Phase Zeros Research Articles

Optimal tracking performance of networked control systems with communication delays under channel input power constraint

The optimal tracking performance of networked control systems with communication delay and white Gaussian noise under the consideration of the channel input power constraint is studied in this paper. The tracking performance is measured by the energy of the system’s error signal and channel input power. The tracking performance is minimized by considering the channel input power constraint searching through all stabilizing two-parameter controllers. The optimal tracking performance of networked control systems under the communication delays, packet dropout and white Gaussian noise of the communication channel has been studied. The explicit expressions of the optimal tracking performance are obtained by applying the spectral factorization and inner–outer factorization techniques. It is shown that the optimal tracking performance depends on the non-minimum phase zeros, unstable poles of the given plant, communication delay, packet dropouts probability and white Gaussian noise. It is also shown that if the constraint of the communication channel does not exist, the optimal tracking performance reduces to the existing tracking performance of the control system without communication. The result shows how the communication delay, packet dropout probability and white Gaussian noise may fundamentally constrain a networked system’s tracking capability. Finally, some typical examples are given to illustrate the theoretical results.

High speed laser scanning microscopy by iterative learning control of a galvanometer scanner

Iterative learning control (ILC) for a galvanometer scanner is proposed to achieve high speed, linear, and accurate bidirectional scanning for scanning laser microscopy. A galvanometer scanner, as a low stiffness actuator, is first stabilized with a feedback control compensating for disturbances and nonlinearities at low frequencies, and ILC is applied for the control of the fast scanning motion. For stable inversion of the non-minimum phase zeros, a time delay approximation and a zero phase approximation are used for design of ILC, and their attainable bandwidths are analyzed. Experimental results verify the benefits of ILC of its wide control bandwidth, enabling a faster, more linear, and more accurate scanning without a phase lag and a gain mismatch. At the scan rate of 4112 lines per second, the root mean square (RMS) error of the ILC can be reduced by a factor of 73 in comparison with the feedback controlled galvanometer scanner of the commercial system.

Optimal modified tracking performance for MIMO systems under bandwidth constraint

This paper investigates the optimal modified tracking performance of multi-input multi-output (MIMO) networked control systems (NCSs) with bandwidth and channel noise constraints. A new modified tracking performance index is proposed which prevents variations in the tracking error from leading to invalid data where there is no integrator in the plant. An expression for the optimal modified tracking performance is obtained using a method which includes co-prime factorization, partial factorization, spectral decomposition and H2 norm. The obtained results show that the optimal modified tracking performance is influenced by the non-minimum phase (NMP) zeros, unstable poles, and their directions. Furthermore, the characteristics of the input signal, the modification factor, the bandwidth and the channel noise are also shown to be closely related to the optimal modified tracking performance. Finally, the efficiency of the result is verified using some typical examples.

Model‐reference impedance and admittance control of linear systems

SummaryA variable structure model‐reference adaptive control (VS‐MRAC) of impedances and admittances (driving‐point (DP) functions) is proposed. Only voltage and current measurements are required to implement the controllers. The inclusion of a prefilter in the reference model allows the synthesis of quite general DP functions, even with nonminimum phase zeros and unstable poles. It is shown that the stability of the closed‐loop system depends only on the source DP function and the chosen reference model. The VS‐MRAC guarantees global exponential stability properties, robustness to parameter uncertainties, disturbances, and unmodelled dynamics. Simulation results illustrate the performance and robustness of the VS‐MRAC. Copyright © 2016 John Wiley & Sons, Ltd.

Ramp Tracking in Systems With Nonminimum Phase Zeros: One-and-a-Half Integrator Approach

In this paper, a simple fractional calculus-based control law is proposed for asymptotic tracking of ramp reference inputs in dynamical systems. Without need to add any zero to the loop transfer function, the proposed technique can guarantee asymptotic ramp tracking in plants having nonminimum phase zeros. The appropriate range for determining the parameters of the proposed control law is also specified. Moreover, the performance of the designed control system in tracking ramp reference inputs is illustrated by different numerical examples.

