Ripple-free deadbeat control for sampled-data systems

In this paper the ripple-free deadbeat control problem for sampled-data systems is considered. This control objective is to settle the error to zero for all time after some finite settling time, in other words to eliminate the ripples between the sampling instants in deadbeat control of sampled-data systems. The necessary and sufficient conditions to solve this problem are derived and related to the system type, and a method of constructing the ripple-free deadbeat control system is presented.     

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     

Stabilizing and deadbeat properties of receding-horizon controllers

It is shown that receding-horizon controllers with horizon length N ≥ v (v being the controllability index of the system) stabilize a given discrete-time linear multi-variable system. Necessary and sufficient conditions for a receding-horizon controller to be a deadbeat controller are also given. It is further shown that by modifying a receding-horizon controller m of the poles of the closed-loop system (where m is the dimension of the input space) can be assigned to zero with simultaneous stabilization. The deadbeat properties of such modified receding-horizon controllers are also investigated,     

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.     

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.     

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.     

Deadbeat观测器的一种新的设计方法及实现

ｄｅａｄｂｅａｔ观测器由于极点在原点而具有系统阵幂零的性质,本文充分利用这一性质,针对离散线性系统,提出了一种新的ｄｅａｄｂｅａｔ观测器设计方法,该方法直接利用的Ｉ／Ｏ数据估计系统内部状态,无需对系统状态有个寝估计,相应的也就可以不受寝估计误差的影响,文中给出了该观测器的具体实现步骤,并通过仿真验证了所提出方法的正确性与有效性。     

A note on parameterization of the class of deadbeat controllers

The problem of parameterizing the class of deadbeat controllers for a given discrete-time system through the minimum number of parameters was solved by Schlegel [1]. This note shows how to utilize the above solution to study some problems in designing deadbeat controllers. First, an algorithm is developed to compute a controller which minimizes-in an average sense-a given objective function. Second, a necessary and sufficient condition is given for the existence of an output deadbeat controller. Finally, the problem of parameterizing the set of deadbeat controllers for those systems transformable to the phase-variable block-canonical form is reconsidered.     

Parametrization of all ripple-free deadbeat controllers

This paper is concerned with deadbeat control in sampled-data systems. Deadbeat control achieves finite-time settling (deadbeat settling) at sampling instants, but there may exist error called ripple “between” sampling instants even after the response is settled “at” sampling instants. The objective of this paper is to give a parametrization of all ripple-free deadbeat controllers (controllers which achieve deadbeat settling without ripple) in sampled-data systems. It is also shown that the following holds in general: minimum-time deadbeat control causes ripple when the pulse transfer function to be controlled has stable zeros.     

Explicit parameterization of state deadbeat controllers

A general state deadbeat control problem, not restricted to the controllability indexes, is posed and solved. A result for the explicit parameterization of deadbeat controllers is obtained. With the parameterization, only the genuine independent free parameters appear in the deadbeat controllers     

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     

Deadbeat servoproblem for multivariable n-D systems

Sufficient conditions are given for the existence of a solution to the deadbeat servoproblem for multivariablen-Dlinear systems. An algorithm is presented for finding matrices of ann-Dlinear controller. The algorithm is illustrated by a simple example.     

Dead-beat servo problem for 2-dimensional linear systems

Necessary and sufficient conditions for the existence of a solution to the deadbeat servo problem for single-input single-output 2D linear systems are given. An algorithm is presented for finding a control law such that the tracking error vanishes in the shortest time possible. The algorithm is illustrated by a simple example.     

Output deadbeat control of nonlinear discrete-time systems withone-dimensional zero dynamics: global stability conditions

Output deadbeat control in one step is considered for a class of discrete-time systems described by a nonlinear single-input/single-output recursive representation. Global stability conditions are established for the particular subclass of systems with one-dimensional zero dynamics. The results are illustrated with applications to polynomial and neural dynamical systems     

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.     

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     

A direct computation of state deadbeat feedback gains

A method for computing a feedback gain that achieves state deadbeat control is given. From systems given in the staircase form, this method derives the deadbeat gain in a numerically reliable way. It is shown that the gain turns out to be LQ optimal for some weightings     

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。     

A note on the receding-horizon control method

In this correspondence, the relation of receding-horizon control method with the state deadbeat control is brought out. It is shown for single-input systems that the receding-horizon control is a state deadbeat control if the horizon length is taken to be equal to the state dimension.