A polynomial approach to the l1-mixed sensitivityoptimal control problem

It is shown how discrete-time, mixed-sensitivity, l₁-optimal control problems can be converted via polynomial techniques to linear “least absolute data fitting” problems and solved via efficient and stable numerical methods. In particular, two new sub/superoptimization schemes are introduced by expressing the closed-loop sensitivity and complementary sensitivity maps in terms of the free parameter of a stabilizing deadbeat controller parameterization and exploiting the underlying algebraic structure. This approach induces the application of a consistent truncation strategy that leads to a redundance-free constraint formulation and, as a consequence, to linear programming problems less affected by degeneracy. Further, more insight on the algebraic structure of the problem and on the achievement of exact rational solutions is provided, allowing the development of a simple and conceptually attractive theory     

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.     

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     

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.     

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.     

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.     

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,     

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.     

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     

Optimal control of Takagi–Sugeno fuzzy-model-based systems representing dynamic ship positioning systems

Orthogonal function approach (OFA) and the hybrid Taguchi-genetic algorithm (HTGA) are used to solve quadratic finite-horizon optimal controller design problems in both a fuzzy parallel distributed compensation (PDC) controller and a non-PDC controller (linear state feedback controller) for Takagi–Sugeno (TS) fuzzy-model-based control systems for dynamic ship positioning systems (TS-DSPS). Based on the OFA, an algorithm requiring only algebraic computation is used to solve dynamic equations for TS-fuzzy-model-based feedback and is then integrated with HTGA to design quadratic finite-horizon optimal controllers for TS-DSPS under the criterion of minimizing a quadratic finite-horizon integral performance index, which is also converted to algebraic form by the OFA. Integration of OFA and HTGA in the proposed approach enables use of simple algebraic computation and is well adapted to the computer implementation. Therefore, it facilitates design tasks of quadratic finite-horizon optimal controllers for the TS-DSPS. The applicability of the proposed approach is demonstrated in the example of a moored tanker designed using quadratic finite-horizon optimal controllers.     

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.     

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.     

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.     

电液伺服试验机力控系统负载刚度自适应控制

负载刚度的变化会导致电液伺服力控系统的控制特性发生改变,从而降低系统的稳定性与控制精度.本文以电液伺服万能试验机为研究对象,首先建立了考虑负载刚度的力控系统数学模型,分析了负载刚度的变化对控制特性的影响;其次设计了模型参考自适应(MRAC)控制器,并根据试验机力控系统的设计目标提出了一种具有最小拍响应特性且满足严格正实要求的参考模型;然后利用Simulink对最小拍参考模型MRAC控制器及PID控制器进行了仿真,并在自制的实验平台上采用两种不同刚度的试样分别进行了等速力加载实验,仿真及实验结果表明所设计的控制器能有效的抑制试样刚度的差异所引起的控制特性的变化,使电液伺服力控系统的响应具有良好的一致性.     

有限拍控制研究

设计了一种新的有限拍控制方法.由于控制器结构的改变,改善了开环系统的性质,使具有不稳定极点的被控对象也可以应用有限拍控制,扩大了有限拍控制的应用范围.     

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。     

Optimal pole placement design for SISO discrete-time systems

In this paper, we incorporate the placement of one real closed-loop pole into a compensator design framework based upon the Youla parameterization, duality theory, and linear programming. This framework has been used to design discrete-time compensators to solve the l₁ controller design problem as well as other related time-domain optimization problems. Previous work on these problems has focused on deadbeat systems. It is known that these can require high-order controllers. Part of the motivation for this work is to improve the tradeoff between controller order and performance over that, using deadbeat control     

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.     

Performance recovery under output feedback sampled-data stabilization of a class of nonlinear systems

This paper studies sampled-data output feedback control of a class of nonlinear systems. It is shown that the performance of a stabilizing continuous-time state feedback controller can be recovered by a sampled-data output feedback controller when the sampling period is sufficiently small. The output feedback controller uses a deadbeat discrete-time observer to estimate the unmeasured states. Two schemes are proposed to overcome large initial transients when the controller is switched on.     

自适应有限拍感应电机电流控制器设计

基于有限拍方法设计了一种自适应矢量控制感应电机的电流控制器.通过差分消去电机模型中的反电动势,利用补偿电压进一步消除电流误差.针对电流控制器对电机参数变化敏感的问题,对电机参数进行在线辨识,保证控制器参数与电机的实际参数一致.仿真结果表明,定子电流在参数变化时能够实现对参考电流的快速跟踪,同时能获得良好的稳态性能.