Non-preemptible last section assignment for reducing feedback latency in real-time control systems

A real-time control system design procedure consists of the controller design stage and the implementation stage. In the controller design stage, various digital control theories are used with assumptions, such as synchronous sampling, no sampling jitter and negligible feedback latency (latency from sensing to actuation). However, in the implementation stage, multiple control tasks are usually scheduled on a processor, which creates a finite sampling period, varying feedback latency and sampling jitter, and therefore the controller's performance is degraded. In this article, we investigate the relationship between control performance and timing parameters. In the course of this investigation, we found that the feedback latency is the dominant factor affecting control performance. In addition, we propose a rate monotonic (RM) scheduler with non-preemptible last section algorithm, which can reduce the feedback latency considerably. The proposed algorithm provides better control performance than a preemptive RM scheduler, in most cases. The effectiveness of the proposed algorithm is shown in illustrative examples.     

随机延迟网络控制系统中的分段时戳动态矩阵控制

针对网络控制系统中小于一个采样周期的随机延迟,引入了分段时戳动态矩阵控制算法.通过时戳方法测量网络延迟,在线校正系统的阶跃响应系数向量和控制系数向量,并采用分段算法来减少所需的在线计算量.给出了算法的推导过程和程序实现方法,并基于实时控制系统仿真平台TrueTime进行仿真研究.应用该算法对共享以太网中直流电机进行控制,取得了比标准动态矩阵控制算法更好的控制品质.     

Output tracking control for networked control systems with time delay and packet dropout

This article studies the problems of H _∞ output tracking performance analysis and controller design for networked control systems (NCSs) with time delay and packet dropout. By using linear matrix inequality (LMI)-based method, H _∞ output tracking performance analysis and controller design are presented for NCSs with constant sampling period. For NCSs with time-varying sampling period, a multi-objective optimisation methodology in terms of LMIs is used to deal with H _∞ output tracking performance analysis and controller design. The designed controllers can guarantee asymptotic tracking of prescribed reference outputs while rejecting disturbances. The simulation results illustrate the effectiveness of the proposed H _∞ output tracking controller design.     

Properties of sensitivity and complementary sensitivity functions in single-input single-output digital control systems

Sensitivity and complementary sensitivity functions play a key role in feedback control system design. This paper is concerned with the relation between the sampling period and the properties of these functions in digital control systems. Some integral constraints and the lower bounds of the H ^∞-norm are derived, which show that the feedback performance for the unstable plant with the stable digital compensator can be improved as the sampling period goes to zero.     

流水线型并行控制器

通常高采样速率有助于提高控制系统性能,但采样速率受限于控制器的执行周期.并行计算是缩短控制器执行周期的有效方法之一,网络化控制系统为控制器的并行执行提供了必要的条件.利用流水线思想,通过在现场总线控制系统中集成控制与调度,实现了控制器以流水线的方式并行执行,使得控制系统的采样周期小于控制器的执行时间,从而获得控制系统性能的提高.仿真结果及理论分析证明了这一方法的有效性.     

Time delay and sampling rate effect on dual-stage servo control performance

Dual-stage servo control loops are modeled for hard disk drives (HDDs) with the consideration of time delay which is due to the time taken for position error signal measurement and controller computing. The time delays are involved in controller design and the closed servo control loop is investigated to show the effects of the time delay on servo control performance. The studied actuation system is a PZT milliactuator based dual-stage servo system. The delay time within and over the sampling interval is separately considered for 62.5 kHz sampling rate. To show the effect of sampling rate on servo control performance, a control system designed with 40 kHz sampling rate is also studied. As a result, significant improvement of servo performance is attained with this increased sampling rate and a reasonable time delay for the dual-stage actuation system.     

LESO-based Position Synchronization Control for Networked Multi-Axis Servo Systems With Time-Varying Delay

The position synchronization control (PSC) problem is studied for networked multi-axis servo systems (NMASSs) with time-varying delay that is smaller than one sampling period. To improve the control performance of the system, time-varying delays, modeling uncertainties, and external disturbances are first modeled as a lumped disturbance. Then, a linear extended state observer (LESO) is devised to estimate the system state and the lumped disturbance, and a linear feedback controller with disturbance compensation is designed to perform individual-axis tracking control. After that, a cross-coupled control approach is used to further improve synchronization performance. The bounded-input-bounded-output (BIBO) stability of the closed-loop control system is analyzed. Finally, both simulation and experiment are carried out to demonstrate the effectiveness of the proposed method.      

