Pole assignment using dynamic compensators with prespecified poles

The paper describes a simple method for the design of physically realizable dynamic output feedback compensators with prespecified poles to achieve pole assignment in single-input, single-output and multivariable systems. In this method, the numerator parameters of the compensator transfer function are used to position the poles of the augmented closed-loop system consisting of the plant and the compensator at specified locations in the complex plane. It is shown that some or all poles of the closed-loop system can be positioned arbitrarily depending on the order of the compensator. The method is first developed for single-input systems. It is then shown to apply directly to single-output systems and is extended to multivariable systems by restricting the compensators to have unity rank. A number of illustrative numerical examples are given     

Block decoupling and arbitrary pole assignment for a linear right-invertible system by dynamic compensation

The block decoupling of a linear right-invertible system by dynamic compensation is studied. The system structure of the block-decoupled system is clarified from the viewpoint of the closed-loop poles. A dynamic compensator that realizes block decoupling and arbitrary pole assignment is proposed. Two examples are given to illustrate the design procedure of the dynamic compensator and its effectiveness.     

A parametric solution to the pole assignment problem using dynamicoutput-feedback

A technique is presented for pole placement of linear time-invariant systems using dynamic feedback. A previously developed method for partial pole assignment using constant feedback is generalized to the dynamic output-feedback case. Subject to a mild assumption on the number of complex conjugate poles to be assigned, it is almost always possible to arbitrarily assign all the closed-loop system poles using a compensator of order [(n-φ)/max(m,l)] using this new method. Here, n, m, and l are the order of the system, and the number of inputs and outputs, respectively, and φ Δ/=max(m,l)+[max(m,l)/2]+…+[max(m,l)/min(m,l)] where [x] denotes the nearest integer lower than or equal to x (i.e., floor (x)), and [x] denotes the nearest integer greater than or equal to x (i.e., ceiling (x)). An equivalent result is that using a compensator of order q, it is almost always possible to arbitrarily assign min(n+q,(max(m,l)+1)q+φ) closed-loop system poles. Only the normal procedures of linear algebra are required to implement the technique. Note that φ⩾l+m-1 and, therefore, the result is stronger than previous exact pole assignment results. Since it does not involve iteration or any other numerical techniques, it is possible to implement the method symbolically and, therefore, to obtain general parametric solutions to the pole assignment problem. The freedom in this design approach can also often be used to guarantee the internal stability and/or robustness of the resulting closed-loop system     

Assigning the set of zeros in control systems with parallel compensation

The problem of ensuring a given set of zeros in a linear multivariable dynamical system with the equal number of inputs and outputs that includes a parallel compensator and feedback loop is considered. Methods reducing this problem to the control of eigenvalues of a certain matrix are proposed; the simultaneous assignment of poles and zeros is reduced to the control of poles of two plants using a single controller. The calculations are based on well-known and well-tested modal control techniques.     

Pole-shifting using output feedback

A simple test is given in analytic (matrix) terms which provides both necessary and sufficient conditions for arbitrary assignment of all of the system poles using only constant output feedback. A formula to determine the required output compensator is presented, and the whole procedure is illustrated by an example.     

滑动模态补偿器在变结构控制设计中的应用

借助于滑动模态补偿器，首先对一类广义控制系统提出一种变结构预测器设计方法，并且给出了具体观察器的设计，随后对一类分布参数系统与广义集中参数系统的耦合系统进行研究，讨论了其极点配置以及变结构控制器的设计等问题，由于引用了滑动模态补偿器，使得设计过程简单明了。     

配置特征结构的动态补偿器设计

本文讨论了配置特征结构的动态补偿器的设计问题,给出了达到阶次下限的动态补偿器 存在的充分必要条件.当上述存在性条件不能满足时,提出了构成最小阶次的具有给定特征 结构的动态补偿器的逐步扩展方法.     

