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     

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.     

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.     

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     

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     

Deadbeat control of discrete-time systems with singular state matrix using canonical decomposition

The problem of deadbeat control of controllable discrete-time systems with singular state matrix is considered. Our approach is based on the representation of the system obtained by isolating the reachable part of the system and the controllable but unreachable part using the Kalman structure theorem. It is shown that, eigenvalue assignment for controllable but unreachable single-input systems does not lead to a unique control law. In fact, the extra degrees of freedom available can be used to shape the transient response characteristics of the system.     

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.     

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.     

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.     

Dead-beat control and the Riccati equation

Connections between dead-beat control strategies and optimal control policies for linear, time-invariant, discrete-time systems are established. The performance index of the system is quadratic and only the terminal state of the system is penalized. An explicit solution to the singular Riccati equation, associated with this optimization problem, is given. Properties of the time-variable gain matrices, generating the optimal cantrol policy, are presented. In particular, necessary and sufficient conditions for each of these gain matrices to be a time-invariant deadbeat controller are given.     

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.     

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.     

Comments on "An explicit pole-assigning feedback formula with application to deadbeat feedback construction in discrete linear systems"

A corrected expression is given for the feedback gain matrix, presented in the above paper, so as to obtain arbitrary pole assignment in linear multiinput systems by linear state variable feedback. It is noted that specialization to discrete deadbeat controller design results in deadbeat performance in at most νcsteps where νcis the system controllability index, which is in general less thann + m - 1wherenandmare the dimensions of the state vector and control input vector, respectively.     

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.     

Ripple-free deadbeat control of SISO discrete systems

The ripple-free deadbeat control problem for arbitrary (not necessarily stable) SISO linear discrete plants and reference signals is treated. It is established that a causal, stabilizing ripple-free deadbeat controller exists if and only if the zeros of the plant and the poles of the reference signal are disjoint, and a complete characterization of all such controllers is obtained. Solutions to two illustrative problems are presented.     

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 control and tracking of discrete-time systems

A new approach for forcing the state of a linear discrete-time system to zero in a minimum number of steps is discussed. The problem is formulated as the solution to a steady-state optimal control problem with no cost on the control. This problem in turn is set up as the solution to an associated eigenvalue problem. No special assumption on the open loop system matrix and/or the ratio of the number of states to controls is required. Stable numerical techniques are presented for solving for the feedback gain. Robust deadbeat tracking is also discussed.     

Continuous-time deadbeat control for sampled-data systems

In this paper, the continuous-time deadbeat control problem for the sampled-data systems is considered. We derived the class of all controllers that achieve the continuous-time deadbeat control     

The discrete linear time invariant time-optimal control problem—An overview

A review of two decades of investigation into one of the fundamental problems of control theory, the discrete linear time invariant time optimal control problem, is presented. Two classes of multi-input time optimal controller, one based on system controllability and the other on eigenvalue assignment, are considered in some detail. Also discussed are the dual state reconstruction problem, the deadbeat control of linear systems with inaccessible state, and other extensions. The exposition is a unifying one and involves only that matrix algebra commonly encountered in control theory.     

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.