs. The corresponding necessary and sufficient conditions to the MS stability in the distributed case are also characterized by relationships between data arrival rates and the Mahler measure of the plant. Finally, an example is presented to validate the current design method.

Optimal tracking performance of communication‐constrained systems under energy constraints

AbstractThis paper investigates the optimal tracking performance of systems by considering packet dropouts, additive white Gaussian noise(AWGN), and coding under energy constraints. The optimal tracking performance of communication‐constrained systems is obtained by spectral decomposition and partial factorization. The results show that the optimal tracking performance of the system is related to intrinsic properties such as non‐minimum phase zeros and unstable poles. What's more, encoding, data loss rate, and AWGN are also able to affect the performance of the system. Finally, the correctness of the results is verified by specific examples.

Control based on a hybrid predictor for linear unstable delayed systems with a pair of complex conjugate poles

This paper presents a methodology to design a hybrid predictor of continuous signals to solve the stabilization problema of unstable linear systems with time delay, specifically systems with an unstable pole and a pair of stable conjugate complex poles. Among the main contributions of this work is to guarantee the existence of the predictor device, regardless of the size of the delay. To solve the stabilization problem, the necessary and sufficient conditions are obtained for a Proportional-Integral (PI) controller that can guarantee the stability of the system using the designed predictor. The performance of this control strategy is evaluated by means of a numerical simulation.

SnOx as Bottom Hole Extraction Layer and Top In Situ Protection Layer Yields over 14% Efficiency in Sn-Based Perovskite Solar Cells

Sn-based perovskite solar cells (S-PSCs) are a promising candidate to replace toxic Pb-based PSCs. For promoting their industrial application, developing inorganic substitutions of unstable poly(3,4-ethylenedioxythiophene) polystyrene sulfonate (PEDOT:PSS) is also an important part due to its intrinsic stability and low cost. Here, we in situ prepared ambipolar SnOx by a simple and fast plasma-assistant strategy (P-SnOx). The as-prepared P-SnOx works as a hole transport layer directly, yielding a 10.89 ± 0.51% power conversion efficiency (PCE) comparable to a PEDOT:PSS-based device (10.39 ± 0.72%). The top SnOx (T-SnOx), composed of SnO2 and Sn metal, as a modifier and a protection layer of the perovskite by reducing Sn4+ to Sn2+, gives a 13.08 ± 0.33% device performance. This in situ top protective strategy combined with P-SnOx as a hole transport layer further boosts the champion PCE of S-PSCs to 14.09% (13.5 ± 0.32%).

Regulation performance limitation of networked time‐delay systems with incomplete information

AbstractIn this paper, the regulation performance limitation of networked time‐delay systems is studied. The communication network is mainly affected by parameters such as packet dropouts, encoding‐decoding, interference signal, and channel noises. Non‐minimum phase zeros, unstable poles, and time delay are all considered for a given plant. The corresponding regulation performance expression is derived using coprime factorization and spectral decomposition techniques in the frequency domain. The results indicate that the regulation performance of the system is related to the inherent characteristics of the given plant, including non‐minimum phase zeros, unstable poles, and time delay. Additionally, network communication parameters such as white Gaussian noise, packet dropouts, encoding‐decoding, and external interference signals all affect the regulation performance of networked time‐delay systems. Finally, some simulation examples are provided to demonstrate the effectiveness of the theory.

Tracking and Regulation Performance Limitations of Networked Control Systems Over Erasure Channel With Input Quantization

Limitations in communication networks, such as delays, packet dropouts, and insufficient bandwidth, create great challenges in the output tracking control and regulation performance of networked control systems. In this article, we propose some novel performance indexes for achieving the optimal tracking and regulation performance. By considering the influences of noise, packet dropouts, and logarithmic quantization on the channel input, the performance limitations of the networked systems are investigated by applying a two-degree-of-freedom (TDOF) control technique. The results obtained prove that the tracking and regulation performance is dependent not only on the position of the plant’s nonminimum phase zeros and unstable poles, but also on the directions. Furthermore, it is demonstrated that noise and quantization error have a negative influence on the control performance, and the design of the TDOF controller can eliminate the effect of packet dropouts on control performance. To validate the innovation results, several simulations are conducted.

