Tracking Performance Limitation Research Articles

Tracking performance limitations of MIMO discrete-time networked control systems with multiple constraints

Tracking performance limitations of MIMO discrete-time networked control systems with multiple constraints

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.

Output Tracking Control Performance of Discrete Networked Systems Over Erasure Channel With Model Uncertainty

For networked control systems, it is known that various communication parameters in the channel will pose some fundamental limitations on output tracking control (OTC) performance. In this study, we mainly discuss the limitations resulting from model uncertainties, involving channel and plant. Through using the bivariate stochastic process to model packet loss, and the assumption that channel noise is additive white Gaussian noise (AWGN), two explicit expressions of output tracking performance limitations are derived with the single-degree-of-freedom (SDOF) and two-degree-of-freedom (TDOF) control structure, which shows that the performance of OTC is closely related to the inherent characteristics of the plant, as well as the packet loss rate and power spectral density (PSD) of AWGN. Finally, by considering an illustrative example, the simulation results are verified and analyzed to ensure the effectiveness of treatment methods and results.

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.

Output Tracking Control of Single-Input-Multioutput Systems Over an Erasure Channel.

The output tracking control problem is investigated in this article. First, a new tradeoff performance index is presented for single-input-multioutput (SIMO) systems. Based on the frequency-domain method, the tracking performance limitations under time delay, packet loss, and channel noise effects are derived. We use a bivariate stochastic process to model the packet loss, and assume that channel noise is additive white Gaussian noise (AWGN). Two explicit expressions of the best tradeoff performance are given with the single-degree-of-freedom (SDOF) and two-degree-of-freedom (TDOF) control structures. It is shown that the tracking control performance has a close relation with the intrinsic characteristic of the plant, as well as the time delay, packet-dropouts rate, and power spectral density of AWGN. We also demonstrate that compared with the SDOF control structure, the TDOF control structure can improve the systems' attainable performance. A simulation example is finally discussed to validate the conclusions.

Tracking Performance Limitations of Networked Control Systems With Repeated Zeros and Poles

In this article, the performance limitations problem are investigated for a class of signal-input, signal-output networked control systems with repeated zeros and poles. The additive white noise is adopted in the communication channel. The tracking performance limitations are investigated based on a two-degree of freedom (2DOF) controller. The results demonstrate that the multiplicity of nonminimum phase (NMP) zeros and unstable poles of the plant can affect the tracking performance limitations. The explicit quantitative relationship is characterized for the tracking performance limitations, which is derived based on NMP zeros, unstable poles of the plant with corresponding multiplicity, as well as the statistical characteristics of the reference noise and communication noise. The admissible infimal signal-to-noise ratio (SNR) is also obtained for the tracking system by using a 2DOF controller structure, where the admissible infimal SNR can satisfy the stability conditions while achieving tracking performance limitations. Finally, an illustrative example is presented to validate the effectiveness of our proposed scheme.

Modified tracking performance limitation of networked time-delay systems with two-channel constraints

This paper investigates the modified tracking performance limitation of the networked time-delay systems with two-channel constraints. We consider both the white Gaussian noise and packet dropout constraints in the communication channels. In the plant, the non-minimum phase, unstable poles and time-delay are considered. The modified tracking performance limitation expressions will be achieved using the co-prime factorization and the spectral decomposition technique, and the two-parameter controller is adopted. The results show that the modified tracking performance limitation is related to the intrinsic properties of the given plant, including the non-minimum phase zeroes, the unstable poles and the time-delay. Furthermore, the network communication parameters, e.g. the white Gaussian noise, the packet-dropouts probability and the modified factor affect the modified tracking performance limitation of the networked time-delay systems. Finally, some particular examples are provided to illustrate the efficiency of the proposed method.

Optimal performance of LTI systems over power constrained erasure channels

In this paper, the optimal performance of multiple-input multi-output (MIMO) linear time-invariant (LTI) plant is investigated. The communication channel is modeled as a power constrained channel with packet dropouts. The covariance of error signal between reference input and system’s output is chosen as the performance index. Based on the frequency domain analysis method, the exact expressions of the tracking performance limitation are derived. The results reveal that the best performance of NCSs not only has strong connection with both the nonminimum phase zeros and unstable poles of the plant, but also has close relation with the essential feature of reference input signal and communication parameters. Finally, a simulation example is discussed to validate the conclusions.

Tracking Performance Limitations of MIMO Networked Control Systems With Multiple Communication Constraints.

