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.     

Output deadbeat control discrete-time multivariate systems

An algorithm is presented to compute output deadbeat controls for linear multivariable systems. The algorithm, based on quadratic optimization with no cost on control (cheap control), is numerically stable and covers the most general cases. The resulting controls are internally stable and are shown to drive the outputs of the system to zero in minimum time using state feedback. The central part of the algorithm is the construction of the nonunique state-cost matrix. Two alternatives are presented having different complexities and resulting in solutions having different properties     

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     

Deadbeat control with disturbance rejection

A deadbeat control problem with disturbance rejection is considered for a SISO discrete time plant. Disturbances are supposed to enter into the input to the plant and the output from the plant. The two-degree-of-freedom controllers are employed to internally stabilize the feedback control system, to make the output of the plant track a reference signal and to reject the disturbances in the sense of the deadbeat response. Necessary and sufficient conditions for the problem to have a solution are shown. And the set of all controllers meeting the design requirements are represented using two free polynomials.     

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.     

Finite settling time stabilisation: the robust SISO case

This article deals with the problem of robustness to multiplicative plant perturbations for the case of finite settling time stabilisation (FSTS) of single input single output (SISO), linear, discrete-time systems. FSTS is a generalisation of the deadbeat control and as in the case of deadbeat control the main feature of FSTS is the placement of all closed-loop poles at the origin of the z-plane. This makes FSTS sensitive to plant perturbations hence, the need of robust design. An efficient robustness index is introduced and the problem is reduced to a finite linear programme where all the benefits of the simplex method, such as effectiveness, efficiency and ability to provide complete solution to the optimisation problem, can be exploited.     

无差拍控制策略在数字化UPS逆变系统中的应用

为了改善逆变电源的输出性能.提高逆变电源输出响应速度和精度,研究了无差拍控制策略地数字化UPS(Uninterruptible Power Supply)逆变系统中的应用.给出了无差拍控制的数学建模方法,并采用Matlab/Simulink进行了仿真研究.经过理论分析和仿真结果表明,采用无差拍控制策略设计的控制器用于逆变电源系统具有的突出优点是响应速度快,可大幅提高系统的动态响应性能.     

Designing suboptimal discrete output control laws for damping bounded perturbations

The suboptimal linear discrete output control laws were designed which are capable of minimizing the upper estimate of the maximal value of the norm of controlled output for any bounded perturbations and all initial system conditions from some domain. The laws were designed using the method of invariant ellipsoids and the apparatus of linear matrix inequalities.     

On deadbeat controllers

The possibility of achieving a deadbeat regulation and tracking in linear multivariable systems independently of their initial conditions is investigated. Necessary and sufficient conditions for the existence of various deadbeat controllers are established in a constructive way. A detailed analysis of the control sequence generated by any deadbeat controller is then presented.     

Deadbeat output regulators for decouplable recursive non-linear systems

The deadbeat output regulator problem is formulated and solved in a straight-forward way for a class of decouplable multivarialbe recursive non-linear systems. It is shown that the decoupling control sequences drive each regulated output to zero and remain at zero thereafter in a minimum number of control iterations; this number is equal to the relative degree of the corresponding output. In addition, we show that the internal stability of a deadbeat closed-loop system is guaranteed only if the system is minimum phase.     

Output deadbeat controllers with stability for discrete-time multivariable linear systems

This short paper Treats the problem of designing output deadbeat controllers having the property that the control input to the system converges to zero as time goes to infinity, for discrete-time multivariable linear systems. Two configurations of controllers are considered: one is of state feedback; the other is a dynamic controller using an observer. The existence of such controllers is examined, and the methods are presented for designing such controllers when they exist. The controller using a state feedback obtained in this paper is optimal in the sense that the controller settles the output in zero for any initial state in the minimum number of steps. On the other hand, the dynamic controller is not optimal in that sense, but it minimizest, wheretis defined as an integer such that the controller drives the output to zero in no more thantsteps for any set of initial conditions of the system and the observer.     