Design of pole-placement compensators for multivariable systems

The paper describes a two-stage method for the design of dynamic compensators for pole placement in linear multivariable systems. In the first stage, a number of poles are assigned by means of constant output feedback. In the second stage, the assigned poles are preserved and a number of additional poles are placed using dynamic output feedback. The pole placement is achieved using a compensator of lower order than required by the existing methods, since now the compensator has non-unity rank transfer function matrix. In particular, for a compensator of given order, a larger number of poles can be placed using this method compared to the existing methods.     

基于高阶补偿器的加速度传感器动态误差补偿方法

加速度传感器动态特性对其动态测量结果具有重要影响。为了改善加速度传感器动态性能,减小动态误差,提出了一种基于高阶补偿器的加速度传感器动态误差补偿方法,该方法通过建立加速度传感器ARX模型,利用加速度传感器模型极点确定高阶补偿器的阶次,并应用误差白化算法（EWC）获得高阶补偿器的参数,实现加速度传感器的动态误差补偿。实验结果表明,该方法有效改善了加速度传感器的动态特性,且高阶补偿器的补偿效果优于低阶补偿器的补偿效果。高阶补偿器补偿后传感器输出超调量和残差均是低阶补偿后的三分之一,响应时间是低阶补偿后响应时间的一半左右。     

A parametric approach to finite-dimensional control of linear distributed-parameter systems

This article considers the design of finite-dimensional compensators for distributed-parameter systems using eigenvalue assignment. The proposed compensator consists of an observer estimating additional outputs and a static feedback of the measurable and the estimated outputs. Since the additional outputs can be asymptotically reconstructed, the compensator can be designed using the separation principle, i.e. the closed-loop eigenvalues are given by the observer eigenvalues and the eigenvalues resulting from the static output feedback control. In order to solve the corresponding eigenvalue assignment problem, the parametric approach for the design of static output feedback controllers in finite-dimensions is extended to distributed-parameter systems. By using a parameter optimisation it is possible to assign all closed-loop eigenvalues within specified regions of the complex plane in order to stabilise the system and to assure a desired control performance. A heat conductor is used to demonstrate the proposed design procedure.     

Relatively optimal control and its linear implementation

Motivated by the fact that determining a feedback solution for the optimal control problem under constraints is a hard task we introduce the concept of relative optimality, roughly optimality for a specific (nominal) plant initial condition. We consider a generic discrete-time finite-horizon constrained optimal control problem for linear systems, and we seek for a state feedback (possibly dynamic) controller. As a fundamental requirement, we do not admit preactions or controller-state initialization based on the plant initial state and we assume our controller to be time-invariant. In particular, we do not consider controllers simply achieved by the feedforward and tracking of the optimal trajectory. A relatively optimal control is a stabilizing controller such that, if initialized at its zero state, produces the optimal (constrained) trajectory for the nominal initial condition of the plant. We show that one of such controllers is linear, dead-beat, and its order is equal to the length of the horizon minus the plant order, thus, of complexity which is known a priori. Some additional features such as the assignment of the compensator poles to achieve strong stabilization are proposed. We show that, by means of the proposed approach, we can face several problems such as optimal point-to-point operations, optimal impulse response and optimal tracking.     

离散线性周期系统的模型匹配

考虑离散线性周期系统的模型匹配问题, 提出一种基于参数化极点配置的模型匹配方法. 该方法从时域的角度出发, 采用周期状态反馈, 使得闭环系统充分接近目标系统. 由于所采用的参数化极点配置算法提供了充分的自由度, 所提出的方法能够实现零误差匹配. 数值算例验证了所提出算法的有效性.

     

输出反馈极点配置的直接方法

本文研究了线性时不变能控能观系统x=Ax+Bu,y=Cx应用输出比例反馈和动态 补偿器任意配置闭路极点问题.文中借助于[sI-A]-1B矩阵的右既约分解矩阵,将闭路系统 特征多项式表示成p×p维矩阵行列式表示式,基于这一表示式建立了计算反馈矩阵和设计 动态补偿器的简单、实用的新方法.证明了应用输出比例反馈和动态补偿器可任意配置闭路 极点数分别为η≤min{max {m+(p-1) [m/p], p+(m-1) [p/m],n}和η0≤min {v+max {vm+m+(p-1)[m/p],vp+p+(m-1)[p/m]},n+v} (其中n和v分别为控制对 象和动态补偿器的阶数,p=rankB,m=rankC),文章最后举例说明了这种方法的应用.     