In this paper, the tracking performance limitation of networked control systems (NCSs) is studied. The NCSs are considered as continuous-time linear multi-input multioutput (MIMO) systems with random reference noises. The controlled plants include unstable poles and nonminimum phase (NMP) zeros. The output feedback path is affected by multiple communication constraints. We focus on some basic communication constraints, including additive white noise (AWN), quantization noise, bandwidth, as well as encoder-decoder. The system performance is evaluated with the tracking error energy, and used a two-degree-of-freedom (2DOF) controller. The explicit representation of the tracking performance is given in this paper. The results indicate the tracking performance limitations rely to internal characteristics of the plant (unstable poles and NMP zeros), reference noises [the reference noise power distribution (RNPD) and its directions], and the characteristics of communication constraints. The characteristics of communication constraints include communication noise power distribution (CNPD); quantization noise power distribution (QNPD), and their distribution directions; transform bandwidth allocation (TBA); transform encoder-decoder allocation (TEA), and their allocation directions; and NMP zeros and MP part of bandwidth. Moreover, the tracking performance limitations are also affected by the angles between the each transform NMP zero direction and RNPD direction, and these angles between each transform unstable poles direction and the direction of communication constraint distribution/allocation. In addition, for MIMO NCSs, bandwidth (there are not identical two channels) can always affect the direction of unstable poles, and the channel allocation of bandwidth and encode-decode may be used for a feasible method for the performance allocation of each channel. Finally, an instance is given for verifying the effectiveness of the theoretical outcomes.

Modified performance of MIMO wireless networked time‐delay systems over fading channels

AbstractIn this paper, the modified performance limitation of multi‐input multi‐output (MIMO) wireless networked time‐delay systems over fading channels is investigated, where the characteristic of the fading channels is assumed to be a random process. The modified tracking performance limitation is considered based on frequency domain representation. The display expressions of performance limitation are achieved by using the co‐prime factorization and the spectral decomposition techniques. The obtained results show that the modified performance limitation of the wireless networked time‐delay systems is related to the inherent characteristics of the given plant, including the non‐minimum phase zeroes, the unstable poles, the encoding‐decoding, the fading channels, the bandwidth and the modified factor. Finally, some numerical examples are provided to demonstrate the efficiency of the proposed design method.

On the achievable tracking performance of NCSs over SNR limited channels

In this paper, the achievable tracking performance limitations of discrete-time, multi-input multi-output (MIMO) networked control systems (NCSs) are studied. The channel is modeled as an additive white Gaussian noise and signal-to-noise ratio (SNR) limited channel with feedback. Under this framework, the closed relationships among stabilization, tracking performance, and SNR limited are quantitatively revealed. Some new results a.erived according to the allpass factorization and Youla parameterization of two degrees of freedom controller. The results show that the best tracking performance is in connection with the unstable poles, non-minimum phase zeros of the system. It is also demonstrated that the tracking performance will be badly degraded by feedback channel noise and due to the SNR limited. Finally, a simulation example is presented to validate the conclusions.

Performance limitation of networked control systems with networked delay and two-channel noises constraints

ABSTRACTThe performance limitation of networked control systems (NCSs) with networked delay and two-channel noises constraints are studied in this paper. The networked parameters mainly consider the networked delay in the forward channel and white Gaussian noise constraint existing in forward channel and feedback channel. The tracking performance limitation expression is achieved by using the spectral decomposition technique and selecting the optimal one-parameter structure. The obtained result shows that the tracking performance limitation of NCSs is related to the position of the non-minimum phase zeroes, the position of the unstable poles, networked delay, two-channel noises and input signal. We can also know that the networked delay and white Gaussian noise have influence on the tracking performance limitation of NCSs. Finally, a simulation example is given to demonstrate effectiveness of the theoretical results.

Evaluation of the Transverse Oscillation Technique for Cardiac Phased Array Imaging: A Theoretical Study.

The transverse oscillation (TO) technique can improve the estimation of tissue motion perpendicular to the ultrasound beam direction. TOs can be introduced using plane wave (PW) insonification and bilobed Gaussian apodization (BA) on receive (abbreviated as PWTO). Furthermore, the TO frequency of PWTO can be doubled after a heterodyning demodulation process is performed (abbreviated as PWTO*). This paper is concerned with identifying the limitations of the PWTO technique in the specific context of myocardial deformation imaging with phased arrays and investigating the conditions in which it remains advantageous over traditional focused (FOC) beamforming. For this purpose, several tissue phantoms were simulated using Field II, undergoing a wide range of displacement magnitudes and modes (lateral, axial, and rotational motions). The Cramer-Rao lower bound was used to optimize TO beamforming parameters and theoretically predict the fundamental tracking performance limits associated with the FOC, PWTO, and PWTO* beamforming scenarios. This framework was extended to also predict the performance for BA functions that are windowed by the physical aperture of the transducer, leading to higher lateral oscillations. It was found that windowed BA functions resulted in lower jitter errors compared with traditional BA functions. PWTO* outperformed FOC at all investigated signal-to-noise ratio (SNR) levels but only up to a certain displacement, with the advantage rapidly decreasing when the SNR increased. These results suggest that PWTO* improves lateral tracking performance, but only when interframe displacements remain relatively low. This paper concludes by translating these findings into a clinical environment by suggesting optimal scanner settings.