网络化控制系统中的抖动优化调度算法

在令牌型总线网环境下，提出折衷网络带宽资源占用和传输周期抖动的两步优化调度算法，在满足实时性要求的前提下，通过确定网络化控制系统中各控制闭环节点的采样周期及其在最小倍周期时段内的数据传输序列，在兼顾周期抖动对控制闭环动态性能影响的同时合理地调配了带宽资源，使系统具有较高的网络资源利用率。     

Stability and robustness analysis of cyclic pseudo-downsampled iterative learning control

Cyclic pseudo-downsampled iterative learning control (ILC) has shown advantages to achieve good learning performance for trajectories containing high-frequency components and has been verified on industrial robot application. This scheme is a multirate ILC in nature and downsamples the fast rate signals (with a sampling period T) to slow rate signals (with a sampling period mT) with a ratio m. Then ILC is carried out on the downsampled signals and interpolates its output to a fast rate signal. For the next iteration, ILC scheme downsamples the signals with the same ratio m but at different sampling points with a time shift T. This process is repeated on the iteration axis so that ILC updates the input of all the sampling points once every m cycles. By experiments [Zhang, B., Wang, D., Ye, Y., Zhou, K. and Wang, Y. (2009) ‘Cyclic Pseudo-downsampled Iterative Learning Control for High Performance Tracking’, Control Engineering Practice, 17, 957–965], this scheme has been shown effective and comparisons with other relevant schemes demonstrate its superior performance. In this article, this cyclic pseudo-downsampled ILC scheme is examined analytically and proved mathematically to be stable and robust. Extensions and insights are also established based on the theoretical developments and simulation verification. pseudo-downsampled ILC scheme.     

Asymptotic properties of the best sampled-data control performance

Properties of the best achievable performance of sampled-data control systems are investigated. Contrary to our intuition, the best sampled-data control performance does not always converge to the best continuous-time control performance, even as the sampling period approaches zero. A counterexample is presented and a lifting-based analysis is performed. It is shown that the performance convergence is guaranteed if, and only if, a certain Hankel norm and an aliasing effect computed from a specified antialiasing filter tend to vanish with a decreasing sampling period. It is also shown that this condition is reduced to a simpler form if the specified filter has special forms. These results can be generalized to a system involving a generalized hold     

Control of constrained linear systems using fast sampling rates

This paper addresses the problem of optimal control of constrained linear systems when fast sampling rates are utilised. We show that there exists a well-defined limit as the sampling rate increases. An immediate consequence of this result is the existence of a finite sampling period such that the achieved performance is arbitrarily close to the limiting performance.     

网络传输迟延与丢包的补偿及系统稳定性分析

针对网络传输在控制系统中引发的问题,提出在控制器节点采用针对迟延和丢包的补偿估计器．以提高控制系统的性能。当迟延小于一个采样周期且数据包传输率已定时,将包含该补偿估计器的网络控制系统（CEDPNCS）,描述为具有两个事件的异步动态系统,并推导出保证系统稳定的时变双线性矩阵不等式．仿真结果表明．所提出的方法能有效提高控制系统的性能．     

Stochastic Bounded Consensus Tracking of Second-Order Multi-Agent Systems with Measurement Noises and Sampled-Data

This paper investigates the stochastic bounded consensus tracking problems of second-order multi-agent systems, where the control input of an agent can only use the information measured at the sampling instants from its neighbors or the virtual leader with a time-varying reference state, and the measurements are corrupted by random noises. The probability limit theory, the algebra graph theory, and some other techniques are employed to derive the necessary and sufficient condition guaranteeing the mean square bounded consensus tracking. It turns out that the maximum allowable sampling period depends on not only the network topology but also the constant feedback gains. Furthermore, the effects of the sampling period on tracking performance, including the tracking speed and the static tracking error, are also analyzed. The results show that reducing the sampling period can accelerate the tracking speed and decrease the static tracking error. Simulations are provided to demonstrate the effectiveness of the theoretical results.     

网络控制系统的一种变采样周期动态调度策略

提出一种基于网络运行状态的网络控制系统动态调度器的设计方法．首先利用监测器在线获取当前的网络利用率、网络诱导误差和数据包执行时间，基于获取的网络状态，预测下一监测周期内的网络利用率和数据包执行时间．然后按照网络运行性能和控制性能的需求，基于网络利用率和数据包执行时间的预估值分配网络资源，计算控制系统新的采样周期．当数据包传输发生冲突时，采用MEF（Maximum Error First）作为辅助调度策略，确定数据包的发送优先级．最后通过一组仿真结果验证了所设计的动态调度器的有效性．     

Optimal sampling-rates and tracking properties of digital LQ and LQG tracking controllers for systems with an exogenous component and costs associated to sampling