Pole assignment in a specified disk

The problem of assigning all poles of a closed-loop system in a specified disk by state feedback is considered for both continuous and discrete systems. A state feedback control law is determined by using a discrete Riccati equation. This kind of pole assignment problem is namedD-pole assignment, and its relation to the optimal control problem and its robustness properties are discussed. The gain and phase margins for all closed-loop poles to stay inside the specified diskDare determined for the proposed control.     

圆形区域内鲁棒极点配置优化

本文基于和声搜索算法将精确极点配置的思想推广到圆形区域极点配置,通过对圆域内极点全局优化的方法,实现圆域内鲁棒极点配置问题.首先,基于几何原理描述极点在圆形区域内的位置信息,确定了在圆形区域内动态选择极点的规则,可以保证算法在圆形区域内动态选取极点.然后,对圆形区域内的极点,基于精确鲁棒极点配置的思想,利用和声搜索算法优化摄动或不确定性的谱范数上界,从而得到一组允许闭环系统具有更大摄动或不确定性的极点及相应的状态反馈控制器.最后,通过实例进行仿真,仿真结果表明本文采用和声搜索算法全局优化动态选择极点方法得到的闭环系统具有更好的鲁棒性.     

A geometric framework for pole assignment algorithms

The problem of pole assignment by gain output feedback or by low-order dynamical compensator is considered from a geometric point of view. This makes it possible to unify, in a general framework, most of the existing pole assignment methods formulated in a state-space context, such as the minimal-order observers, the Brasch-Pearson compensator, and the methods proposed by H. Kimura, and to simplify their presentation. Moreover, new pole assignment algorithms may be derived from this general formulation     

Stability and exponential stability of an adaptive control schemefor plants of any relative degree

Relying on a new adaptive pole assignment control scheme for plants with unknown relative degree and uncertain order which can be made minimum phase by means of a relative-degree-one first order parallel compensator, a new adaptation mechanism is proposed in this note in order to tackle with the problem of the attainment of an exponentially stable behavior of the output error. In particular, the connection between exponential stability and persistent excitation is outlined, and a complete stability analysis is performed     

Robust pole assignment for linear control systems in a circular region using novel global harmony search algorithm

This paper presents a new approach to the problem of robust pole assignment in a circular region using novel global harmony search (NGHS) algorithm. Based on geometric principles, the position information of poles in the circular region is depicted and the rules of dynamic selection of poles from the circular region are determined. This ensures the algorithm select poles dynamically from the circular region. In order to get a set of poles and the state feedback controller which allow the system to have a maximum allowable perturbation or uncertainty, the upper bound of perturbation or uncertainty is optimized by the NGHS algorithm for the poles in the circular region. In contrast to most existing methods, an optimization method using NGHS algorithm for the dynamic selection of poles, makes the closed-loop system show better robustness. Finally, the simulation results demonstrate the effectiveness of the proposed approach.     

配置特征结构的n-l阶补偿器设计

本文证明了若系统可观测,n-l阶的动态补偿器不仅可以达到给定特征结构的配置,而且可以任意设置附加的特征值。由于这一结果,n-l阶动态补偿器可用配置全部特征结构的方法进行设计。     

磁县浮实验列车模型的解耦控制系统

本文主要讨论磁悬浮实验列车模型的解耦控制问题.在分析列车动力学模型的基础上, 利用信号变换技巧,实现了系统的解耦,对解耦系统根据性能要求配置了闭环系统的极点,通 过状态反馈给出了反馈阵F,应用Pearson动态补偿器理论设计了补偿器,研究了磁悬浮控 制系统的具体实现问题.