有限字长数字控制器的一种极点灵敏度优化结构

研究了有限字长数字控制器的一种最优实现,主要考虑了系统的主导极点相对于控制器实现的灵敏度。通过定义该灵敏度,并分析它与实现所在坐标系的关系,得到了最小化该测度的一类结构。     

基于有限字长考虑的采样系统最优控制器实现

提出了有限字长约束下采样控制器最优实现的新的有效算法：将最优实现问题演化为非线性规划问题,从而可以利用现有的优化技术来求解。理论推导和数值实例表明：该算法计算简便,所得的最优实现结果较已有研究结果有更大的稳定界和更短的稳定字长。     

Z变换和△变换的有限字长特性研究

计算机的有限字长对数字控制器的实现有重要影响.本文介绍了△变换及其δ算子的数 字控制器的实现方法,证明了δ算子实现方法在系数有限字长表示、运算中对舍入及截尾误差 的影响;有限字长非线性因素对极限环振荡的影响等方面,都优于常用的z变换及其q算子的 数字控制器实现方法.本文还提供了某型飞机的数字控制器在z变换和△变换下的不同有限 字长特性的数字仿真.     

Z变换和Δ变换的有限字长特性研究

计算机的有限字长对数字控制器的实现有重要影响。本文介绍了△变换及其δ算子的数字控制器的实现方法,证明了δ算子实现方法在系数有限字长表示、运算中对舍入及截尾误差的影响;有限字长非线性因素对极限环振荡的影响等方面,都优于常用的z变换及其q算子的数字控制器实现方法。本文还提供了某型飞机的数字控制器在z变换和△变换下的不同有限字长特性的数字仿真。     

模糊非脆弱动态输出反馈H∞控制器设计

本文考虑受有限字长影响的离散时间模糊系统的非脆弱H∞控制问题. 假定所设计的控制器具有加性区间型增益变量, 该增益变量反映了控制器数字执行过程中有限字长的影响. 区间型增益变量导致控制器设计具有数值计算问题, 而模糊性质的引入进一步增加了控制器设计的复杂性, 使问题变得更具有挑战性. 本文采用结构的顶点分离器方法来解决数值计算问题, 从而给出一个基于线性矩阵不等式的模糊非脆弱H∞控制器设计的两步算法. 该设计结果保证闭环系统渐进稳定并具有指定的H∞性能指标. 最后给出一个数值例子验证所提出方法的有效性.     

一类受约束非线性系统的有限时间优化镇定

优化控制方法可以考虑系统性能和节省能源,但是不能给出初始稳定区域的描述.本文阐述的优化控制方法可以给出初始稳定区域的描述,使得约束非线性系统有限时间稳定.首先设计有限时间优化控制器使得系统的状态在有限时间内进入初始稳定区域,同时优化目标函数,系统实现性能最优和消耗最小.进而设计有限时间鲁棒镇定控制器使得系统的状态在有限时间内收敛到原点. Lyapunov函数分析方法给出了吸引域的估计,并确保在不同状态下,设计的控制器使得闭环系统有限时间稳定.最后给出了一个仿真实例验证算法的有效性.     

球形对象族的最优鲁棒镇定

本文对球形对象族系统最优鲁棒镇定问题进行了研究.利用最小范数解方法求解球形对象族的可镇定性半径.可镇定性半径是系统稳定性半径的上界,最优控制器的稳定性半径等于镇定性半径.文中给出球形对象族最优鲁棒控制器的形式,并通过示例具体说明球形对象族最优鲁棒控制器的设计方法.     

MIMO线性离散系统的最优鲁棒跟踪控制

将MIMO线性离散定常系统在指定信号输入下获取最优时域指标的最优跟踪控制器设计问题归纳为求解一个有限维线性规划问题, 并证明这种最优跟踪控制器也是鲁棒稳定控制器.     

