Implementation of digital controllers

The variance of error at the output of a digital control system due to input data quantization and product rounding in a digital controller is derived. Two forms of controller implementations are considered. Then an expression for the word length that yields a specified variance of error is determined. Scaling is then discussed and an example consisting of a discrete integral plus proportional controller is presented.     

一类具有量化误差的多步长非线性采样系统的镇定

基于连续时间系统模型进行控制器设计,离散化后执行采样控制的方法,研究一类具有量化误差的多步长非线性采样系统的镇定问题.由于非线性因素而无法使用提升技术以及系统状态仅在采样时刻可检测的事实,控制器中不可检测的系统状态被以采样时刻的状态为初始状态的欧拉叠代近似所获得的近似状态所替换.在采样系统的保持周期可调节的情况下,运用此修正控制器来镇定整个多步长非线性采样系统,可得系统近似误差和采样量化误差可分离的结果;同时利用李雅普诺夫函数方法,克服近似误差和量化误差的双重影响,得到系统实用镇定的结果.最后,仿真例子验证了本文的结果有效.     

A strategy for coefficient quantization in digital control algorithms

A strategy for quantizing the coefficients in a general second order digital control algorithm is presented. First, the errors in the magnitude and phase functions for the algorithm are derived in terms of the filter coefficients. By specifying a maximum allowable error for each function over a given frequency range, quantization regions can then be established. An example consisting of a lag-lead digital control algorithm is included to illustrate the procedure.     

基于事件触发的网络化控制系统的L2稳定性分析

网络化控制系统中反馈信号通过数字通信网络传输,在传输前需要进行量化,但其不可避免会带来量化误差,损害系统的性能甚至稳定性．因此,为降低由量化误差引起的损害,采用事件触发的采样方法进行数据采样和控制．在事件触发控制中,微型处理器只在特定事件发生时进行采样,故多数情况下会以某个误差量超过一个范围作为触发条件．本文给出量化控制下保证系统L₂稳定性的条件、 并且获得比传统固定时间采样更优（更长）的平均采样周期;并针对对数量化器,给出要达到稳定性的对数量化密度的约束条件．最后对线性例子系统进行仿真,结果证明所提事件触发条件能够保证L₂的稳定性,故其在采样间隔上具有更佳的性能．     

同时考虑量化误差的网络化控制系统鲁棒H∞完整性设计

针对同时存在时变时延、丢包和信息量化的参数线性不确定网络化控制系统,在执行器失效故障和外界有限能量扰动共存的情形下,基于状态多时延模型,通过构造时滞且量化误差依赖的Lyapunov-Krasovskii泛函,给出了使不确定网络化控制系统具有鲁棒H∞完整性的判决准则和控制器的设计方法。还进一步讨论了故障网络化控制系统稳定运行的最大允许时延和最大允许量化误差,并以此为依据对H∞性能指标进行了优化,给出了鲁棒H∞最优容错控制器设计方法。由于模型中考虑了时延下界,证明过程引入适当自由权矩阵变量且未进行模型转换,使得其结果具有较少保守性。仿真结果验证了该方法的有效性。     

带宽受限的CAN总线对数量化调度策略

研究了使用量化技术解决控制器局域网络（CAN）总线网络控制系统的带宽受限问题.首先,建立了多控制回路的网络控制系统模型,该模型综合考虑了采用对数量化器对采样信号进行量化和Bernoulli随机网络丢包过程.并针对量化误差和数据丢包,设计了控制器和观测器使得闭环系统指数均方稳定.然后根据控制性能最优化要求,设计了在带宽受限情况下的反馈网络调度器,提出了量化反馈调度策略.最后通过对3个独立控制回路组成的CAN总线系统进行仿真实验,验证了此调度策略的有效性和可行性.     

