On the general solution of the state deadbeat control problem

In this note, the state deadbeat control problem is considered. It is shown that, after appropriate change of basis of input and state spaces, the general solution of the state deadbeat control problem can be expressed completely by the rows of the powers of system matrix. This result yields a very simple procedure for the calculation of a state feedback deadbeat control gain. It also provides the number of free parameters which could be used for further design purposes. The results are illustrated by an example at the end of the note     

Deadbeat control system with time-varying uncertainty: Minimization of worst case steady-state tracking error

This paper poses and solves a new problem of the synthesis of a controller that minimizes the worst case steady-state controlled error in the presence of time-varying unstructured uncertainty. We present an easy, straightforward design method for obtaining a controller that minimizes the worst case steady-state controlled error under the assumption that the plant is strictly proper. The detailed contributions are as follows. First, we derive a new, simple expression for calculating the worst steady-state error, which gives useful and interesting suggestions about the controller design. We then show that the synthesis problem is reduced to a simple and tractable l1 -norm minimization problem. Therefore, this reduction provides a feasible method for solving the design problem of a controller that minimizes the worst case steadystate error. Second, a deadbeat tracking control problem is considered and a straightforward design method is presented for obtaining a deadbeat controller with given settling steps both to guarantee robust stability and to minimize the worst case steady-state error. The proposed controller is easily obtained by solving a simple linear programming problem. Finally, we show that the proposed controller minimizes the maximum error bound of the controlled output to persistent bounded disturbance.     

State deadbeat control of nonlinear systems: Construction via sets

A geometric generalization of the discrete-time linear deadbeat control problem is studied. The proposed method to generate a deadbeat tracker for a given nonlinear system is constructive and makes use of sets that can be computed iteratively. For demonstration, derivations of the deadbeat feedback law and tracker dynamics are provided for an example system. Based on the method, a simple algorithm that computes the deadbeat gain for a linear system with scalar input is given.     

The design of deadbeat controllers by state transition graph

Two kinds of deadbeat control problems are considered. One is the state deadbeat control problem and the other is the pointwise minimum-time deadbeat control problem. A simple graph called the state transition graph of a matrix is introduced, and simple algorithms based on it giving deadbeat controllers are presented. The set of pointwise minimum-time deadbeat controllers is characterized. The set of output feedback deadbeat controller is also considered     

二次型最优的有限拍内模控制器设计

针对生产中常见的时滞系统采用2自由度内模控制结构,使用计算机离散控制理论以及最优控制理论,提出了一种综合考虑控制能量及跟踪误差二次型最优的有限拍内模控制器设计方法;从而可以有效地保证系统在有限个采样周期内以较小能量实现良好的跟踪性能,提高控制的精度;然后使用Matlab仿真工具,选用一时滞系统实例进行最优有限拍控制器设计并在simulink下进行系统仿真,结果表明该设计方法可行,控制性能好,且控制器设计简单,调节参数少,具有良好的应用前景。     

Simultaneous deadbeat tracking controller synthesis

A direct and simple design algorithm for the problem of simultaneously deadbeat tracking a prespecified class of inputs by only one controller is presented. This novel approach is based on polynomial algebra and the principle of system realizability. Without solving linear polynomial diophantine equations, the proposed procedure consists of solving a set of linear equations depending on system dynamics, and yields the deadbeat controller in a compact form well suited for system with inaccessible states and changeable reference signals. Since all solutions are described in a parametric form, some performance criteria can be easily incorporated as well. Examples are presented to illustrate the usefulness and computational easiness of this simple design algorithm.     

Multivariable closed-loop deadbeat control: a polynomial-matrix approach

The closed-loop deadbeat servo problem (CDSP), considered in this paper, consists of the synthesis of a linear, output feedback controller such that the control signal and tracking error both vanish, after a finite period of time, for every reference sequence from a prespecified class and for every initial state of a plant and the controller. The closed-loop structure is determined by studying necessary and sufficient conditions for deadbeat tracking performance. A new theorem asserts that if an open-loop deadbeat control strategy exists for every initial state of the plant and every reference function from a given class, then CDSP is solvable and all desired control laws are found in an explicit parametric form by solving simple, unilateral, linear equations in polynomial matrices. On the basis of this theorem a design algorithm is developed. Asymptotic stability of the closed-loop system exhibiting deadbeat properties is demonstrated. A numerical example is given to illustrate the usefulness and computational efficiency of the new design algorithm presented.     