Optimal tracking performance of control systems with two-channel constraints

This paper focuses on the tracking performance limitation for a class of networked control systems (NCSs) with two-channel constraints. In communication channels, we consider bandwidth, energy constraints and additive colored Gaussian noise (ACGN) simultaneously. In plant, non-minimal zeros and unstable poles are considered; multi-repeated zeros and poles are also applicable. To obtain the optimal performance, the two-parameter controller is adopted. The theoretical results show that the optimal tracking performance is influenced by the non-minimum phase zeros, unstable poles, gain at all frequencies of the given plant, and the reference input signal for NCSs. Moreover, the performance limitation is also affected by the limited bandwidth, additive colored Gaussian noise, and the corresponding multiples for the non-minimum phase zeros and unstable poles. Additionally, the channel minimal input power constraints are given under the condition ensuring the stability of the system and acquiring system performance limitation. Finally, simulation examples are given to illustrate the theoretical results.

Tracking Performance Limitation for 1-DOF Control Systems Using a Set of Attainable Outputs

This paper deals with analysis of fundamental limitation in tracking control problem. The authors have given the tracking performance limitation of two degree of freedom systems for a class of refe...

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 Limitation of Networked Control Systems With Limited Bandwidth and Additive Colored White Gaussian Noise

This paper studies optimal tracking performance issues for multi-input-multi-output linear time-invariant systems under networked control with limited bandwidth and additive colored white Gaussian noise channel. The tracking performance is measured by control input energy and the energy of the error signal between the output of the system and the reference signal with respect to a Brownian motion random process. This paper focuses on two kinds of network parameters, the basic network parameter-bandwidth and the additive colored white Gaussian noise, and studies the tracking performance limitation problem. The best attainable tracking performance is obtained, and the impact of limited bandwidth and additive colored white Gaussian noise of the communication channel on the attainable tracking performance is revealed. It is shown that the optimal tracking performance depends on nonminimum phase zeros, gain at all frequencies and their directions unitary vector of the given plant, as well as the limited bandwidth and additive colored white Gaussian noise of the communication channel. The simulation results are finally given to illustrate the theoretical results.

Performance Limitation of Tracking Control Problem for a Class of References

This technical note deals with analysis of fundamental limitations for SISO systems in tracking control problems. In the existing results, the fundamental limitations are analyzed based on detailed assumptions of reference signals such as the step, the trigonometrical signals and so on. On the other hand, we define a class of reference signals in an abstract but general manner. For the general class of reference inputs, we give the analysis of the tracking performance limitations based on the achievable set of the outputs. The analysis results can separate the contributions of the plant and the reference signal clearly.

On tracking performance limits for tall systems

AbstractIn this paper, a methodology to compute achievable performance bounds for stable, discrete-time tall MIMO systems is proposed. The methodology is based on a performance index, which cumulates the squared deviations of the system output with respect to the nearest vector to a constant reference direction. The results include expressions for the optimal value of this performance index and characterize the controllers that achieve such performance. For SIMO plants, closed form expressions depending on the dynamic features of the plant are also obtained. An example is presented to illustrate the results.

Tracking Performance Limitations of Random Signal in Multivariable Discrete-time Systems

摘要: 研究线性时不变、多变量、离散系统对随机信号的跟踪性能极限问题, 所考虑的随机参考输入信号为布朗运动序列. 研究结果表明此类系统的跟 踪性能极限完全由被控对象的结构特征和参考输入的统计特征决定, 其中, 结构特征指被控对象的非最小相位零点和不稳定极点的位置和方向. 作为特殊情形, 本文给出了参考输入为一致随机信号以及被控对象仅含有单个非最小相位零点和单个不稳定极点时系统跟踪性能极限问题的解. 最后, 给出了两自由度补偿器跟踪系统对随机信号的跟踪性能极限. 关键词: 多变量离散系统 / 随机信号 / 跟踪性能极限 / 非最小相位零点 / 不稳定极点