Fundamental Bounds for Stabilizability of Continuous-Time Systems under Stochastic Multiplicative Uncertainty and Delay

This paper is devoted to stabilization problem of linear time-invariant (LTI) continuous-time systems under stochastic multiplicalive uncertainty and time-delay. In its full generality, we model the stochastic multiplicative uncertainty as a random process with a certain distribution. We assess the stability of system based on mean-square criteria. Our main contribution includes the fundamental condition, both necessary and sufficient, which insures that the single-input single-output systems (SISO) can be mean-square stabilized by output feedback. This condition provides explicitly a fundamental limit on mean-square staibilizability imposed by the signal-to-noise ratio (SNR), the system’s unstable poles, nonminimum phase zeros and time-delay.

Optimal performance of networked control systems with bandwidth and coding constraints

The optimal tracking performance of multiple-input multiple-output (MIMO) discrete-time networked control systems with bandwidth and coding constraints is studied in this paper. The optimal tracking performance of networked control system is obtained by using spectral factorization technique and partial fraction. The obtained results demonstrate that the optimal performance is influenced by the directions and locations of the nonminimum phase zeros and unstable poles of the given plant. In addition to that, the characters of the reference signal, encoding, the bandwidth and additive white Gaussian noise (AWGN) of the communication channel are also closely influenced by the optimal tracking performance. Some typical examples are given to illustrate the theoretical results.

Tracking Performance Bound with Finite Control Energy and Erasure Channel Energy Constraint

AbstractThis paper studies the tracking performance of the single‐input single‐output (SISO), finite dimensional, linear and time‐invariant (LTI) system under the channel input energy constraint over the Erasure channel. A new performance index is proposed which is minimized over all two‐degree‐of‐freedom stabilizing controllers. The explicit expressions of the lower bound of the performance index and the minimum of the signal‐to‐noise ratio are obtained. The results show that the performance bound is correlated to unstable poles, non‐minimum phase zeros and the packet loss probability. Finally, examples are given to validate the conclusions derived.

Optimal performance of networked control systems under the packet dropouts and channel noise

The optimal tracking performance of single-input single-output (SISO) discrete-time networked control systems (NCSs) with the packet dropouts and channel noise is studied in this paper. The communication channel is characterized by three parameters: the packet dropouts, channel noise and the encoding and decoding. The explicit expression of the optimal tracking performance is obtained by using the spectral factorization. It is shown that the optimal tracking performance dependents on the nonminimum phase zeros, unstable poles of the given plant, as well as the packet dropout probability, channel noise and the encoding and decoding. The optimal tracking performance is improved by two-parameter compensator. Finally, a typical example is given to illustrate the theoretical results.

Performance Limitation of Networked Systems with Network‐Induced Delay and Packet‐Dropout Constraints

AbstractIn this paper, we deeply investigate the tracking performance limitation of single‐input single‐output (SISO) networked systems with packet dropouts and network‐induced delay constrains, where the power of the tracking error is adopted to measure of the performance and is minimized by searching through all stabilizing one‐parameter controllers, with/without considering the channel input power. Moreover, the explicit expressions of the tracking performance limitation are obtained by applying the spectral factorization technique. Theoretical analysis shows that the tracking performance limitation is closely dependent on non‐minimum phase zeros, unstable poles of a given plant, the characteristics of the reference signals, network‐induced delay and packet dropouts probability of communication channel. Finally, some typical examples and simulations are conducted to illustrate the theoretical results.

Optimal tracking performance for non-square plant models with input disturbance and feedback channel noise

In this paper, the optimal tracking performance for linear time invariant (LTI) and non-square plants was investigated. An H2 norm of error signal between the reference input and the output of system is used as the tracking performance index. Due to the limitations of non-square plants in tracking reference input signals, two-degrees-of-freedom controller was adopted to control the system. The reference input under consideration is a step signal and there exists input stochastic disturbance and feedback channel noise. Explicit expression is given to show that the tracking performance in these kinds of systems is critically dependent on the intrinsic characteristics of the given plant, including the locations not the directions of the nonminimum phase zeros and unstable poles, which is different from the plants that have the same input and output dimensions. It is also shown that the input disturbance and feedback channel noise may degenerate the tracking performance. Finally, computer simulation is provided to illustrate the analytical results.