基于信息融合的离散系统最优预见重复控制

针对现有控制器中预见补偿器和重复控制器相对独立作用的最优跟踪问题,提出从信息融合的角度构造线性离散系统的最优预见重复控制器的设计方法.首先,在离散系统中引入L阶差分算子,将预见重复控制设计问题转化为调节稳定性问题;然后,使用协状态和信息量的概念获得控制软约束信息来描述最优融合的过程,得到控制增量信息和增广误差系统协状态的最优估计滤波;最后,将有关预见重复控制器控制律所有信息融合,得到由状态反馈、重复控制和预见补偿构成的最优预见重复控制器.数字仿真结果表明,与独立的最优预见重复控制器相比,基于信息融合的最优预见重复控制器在更少的周期内达到稳定,且在有限的步数下,更能有效利用系统的未来有效信息,从而大幅提高跟踪精度.     

H2最优控制器的不唯一性及闭环性能的改善

本文研究了H~2最优控制器的不唯一性问题,给出了H_2最优控制器集合存在的条件,并给出了一种将多变量H~2最优设计问题化为一组单变量的H~2最优设计问题的方法,给出了最优控制器集合的参数化公式,本文还给出了利用最优控制器集合中的自由参数提高闭环系统鲁棒性能及求取稳定最优控制器的方法。实例表明,这种设计方法可以充分利用控制器的自由度,实现提高系统鲁棒性以及求取稳定控制器的目的。     

Stability issues of finite-precision controller structures for sampled-data systems

The paper investigates the sensitivity of closed-loop stability with respect to (w.r.t.) finite word length (FWL) effects in the implementation of the digital controller coefficients. Both the shift and delta operators are considered for controller parameterization. Two tractable lower-bound measures of closed-loop stability are studied, and the optimal realization of general FWL controller structures is formulated as a constrained non-linear optimization problem. The emphasis of the paper, however, is on the derivation of a new algorithmic approach for the optimal realization of FWL PID controller structures. It is shown that, for PID structures, the optimization can be decoupled into two unconstrained problems with a maximum of four independent variables. An optimization strategy is developed to provide an efficient computational method for searching the optimal FWL PID controller realization with maximum stability bound and minimum bit-length requirement. Simulation results involving an IFAC benchmark PID controller system are presented to illustrate the effectiveness of the proposed strategy.     

Optimal realizations of fixed-point implemented digital controllers with the smallest dynamic range

A novel approach is proposed to design optimal finite word length (FWL) realizations of digital controllers implemented in fixed-point arithmetic. A minimax-based search procedure is first formulated to obtain an optimal controller realization that optimizes an FWL closed-loop stability measure. Since this FWL closed-loop stability measure is solely linked to the fractional part or precision of fixed-point format, the resulting realization may not have the smallest dynamic range. A measure is then derived to indicate the dynamic range of fixed-point implemented realization. By choosing an appropriate orthogonal transformation of this dynamic range measure of the optimal precision controller realization, a numerical optimization method is developed to make the controller realization having the smallest dynamic range without sacrificing FWL closed-loop stability robustness. The proposed approach is more efficient than a direct optimization of some combined FWL closed-loop stability and dynamic range measure via a numerical means. The proposed approach is established within a unified framework that includes both the shift and delta operator parameterizations, which makes it possible to compare the closed-loop stability characteristics of the optimal FWL controller realizations using shift and delta operators, respectively. Through analysing the simulation results of a design example, some useful insights and understandings are obtained regarding the FWL controller realizations based on shift and delta operators.     

Two approaches based on pole sensitivity and stability radius measures for finite precision digital controller realizations

This paper compares the two approaches based on pole sensitivity and the complex stability radius measures, respectively, for optimizing the closed-loop stability robustness of digital controllers with respect to finite word length (FWL) errors in fixed-point implementation. Design details and related optimization procedures are derived for the two methods. The two measures, although derived from different motivations, can both be regarded as lower-bound measures of a true but computationally intractable FWL stability measure in some senses. An example is used to verify the theoretical analysis and to illustrate the two designs for determining optimal FWL controller realizations.     