关联量化系统参数稳定性与控制器设计

量化问题广泛存在于计算机控制系统和数字通信的传输通道中. 本文研究一类非线性关联量化系统的参数稳定性及分散状态反馈控制器的设计问题. 每个控制器的输出经过对数量化器量化后输入到子系统中,其量化密度的大小会影响系统的稳定性. 首先,设计分散状态反馈控制器,使得无量化器存在时的关联闭环系统参数稳定,并确定参数稳定的区域;然后,对每个子系统的控制输入采用对数量化器进行量化,通过局部信息确定子系统中对数量化器量化密度的下界,使得整个闭环关联量化系统在参数稳定域内仍然保持稳定;最后,对给定量化密度,优化控制器使系统能容许最大的非线性. 仿真结果表明,本文所设计的分散量化控制器在参数稳定域内能够镇定关联大系统.     

An iterative learning controller with reduced sampling rate for plants with variations of initial states

In this paper a discrete-time iterative learning controller for single input single output systems is presented. The iterative learning controller works with a reduced sampling rate that ensures the reduction of an appropriate norm of the error trajectory from cycle to cycle and can cope with initial state error. Initial state error occurs when the initial state of the system is different from the initial state that is implicitly given by the reference trajectory. If the initial state changes for every learning iteration, then the controller cannot achieve ideal tracking but the error trajectory is bounded. Using two different sample times together with a potentially time variant learning gain improves the controller performance for dealing with initial state error. Simulation examples are presented to show the results of the proposed iterative learning controller with reduced sampling rate.     

Output-feedback control design for NCSs subject to quantization and dropout

In this paper, the output-feedback control problem is considered for networked systems involving in signal quantization and data packet dropout. The states of the controlled system are unavailable and the output signals are quantized before being communicated. An estimation method is introduced to cope with the effect of random packet loss that is modelled as a Bernoulli process. The quantized measurement signals are dealt with by utilizing the sector bound method, in which the quantization error is treated as sector-bounded uncertainty. The output-feedback controller is designed which guarantees the closed-loop system is exponentially mean-square stable. The simulation example is given to illustrate the proposed method.     

Static and dynamic quantization in model-based networked control systems

In this paper the effects of quantization in an important class of networked control systems called model-based networked control systems (MB-NCS) are considered. The MB-NCS architecture uses an explicit model of the plant in the controller in order to reduce the network traffic, while attempting to prevent excessive performance degradation. Sufficient stability conditions for two types of static and a dynamic quantization schemes for MB-NCS are derived. An important feature is that the stability conditions are explicitly expressed in terms of the plant and controller dynamics, the error between the model and the plant parameters, the transmission or update times, the quantization parameters, and a robustness measure of the system to parameter uncertainty. This is important because it allows the design of the controller and network parameters to achieve the desired goals. Examples are used throughout to illustrate the main results.     

Observer-based feedback stabilization of linear systems with event-triggered sampling and dynamic quantization

We consider the problem of output feedback stabilization in linear systems when the measured outputs and control inputs are subject to event-triggered sampling and dynamic quantization. A new sampling algorithm is proposed for outputs which does not lead to accumulation of sampling times and results in asymptotic stabilization of the system. The approach for output sampling is based on defining an event function that compares the difference between the current output and the most recently transmitted output sample not only with the current value of the output, but also takes into account a certain number of previously transmitted output samples. This allows us to reconstruct the state using an observer with sample-and-hold measurements. The estimated states are used to generate a control input, which is subjected to a different event-triggered sampling routine; hence the sampling times of inputs and outputs are asynchronous. Using Lyapunov-based approach, we prove the asymptotic stabilization of the closed-loop system and show that there exists a minimum inter-sampling time for control inputs and for outputs. To show that these sampling routines are robust with respect to transmission errors, only the quantized (in space) values of outputs and inputs are transmitted to the controller and the plant, respectively. A dynamic quantizer is adopted for this purpose, and an algorithm is proposed to update the range and the centre of the quantizer that results in an asymptotically stable closed-loop system.     

Digitalization of continuous-data systems via time-response matching

A computer-aided method to design a digital controller by matching the output response of the digital control system with that of a continuous-data model is proposed in this paper. Golub's algorithm for solving least-squared-errors problems is used to find the coefficients of the optimum digital controller. The advantages of this method are: (1) the order of the digital controller is low, (2) the required sampling frequency is low, (3) the accuracy is high, and (4) the responses in the intersampling periods can be matched. An illustrative example is provided, and a comparison with the results in the available current literature is also made.     