Adaptive deadbeat control

An adaptive algorithm is presented to incorporate deadbeat control as a principle design criterion. Since this algorithm does not require the solution of the diophantine equation at each sampling step, it possesses a computational advantage over the existing deadbeat control approaches, and so is suitable for application to adaptive systems. The meeting of the internal stability requirement enables this algorithm to handle easily any stable or unstable, minimum or non-minimum phase system. By selecting the zero assignment of the sensitivity function the system can be made to track a class of changeable reference signals and exhibit a deadbeat response with minimum settling time. Some constraints on the transfer function make sure that the derived controller is realizable. The non-linear saturated system and the lathe system are simulated to illustrate the validity of the proposed design algorithm.     

基于最小拍观测器的自抗扰控制器设计与性能分析

自抗扰控制器设计中,扩张状态观测器需要较高的观测带宽,才能更快的观测出状态变量.本文采用最小拍观测器,使得其具有最快的观测速度.以2阶系统为例,得到了离散系统下,基于最小拍观测器的自抗扰控制器的等价复合控制模型,其开环补偿器等价为超前校正器.仿真结果表明,基于最小拍观测器的自抗扰控制器可以最快的观测出系统状态变量,且控制器带宽的选取一般应小于采样周期的倒数.由于不再需要设计观测器带宽,从而简化了参数设计.     

Multipurpose deadbeat controllers for multivariable systems

A simple and direct deadbeat control design algorithm for discrete-time multivariable systems is introduced. Our brief was to synthesize a realizable controller to achieve the following objectives: (1) input-output decoupling, (2) deadbeat tracking of any prespecified class of changeable deterministic reference signals and (3) changeable deterministic disturbances rejection where the changeable reference signals and disturbances can be different at each channel. Since the internal stability requirement is satisfied, our design algorithm can easily handle both unstable and non-minimum phase systems. Some constraints on the transfer function are also derived to make sure that the derived controller is realizable. Since all solutions can be described in parametric form, some of the performance criteria can be combined.     

最小能量有限拍鲁棒控制系统的设计

本文采用2自由度控制器,以传递函数分式分解理论为基础,提出了一种在保证系统内部稳定和最佳鲁棒性前提下,实现最小能量控制的有限拍系统设计法。设计过程本质上是控制能量与响应时间的折衷。本文导出了折衷的最终界限,并给出了确定最佳响应时间的方法。     

Deadbeat control of linear multivariable generalized state-spacesystems

The classic idea of deadbeat control is extended to linear multivariable discrete-time generalized state-space systems using algebraic methods. The asymptotic properties of the linear quadratic regulator theory are used to obtain the classes of deadbeat controllers using stabilizing full semistate feedback. The solution is constructed from a `cheap control' problem. Both semistate and output deadbeat control laws are considered. The main design criteria are to drive the semistate and/or outputs of the system to zero in minimum time and that the closed-loop system be internally stable. Unique properties of these types of control laws are discussed. For semistate deadbeat control, all the (dynamic) poles including the ones at infinity are moved to the origin, whereas for output deadbeat, some of the finite transmission zeros are canceled. Numerically reliable algorithms are developed to solve both problems     

基于无差拍控制的超导磁储能系统

超导磁储能(SMES)系统具有功率密度高和功率指令响应快等特点,在平滑风力发电功率波动、提高电力系统稳定性等方面具有广阔的应用前景。针对当前SMES控制存在超调量大、控制精度不高等缺陷,将无差拍控制引入SMES的控制中。首先建立了SMES数学模型并介绍了无差拍控制的一般设计方法,然后根据SMES数学模型设计了SMES的无差拍控制策略,最后在MATLAB/SIMULINK中对所提控制策略进行了仿真。仿真结果表明,所提的控制方法具有跟踪无过冲、控制精度高和SMES变流器网侧电流谐波含量小等特点;将其应用于平滑双馈风机有功功率输出,有效平滑了双馈风机的功率波动,提高了双馈风机的并网能力。证明了该控制策略的有效性和优越性。     