Observer‐based control for high order delayed systems with an unstable pole and a pole at the origin

AbstractTime delays in dynamical systems are challenging when trying to control them. One of the most common techniques consists in estimating one or more signals of interest before they are delayed, in order to use them in the control stage. In this work, an observer‐based control strategy for unstable linear systems with a pole at the origin and delay is suggested. Also, the proposed observer is extended to be used in the case of a high order unstable delayed system. Likewise, the conditions to ensure the existence of the proposed observer‐predictor are presented. A methodology is introduced to obtain the observer parameters. The proposed observer scheme makes use of a Proportional‐Integral‐Derivative control that makes it possible to ensure the tracking of step‐type references and the rejection of disturbances of the same type in the closed‐loop system.

Optimal Tracking Control of Networked Systems Subject to Model Uncertainty and Additive Colored Gaussian Noise

For control systems with communication links, the various communication parameters can bring negative effects on system’s performance. Taking tracking problem for example, it is extremely difficult to achieve accurate tracking, that is, the tracking error can not be zero because of these communication constraints, such as model uncertainties originate from plant and channel, and additive colored Gaussian noise (ACGN). In this brief, by employing unit feedback controller (UFC) and two-parameters controller (TPC), the output tracking control (OTC) performance of networked systems subject to model uncertainties and ACGN is investigated. Consequently, two exact expressions of OTC performance limitations are derived with UFC and TPC. These results clearly show that OTC performance tightly depends on non-minimum phase zeros (NMPZs) and unstable poles (UPs) of the given plant. Moreover, the existence of uncertainties and ACGN can result in the poor OTC performance.

Passive Scalar Function Approximation Using SOS Polynomials

Signal and power integrity design in the time domain requires equivalent circuit models for interconnects and packages, whose descriptions may only be available as tabulated impedance or admittance parameters. Accurate models for these components should maintain their physical properties including causality, stability, and passivity. Even though a heuristic approach, pole flipping (i.e., changing the sign of the real part of an unstable pole) has proven to be sufficiently accurate for many applications, resulting in models with ensured causality and stability. In this article, we address the problem of generating passive scalar models, such as driving point impedances or admittances, based on an existing causal, stable, but nonpassive model. Our approach is based on using sum-of-squares (SOS) polynomials and results in a convex optimization problem, hence a global optimum is obtained. We obtain approximations through two distinct SOS algorithms: a coefficient and a sampling-based method. We also present a simple passivity test for such functions based on calculating the roots of numerator and denominator polynomials, which provides an intuitive link among existing approaches based on solving an eigenvalue problem.

Controller Design for Plants With Internal Delayed Feedback

A special class of retarded and neutral time delay systems is considered: These are plants with internal delayed feedback, and they may have finitely many or infinitely many unstable poles. Stabilizing controllers are obtained from a particular interpolation. A parameterization of all stabilizing integral action controllers is obtained. Examples are given to illustrate this simple design procedure and its robustness properties for various uncertainties.

Optimal Tracking Performance Analysis of MIMO Control Systems Under Multiple Constraints

This article is concerned with the optimal tracking performance on linear time-invariant (LTI) discrete-time multi-input–multi-output (MIMO) systems based on quantization, channel noise, and encoding–decoding, as well as bandwidth constraints. Meanwhile, power constraint, feedback and feedforward loops constraints of the systems are also taken into account. The tracking performance expression is described by inner–outer factorization, which is obtained by all stabilizing two-degree-of-freedom compensators. The results will illustrate that tracking performance limitation is decided by nonminimum phase zeros and unstable poles of the given plant. Moreover, time delay, encoding–decoding, channel noise, quantization, and bandwidth constraints also impact the performance. The accuracy of the method is verified by simulation examples.

Observer-Based PID Control Strategy for the Stabilization of Delayed High Order Systems with up to Three Unstable Poles

In this paper, a new method to manage the stabilization and control problems of n-dimensional linear systems plus dead time, which includes one, two, or three unstable poles, is proposed. The control methodology proposed in this work is an Observer-based Proportional-Integral-Derivative (PID) strategy, where an observer and a PID controller are used to relocate the original unstable open-loop poles to stabilize the resultant closed-loop system. The observer provides an adequate estimation of the delayed-free variables and the PID uses the delay-free variables estimated by the proposed observer. Also, step-tracking is achieved in the overall control scheme. Necessary and sufficient conditions are presented to ensure closed-loop stability based on the open loop parameters of the system. The observer-based PID strategy considers five to seven constant parameters to obtain a stable closed-loop system. A general procedure to implement the proposed control strategy is presented and its performance is evaluated by means of numerical simulations.