In this paper it is shown that if costs are associated to sampling operations which are added to a performance criterion, the minimization of this new performance criterion results in a controller operated at an optimal sampling rate. This, under the assumptions that the system is periodically sampled, the applied control is kept fixed between every two sampling instances and some technical conditions are met. In case the considered planning horizon in the performance criterion is finite an algorithm is devised which calculates in a finite number of steps the optimal sampling period. It is shown that the technical conditions mentioned above are satisfied by the finite planning horizon time-varying LQG tracking problem. Since stability is a major requirement in controller design we also consider the case of an infinite planning horizon. This analysis is focused on the time-invariant digital LQ tracking problem. Given some mild regularity conditions a numerical algorithm is presented that approximates the optimal solution within any prespecified error norm. It is shown that also in this case an optimal sampling-rate exists. The algorithm for determining the optimal sampling period if the planning horizon is finite is illustrated in an economic example.     

基于T-S 模糊模型的采样数据网络控制系统H∞ 输出跟踪控制

研究具有采样数据的基于T-S (Takagi-Sugeno) 模糊模型网络控制系统H输出跟踪控制问题. 提出将采集器端数据采样周期、数据传输时滞和数据丢包转换为零阶保持器端数据更新周期, 在此基础上, 利用输入时滞法和PDC (Parallel distributed compensation) 技术, 建立网络环境下被控对象和参考模型合并的基于T-S 模糊模型的增广系统模型. 通过Lyapunov 方法, 并充分利用采样特性, 给出系统实现H输出跟踪的充分条件, 以及可靠模糊控制器的设计. 仿真结果表明所设计模糊控制器能够实现该类系统良好的跟踪.     

在连续过程的离散最优控制中采样周期和加权系数的选择

本文提出了在连续过程的离散最优控制中选择采样周期和加权系数的一个方法。这个选择基于:1)线性的时间离散控制器;2)控制变量的范围受到限制;3)根据对系统的实际要求给定输出量的初始偏移。系统的性能则采用时间连续的二次型输出偏移损失函数以及类似的控制损失函数来表示。对不同的采样周期,利用标准的LQ方法来计算控制器,并通过选择控制损失项的加权系数,以使得对于给定的初始偏移,允许的控制范围得到充分利用。最后的采样周期则是权衡了偏移损失和控制损失的一个折衷选择。本文介绍的方法尤其适用于需要尽可能长的采样周期的情况。     

Sampled‐data control of networked nonlinear systems with variable delays and drops

This paper investigates the stabilization problem of the nonlinear networked control systems (NCSs) with drops and variable delays. The NCS is modeled as a sampled‐data system. For such a sampled‐data NCS, the stability properties are studied for delay that can be both shorter and longer than one sampling period, respectively. The exponential stability conditions are derived in terms of the parameters of the plant and time delay. On the other hand, a model‐based control scheme based on an approximate discrete‐time model of the plant is presented to guarantee the stability of the closed‐loop system subject to variable time delays and packet losses. The performance of the proposed control schemes are examined through numerical simulations of an automated rendezvous and docking of spacecraft system. Moreover, the simulations show that by employing the model‐based controller, a higher closed‐loop control performance can be achieved. Copyright © 2013 John Wiley & Sons, Ltd.     

Stability and performance recovery within discretized non-linear control systems

In this paper, a closed-loop fast sampling analysis of a discretized (emulated) continuous-time controller in a sampled-data environment is presented. The analysis involves a general weighted version of the L_p-norm. This allows a qualitative and quantitative stability and performance analysis for an emulated controller. Several examples are used to show the relevance of these results for the analysis of sampled-data implementations and the computation of quantitative upper limits on the sampling period to achieve recovery of stability and performance.     

Period-robust repetitive model predictive control

Repetitive model predictive control (RMPC) incorporates the idea of repetitive control (RC) into the basic formulation of model predictive control (MPC) to enable the user to take full advantage of the constraint handling, multivariable control features of MPC in controlling a periodic process. The RMPC achieves perfect asymptotic setpoint tracking/disturbance rejection in periodic processes, provided that the period length used in the control formulation matches the actual period of the reference/disturbance signal exactly. Even a small mismatch between the actual period of the process and the controller period can deteriorate the RMPCs performance significantly. The period mismatch can occur either from an inaccurate estimation of the actual frequency of disturbance due to resolution limit or from trying to force the controller period to be an integer multiple of the sampling time. For such cases, an extension of RMPC called “period-robust” repetitive model predictive control (pr-RMPC) is proposed. It is based on the idea of using weighted, multiple memory loops in RC, such that small changes in period length do not diminish the tracking/rejection properties by much. Simulation results show that, in case of a slight period mismatch, pr-RMPC achieves significant improvement over the standard RMPC in rejecting periodic disturbances.