Distributed output regulation for linear multi-agent systems with communication delays

In this paper, a distributed output regulation approach is presented for the cooperative control of linear multi-agent systems in the presence of communication delays. Both dynamic state and output feedback control laws are designed for achieving the property of output regulation. Sufficient conditions for the existence of these control laws are provided in terms of linear matrix inequalities. Simulation results are given to support the efficiency of the proposed distributed output regulation approach.     

Nonlinear feedback control of multivariable non-minimum-phase processes

A new method of controlling nonlinear processes with a non-minimum-phase delay-free part is presented. Two control laws are derived for stable, multiple-input multiple-output processes. They are obtained by requesting an approximately linear, input–output response and exploiting the connections between model-predictive control and input–output linearization. Conditions under which the closed-loop system is asymptotically stable are given. The application and performance of the control laws are illustrated using numerical simulation of two chemical reactor examples that exhibit non-minimum-phase behavior.     

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.     

A non-linear controller design method for processes with saturating actuators

An optimization approach is proposed to derive non-linear model-based control laws for non-linear processes with actuator saturation non-linearities. The derived control laws induce a linear closed-loop process output response in the absence of input constraints (are input-output linearizing), are able to minimize the mismatch between the constrained and the linear unconstrained process output responses, and inherently include optimal directionality and windup compensators. Connections between the derived control laws and (a) already available, input-output linearizing, non-linear, control methods, (b) modified internal model control, and (c) model state feedback control, are established. The application and performance of the derived control laws are shown by examples.     

Algorithm for deadbeat tracking

A deadbeat control algorithm is presented for autoregressive process models with unknown parameters. The control signal defined by the deadbeat tracking algorithm depends only on the reference input and output error time sequences. This serves to simplify the process parameter identification task, which then can be delegated to the background of the algorithm     

Digital parameter-adaptive control of an air-conditioning plant

Two parameter-adaptive (self-tuning) control algorithms for multivariable systems are described. The algorithms are designed on the basis of linear input-output system models by the combination of recursive parameter estimation and control algorithms: a parameter-adaptive deadbeat controller and a parameter-adaptive optimal state controller. These controllers are applied to a two-input two-output air-conditioning pilot plant, which consists of an air heater and an air humidifier and whose output variables are the temperature and the relative humidity of the air measured at the air outlet. The air-conditioning plant is a nonlinear system and its linearized static and dynamic behaviour is strongly dependent on the operating point characterized mainly by the output variables and by the air flow rate through the plant. The results of the real-time control experiments indicate that it is possible to use the self-tuning features of the parameter-adaptive controllers to stabilize the controlled system after a short adaption phase and to achieve at least a satisfactory control performance for time varying air flow rates and for time varying setpoints of the output variables.     

Control design with arbitrary information structure constraints

In this paper, a new method is proposed for designing robust control laws that are subject to arbitrary information structure constraints. The computation of the gain matrix is formulated in terms of a static output feedback problem, which can be efficiently solved using linear matrix inequalities. The resulting control laws ensure stability with respect to a broad class of additive nonlinear uncertainties in the system.     

Event‐triggered global leader‐following consensus of a group of neutrally stable linear systems subject to input saturation

This paper studies the global leader‐following consensus problem for a multiagent system using event‐triggered linear feedback control laws. The leader agent is described by a neutrally stable linear system and the follower agents are also described by a neutrally stable linear system but with saturating input. Both the state‐feedback case and the output‐feedback case are considered. In each case, an event‐triggered control law is constructed for each follower agent and an event‐triggering strategy is designed for updating these control laws. These event‐triggered control laws are shown to achieve global leader‐following consensus when the communication topology among the follower agents is strongly connected and detailed balanced and the leader is a neighbor of at least one follower agent. The Zeno behavior is excluded. The theoretical results are illustrated by simulation.     

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.