基于事件触发的直流微电网无差拍预测控制

针对光伏(Photovoltaic, PV)−电池−超级电容直流微电网系统中光伏发电间歇性造成的功率失配问题, 提出一种基于事件触发的无差拍预测控制(Event-triggered deadbeat predictive control, ETDPC)方法, 以实现有效的能量管理. ETDPC方法结合事件触发控制策略和无差拍预测控制策略(Deadbeat predictive control, DPC)的优点, 根据微电网的拓扑结构构建状态空间模型, 用于设计适用于微电网能量管理的触发条件: 当ETDPC的触发条件满足时, ETDPC中无差拍预测控制模块被激活, 可以在一个控制周期内产生最优控制信号, 实现对于扰动的快速响应, 减小母线电压纹波; 当系统状态不满足ETDPC中的触发条件时, 无差拍预测控制模块被挂起, 从而消除非必要运算, 以减轻实现能量管理的运算负担. 因此, 对于电池−超级电容器混合储能系统(Hybrid energy storage system, HESS), ETDPC能够缓解间歇性光伏发电与负荷需求之间的功率失衡, 以稳定母线电压. 最后, 数字仿真和硬件在环(Hardware-in-loop, HIL)实验结果表明, 相较于传统无差拍控制方法, 运算负担减小了50.63%, 母线电压纹波小于0.73%, 验证了ETDPC方法的有效性与性能优势, 为直流微电网的能量管理提供了一种参考.     

带状态观测器的无差拍控制单相UPS设计与仿真

本文介绍了带数字状态观测器的无差拍控制单相UPS的设计，并在Matlab6．5下进行了仿真，验证了带状态观测器的无差拍控制技术能有效地改善系统的动态特性。     

Algebraic method for the design of output deadbeat controller

Based on the deadbeat model approach and the technique of output spectra matching, an algebraic method for the design of an approximate deadbeat controller with a specified configuration has been proposed. The chosen controller is determined by solving a set of simultaneous algebraic equations. One example is given to show the characteristic features of this approach.     

基于MATLAB的双极型矩阵变换器的无差拍控制算法实现

为了解决模型预测控制在双极型矩阵变换器控制中的开关周期不固定以及空间矢量调制控制策略的动态性能较差,提出了使用无差拍控制算法控制双极型矩阵变换器.无差拍控制通过预测模型对输出电压矢量以及电源电流矢量进行最优矢量组选择并进行调制.该方法良好地控制输出与输入电流波形,且对直流侧的电压有优化作用,动态性优异,对于网侧电流也有正弦化的作用.MATLAB作为算法的仿真实验软件,仿真结果有力地证明了该算法的理论研究.     

Optimal anti-windup synthesis for repetitive controllers

Repetitive controllers use internal models that provide very high gain at a selected fundamental frequency and its harmonics, additionally, some of the internal models may result unstable, as in the high order repetitive control approach. These characteristics make the repetitive control system susceptible to exhibit wind-up when actuator saturation occurs. This paper proposes an anti-windup scheme for repetitive control based on the model recovery anti-windup strategy. The proposed scheme provides low order, low computational burden and also isolation of the controller from the saturation effects. The anti-windup compensator is constructed from the plant model and provides an additional linear feedback path aimed at enhancing system performance. This feedback path is designed to obtain a deadbeat behaviour, which makes the system recovery faster. Finally, internal stability and deadbeat features are designed in a compact procedure based on linear matrix inequalities and an optimal linear quadratic design. Experimental validation of the proposed anti-windup compensator is provided using a mechatronic plant.     

Self-tuning deadbeat controllers

A deterministic self-tuning deadbeat control scheme is presented which is extremely simple to implement in the single-variable and multivariable cases. Its convergence properties are analysed by straightforward application of de Larminat's convergence results.     

一类离散时间切换线性系统的无差拍控制

研究一类带多控制器和多传感器离散时间线性系统的无差拍控制.对能控系统,通过适当的状态坐标变换获得系统矩阵的块三角结构,再设计状态反馈和周期切换策略使得状态反馈矩阵在有限周期内为零,从而保证闭环系统的无差拍稳定.进一步,对能观系统,设计具有有限时间精确估计的动态输出反馈,通过适当的周期切换策略实现闭环系统的无差拍稳定.最后,给出一个例子以验证所提设计方法的有效性.