Best achievable tracking performance for networked control systems with encoder–decoder

In this paper, the optimal tracking performance of networked control systems (NCSs) with encoder–decoder was studied. The system under consideration is linear time-invariant, multi-input multi-output and an H2 norm of tracking error signal is used as tracking performance index. The encoder–decoder with an additive white Gaussian noise (AWGN) is employed in feedback channel or feed-forward channel. The aim is to determine the minimal error in tracking a Brownian motion, which can be obtained by all possible stabilizing two-parameter controllers. It is shown that the best achievable tracking performance is closely related to the nonminimum phase zeros and unstable poles of the plant, determined by their locations and directions. We also demonstrated that AWGN may degenerate the tracking performance and encoder–decoder can be designed to eliminate the negative effect of AWGN and improve the systems’ tracking ability. A typical example is given to illustrate the theoretical results.

Broadband Active Noise Control Design through Nonsmooth H∞ Synthesis

This paper deals with active control of a broadband noise in a car cabin. It aims to study the achievable performance of such control in the SISO feedback case. The main limitations involved, known as waterbed effect, are critical for such problem due to the presence of non-minimum phase zeros. To evaluate the intrinsic limitations due to these non-minimum phase zeros, a multi-objective control synthesis is proposed, allowing to cope with classical speciffications (performance and robustness), without pessimism. The control synthesis is based on a H∞ criterion to be minimized under some decoupled constraints. It consists in a non-convex and non-smooth optimization problem, for which a local optimum may be efficiently obtained. A particular control structure is considered in order to reduce the number of decision variables, to set relevant bounds on these parameters and to choose appropriate initial conditions. Then the optimization problem is solved using recent results on non-smooth optimization. The whole design process is detailed, including the identiffication of the synthesis model. The control strategy is then applied to an instrumented cavity, which shares most of the acoustic characteristics of a car cabin. Finally, the analysis of the results gives clear conclusions on SISO feedback possibilities, and paves the way for an efficient multivariable design case.

Culture-centric pre-emptive counterinsurgency and US Africa Command: assessing the role of the US social sciences in US military engagements in Africa

The twenty-first century has seen a continued evolution of the US military’s strategic interest in socio-cultural knowledge of (potential) adversaries for counterinsurgency strategies. This paper explores the implications of the reinvigorated and expanding (post-9/11) relationship between social science research and US military strategy, assessing the implications of US Africa Command strategies for preventive counterinsurgency. Preventative counterinsurgency measures are ‘Phase Zero’ or ‘contingency’ operations that seek to prevent possible outcomes, namely threats to ‘security’ in Africa. The research initiatives of US Africa Command illustrate a culture-centric approach to this strategy, which seeks to draw from detailed socio-cultural knowledge in the prevention of possible populist or popular uprisings. Recent such uprisings, resistance actions and strikes in the continent illustrate a problematic tendency to interpret various forms of populist resistance as ‘terrorist’ actions, thereby condoning the bolstering of African national military capacity. The article considers the implications of these culture-centric counterinsurgency strategies as a means of anticipating and repressing the variety of mobilisations encapsulated within the ‘terrorism’ catchall. We conclude by urging social scientists to reject and disconnect from US Africa Command’s missions and knowledge acquisition efforts in Africa.

Genuine multipartite entanglement in the cluster-Ising model

We evaluate and analyze the exact value of a measure for local genuine tripartite entanglement in the one-dimensional cluster-Ising model for spin- particles. This model is attractive since cluster states are considered to be relevant sources for applying quantum algorithms and the model is experimentally feasible. Whereas bipartite entanglement is identically vanishing, we find that genuine tripartite entanglement is non zero in the anti-ferromagnetic phase and also in the cluster phase well before the critical point. We prove that the measure of local genuine tripartite entanglement captures all the properties of the symmetry-protected topological quantum phase transition. Remarkably, we find that the amount of genuine tripartite entanglement is independent of whether the ground states satisfy or break the symmetries of the Hamiltonian. We provide also strong evidences that local genuine tripartite entanglement represents the unique non-vanishing genuine multipartite entanglement.