Stabilization with data-rate-limited feedback: tightest attainable bounds

This paper investigates the stabilizability of a linear, discrete-time plant with a real-valued output when the controller, which may be nonlinear, receives observation data at a known rate. It is first shown that, under a finite horizon cost equal to the mth output moment, the problem reduces to quantizing the initial output. Asymptotic quantization theory is then applied to directly obtain the limiting coding and control scheme as the horizon approaches infinity. This is proven to minimize a particular infinite horizon cost, the value of which is derived. A necessary and sufficient condition then follows for there to exist a coding and control scheme with the specified data rate that takes the mth output moment to zero asymptotically with time. If the open-loop plant is finite-dimensional and time-invariant, this condition simplifies to an inequality involving the data rate and the unstable plant pole with greatest magnitude. Analagous results automatically hold for the related problem of state estimation with a finite data rate.     

Multimodel Robust Control by Fast Output Sampling-An LMI Approach

An LMI approach to robust multimodel controller design is proposed. The fast output sampling control law considered here allows in theory to realize the effect of a robust state feedback gain simultaneously for a family of linear models. In practice, there are two reasons why exact realization of state feedback may not be desirable or even impossible: poor error dynamics, and noise sensitivity due to large output feedback gains. An LMI formulation of the design problem allows to approximate a robust state feedback design by fast output sampling, in a way that closeness to the original design can be traded against reducing these deteriorating effects. The proposed method is illustrated by a multivariable design example and experimental results.     

网络控制系统动态量化H∞控制

基于线性矩阵不等式技术,采用状态反馈控制,考虑同时带有网络诱导随机丢包 和量化的H∞控制问题。考虑信号经网络从传感器到控制器和从控制器到执行器的传输中存在 通信诱导随机丢包,并采用动态量化器量化信号。设计H∞控制器的同时,提出量化的控制策 略,使得闭环系统在量化器的量化范围条件下指数均方稳定且具有指定的H∞性能指标。通过 数值仿真例子表明设计方法的有效性。     

An algorithm for multirate sampling adaptive control

A stable multirate sampling adaptive control algorithm is presented which enables the fast sampling rate to be applied in closed-loop feedback control. The sampling rate is only restricted by the time needed for the control law computation (as in the nonadaptive control case) plus the estimation error computation. The plant input and output are recorded prior to the currently obtained estimate and used to compute the coming estimate and controller coefficients. Thus, the computation is not dependent upon the inputs and outputs appearing during the updating process. The closed-loop system is shown to be stable     

A high performance simulation methodology for multilevel grid-connected inverters

To design a high reliability multilevel grid-connected inverter,a high performance simulation methodology based on Saber is proposed.The simulation methodology with optimized simulation speed can simulate the factors that have significant impacts on the stability and performance of the control system,such as digital delay,dead band,and the quantization error.The control algorithm in the simulation methodology is implemented using the C language,which facilitates the future porting to an actual system since most actual digital controllers are programmed in the C language.The modeling of the control system is focused mainly on diode-clamped three-level grid-connected inverters,and simulations for other topologies can be easily built based on this simulation.An example of designing a proportional-resonant (PR) controller with the aid of the simulation is introduced.The integer scaling effect in fixed-point digital signal processors (DSPs) on the control system is demonstrated and the performance of the controller is validated through experiments.     

Instabilities caused by floating-point arithmetic quantization

It is shown that an otherwise stable digital control system may become unstable due to signal quantization if the controller operates on floating-point arithmetic. Sufficient conditions for instability are developed.     

Quantized output feedback control with multiplicative measurement noises

In this paper, we consider the problem of quantized quadratic performance control for a class of stochastic systems, which are subject to multiplicative noises in the measurement. A dynamic output feedback controller is designed to guarantee a given level of performance. By using the sector bound approach to characterize the quantization error, the existence of a solution for the quantized quadratic performance control problem is found by solving the so‐called guaranteed cost control problem of the associated system with a sector bounded uncertainty. We show that the latter problem can be solved using LMIs. Copyright © 2014 John Wiley & Sons, Ltd.     

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.