Analysis and Mitigation of DC Voltage Imbalance for Medium-Voltage Cascaded Three-Level Neutral-Point-Clamped Converters

The cascaded three-level neutral-point-clamped (3L-NPC) converter and the modular multi-level converter (MMC) are attractive solutions for medium-voltage direct-current (MVDC) applications. Due to their low cost compared to MMCs, cascaded 3L-NPC converters have been adopted in ANGLE-DCa 30 MVA MVDC link demonstration project in North Wales, UK. DC voltage imbalance across submodules (SMs) is a common challenge for both types of MVDC converters. Such imbalance is topology dependent and remains under-researched for cascaded 3L-NPC converters. In this paper, small-signal model-based analysis has been done to reveal that the dc voltage imbalance in cascaded 3L-NPC converters is caused by an unstable system pole. Two voltage balancing methods are presented. The first method is based on PI controllers to precisely regulate SMs voltages without influencing output power. However, it relies on communication between a central controller and local controllers within SMs. The second method uses inverse-droop based control to take over the dc voltage regulation upon loss of communication. Both balancing methods are experimentally validated using a 30 kVA testbed based on the ANGLE-DC project. It has been demonstrated that the dc voltages of SMs can be effectively balanced with both methods during changes of load conditions and dc bus voltages.

Signal-to-Noise Ratio Based Fault Detection and Identification

In this work, we introduce signal-to-noise ratio (SNR) based fault detection and identification mechanisms for a networked control system feedback loop, where the network component is represented by an additive white noise (AWN) channel. The SNR approach is known to be a steady-state analysis and design tool, thus we first introduce a finite time approximation for the estimated AWN channel SNR. We then consider the case of a general linear time-invariant plant model with one unstable pole. The potential faults that we discuss here cover simultaneously the plant model gain and/or the unstable pole. The fault detection is performed relative to the estimated AWN channel SNR. The fault identification is performed using recursive least squares ideas and then further validated with the observed SNR value, when a fault has been previously detected. We show that the proposed SNR-based fault mechanism (fault detection plus fault identification) is capable of processing the proposed faults. We conclude discussing future research based on the contributions exposed in the present work.

Mechanism of spindle pole organization and instability in human oocytes.

Human oocytes are prone to assembling meiotic spindles with unstable poles, which can favor aneuploidy in human eggs. The underlying causes of spindle instability are unknown. We found that NUMA (nuclear mitotic apparatus protein)-mediated clustering of microtubule minus ends focused the spindle poles in human, bovine, and porcine oocytes and in mouse oocytes depleted of acentriolar microtubule-organizing centers (aMTOCs). However, unlike human oocytes, bovine, porcine, and aMTOC-free mouse oocytes have stable spindles. We identified the molecular motor KIFC1 (kinesin superfamily protein C1) as a spindle-stabilizing protein that is deficient in human oocytes. Depletion of KIFC1 recapitulated spindle instability in bovine and aMTOC-free mouse oocytes, and the introduction of exogenous KIFC1 rescued spindle instability in human oocytes. Thus, the deficiency of KIFC1 contributes to spindle instability in human oocytes.

Observer-Based PD Controller for a Class of High Order Linear Unstable Delayed Systems

In this paper it is considered the stabilization and control of a class of high order linear systems that are subject to constant time delay at the input-output channel. In particular, systems with two unstable poles and any number of real or complex conjugate stable poles are studied. To improve the solutions existing in the literature, a new proposal for the solution of the considered problem is taken into account consisting in the design of an observer and a ProportionalDerivative PD controller to assure stable closedloop performance, establishing by means of a frequency analysis necessary and sufficient conditions for the proposed control strategy. The proposal novelty is the inclusion of the PD control action in the observer that allows to estimate internal signals used in the solution. This configuration offers advantages in the time delay size that can be handled and on the control performance of the closed loop system. A practical design procedure is presented to determine the value of the controller gains. Numerical simulations examples are presented to show the operation of the proposal.

Homotopic policy iteration-based learning design for unknown linear continuous-time systems

Recent results have emerged that policy iteration is a powerful reinforcement learning tool in designing a stabilizing control policy for continuous-time systems with unknown system dynamics. Policy iteration involves a model-based initialization stage, i.e., seeking an initial stabilizing control policy, which is, however, dependent on the full system dynamics including the drift dynamics and system input matrix. To remove such model requirements, this paper utilizes a homotopy-based initialization strategy for policy iteration, wherein a stabilizing control policy for continuous-time systems is obtained by gradually moving a stable system to the original system. We propose two homotopic policy iteration-based stabilizing control schemes, namely, a model-based design and a model-free design using system data, which are proved to place unstable poles into a stable region. The effectiveness of the proposed designs is validated through an illustrative example.