Multivariable Disturbance Observer Based Advanced Feedback Control Design and Its Application to a Grinding Circuit

Design of advanced feedback control (AFC) for optimal process operation has been mostly based on a hierarchical structure for many years. Since many advanced control algorithms (such as the model predictive control) do not handle disturbances directly in their design phase, it is difficult to achieve satisfactory performance in controlling complex process operations in the presence of heavy disturbances and large uncertainties. Focused on this practical challenge, in this paper we propose a novel multivariable disturbance observer (MDOB) to improve the disturbance rejection performance of conventional AFCs. The MDOB formulation is based on the approximate inversion of the multivariable generalized system, which consists of the multivariable operation process and the lower level basic feedback control system. All the stable and realizable MDOBs are characterized in terms of time delays and nonminimum phase zeros of the open-loop generalized systems. In the proposed MDOB-based AFC, the advanced feedback controller acts as a presetting controller to generate the proper pre-setpoint for the lower level basic feedback control (BFC) system such that a desired setpoint tracking is achieved. The MDOB acts as a compensator to enhance the operational performance of the process by dynamically adjusting the setpoints of the BFC according to the observed disturbances and plant uncertainties. Theoretical analysis, simulation comparisons, and experimental evaluation using a hardware-in-loop simulation platform of a grinding circuit are given, showing the effectiveness, validity, and advantages of the proposed approach.

Performance limitations for networked control systems with plant uncertainty

There has recently been significant interest in performance study for networked control systems with communication constraints. But the existing work mainly assumes that the plant has an exact model. The goal of this paper is to investigate the optimal tracking performance for networked control system in the presence of plant uncertainty. The plant under consideration is assumed to be non-minimum phase and unstable, while the two-parameter controller is employed and the integral square criterion is adopted to measure the tracking error. And we formulate the uncertainty by utilising stochastic embedding. The explicit expression of the tracking performance has been obtained. The results show that the network communication noise and the model uncertainty, as well as the unstable poles and non-minimum phase zeros, can worsen the tracking performance.

IP-ZSBT Magnetic Configuration for Parallelization–Serialization of Three-Phase High Power Converters

In this paper, a novel magnetic configuration inter phase zero sequence blocking transformer (IP-ZSBT) is presented. The IP-ZSBT is suitable for the parallelization of two three-phase converters, avoiding the circulation of any zero sequence current. The configuration assures an equated current sharing between the converters, providing the functionality of an Inter-Phase Transformer. In addition, it imposes a high impedance for zero sequence currents, providing also the functionality of a zero sequence blocking transformer. A simulation of the proposed configuration has been carried out by using the Saber simulation tool and it has been validated by experimental results.

Classification of cytochrome P450s in common bean (Phaseolus vulgaris L.)

Genome-wide analysis of Phaseolus vulgaris revealed the presence of 247 cytochrome P450 (CYP450) genes belonging to 10 clans consisting of 47 families. Of the 247 genes, 15 of them are pseudogenes. CYP71 clan was found to represent all A-type genes (144) belonging to 19 families. Nine clans possessed 28 families containing 103 non-A-type genes. Majority (112) of the CYP genes of P. vulgaris were found to contain single intron. Out of 582 introns, 357 exhibited phase zero. P. vulgaris A-type CYPs (141) showed the presence of signature F141G132XG141R137 R140XC141P133G131. While the signature sequence F93XXG93XR85XC93XG92 was found in 93 non-A-type CYPs. However, genes belonging to CYP74 family possessed a unique signature starting with W. CYP genes of P. vulgaris classified in the present investigation can be used as reference for annotating and classifying the CYPs from other legumes.

Influence of Nonminimum Phase Zeros on the Performance of Optimal Continuous-Time Iterative Learning Control

Iterative learning control can be applied to systems that execute the same tracking task over a finite time duration. An execution is known as a trial, and once each is complete, the system resets to the starting location and the next trial begins. All previous trial information is available for use in constructing the control input for the next trial, and the basic idea is to improve tracking performance from trial-to-trial. This brief analyzes the effects of nonminimum phase zeros on the trial-to-trial error norm convergence of norm optimal iterative learning control, a commonly used algorithm, for differential linear systems with supporting experimental results from a test facility.