Optimal finite-precision controller realization of sampled-data systems

We investigate the sensitivity of closed-loop stability with respect to finite word length (FWL) effects in the implementation of digital controller coefficients. The optimal realization of digital controller structures with finite precision consideration is formulated as the solution of a constrained nonlinear optimization problem. A sophisticated optimization strategy involving the adaptive simulated annealing (ASA) optimizer is developed to provide an efficient computational method for searching the optimal FWL controller realization with maximum stability bound and minimum bit length requirement. A numerical simulation example is presented to illustrate the effectiveness of the proposed strategy.     

Comparative study on optimizing closed-loop stability bounds of finite-precision controller structures with shift and delta operators

The paper analyzes the sensitivity of closed-loop stability with respect to (w.r.t.) finite word length (FWL) effects in the implementation of the controller coefficients using both the shift and delta operator parameterizations. A unified approach is established to optimize a closed-loop stability lower bound for FWL controller structures. This provides a general framework to compare the FWL closed-loop stability characteristics of the controller structures based on the shift and delta operators, respectively. Two numerical examples are given, and the simulation results show that the optimal FWL controller realizations with the delta operator have better closed-loop stability margins than those with the shift operator.     

A -based optimal finite-word-length controller design

A novel optimal Finite Word Length (FWL) controller design is proposed in the framework of μ theory. A computationally tractable close-loop stability measure with FWL implementation considerations of the controller is derived based on the μ theory, and the optimal FWL controller realizations are obtained by solving the resulting optimal FWL realization problem using linear matrix inequality techniques.     

An improved closed-loop stability related measure forfinite-precision digital controller realizations

The pole-sensitivity approach is employed to investigate the stability issue of the discrete-time control system, where a digital controller implemented with finite word length (FWL), is used. A stability related measure is derived, which is more accurate in estimating the closed-loop stability robustness of an FWL implemented controller than some existing measures for the pole-sensitivity analysis. This improved stability measure thus provides a better criterion to find the optimal realizations for a generic controller structure that includes output-feedback and observer-based controllers. A numerical example is used to verify the theoretical analysis and to illustrate the design procedure     

Two classes of efficient digital controller structures with stability consideration

In this note, the efficient controller structure problem is investigated subject to minimizing finite word length (FWL) effects. Two classes of sparse controller structures characterized with a set of free parameters are derived. The stability behavior of each class is analyzed with a newly defined stability related measure. The optimal structure problems are studied in terms of maximizing the stability related measure for the two classes of sparse structures as well as the fully parametrized state-space realizations. A design example is given, which shows that the optimized sparse structures can beat the fully parametrized optimal realizations in terms of both stability performance and computation efficiency.     

Guaranteed robust stability of the closed-loop systems for digital controller implementations via orthogonal hermitian transform.

In this paper, an approach for robust stability analysis of a digital closed-loop system for digital controller implementations subject to finite word length (FWL) effects is proposed. Uncertainties caused by the roundoff and computational errors subject to FWL effects are expressed in function of mantissa bit number when the mode of floating-point arithmetic is used in the process. Then, based on the Small Gain Theorem and the Bellman-Grownwall Lemma, a sufficient stability criterion for the digital closed-loop system is derived. The eigenvalue sensitivity of the closed-loop system is developed in terms of mixed matrix-2/Frobenius norms. Then, by minimizing this eigenvalue sensitivity and using orthogonal Hermitian transform as well, an optimal similarity transformation can be obtained. By substituting this optimal transformation into the stability criterion, a minimum mantissa bit number used for implementing the stabilizing digital controllers can be determined. The main contributions are that this approach provides an analytical closed-form solution for obtaining the optimal transformation and, in addition to the stability criterion, leads to the implementation of the stabilizing controllers with a lower mantissa bit number when using this optimal one. Finally, detailed numerical design processes and simulation results are used to illustrate the effectiveness of the proposed scheme.