Robust eigenstructure clustering by non-smooth optimisation

We extend classical eigenstructure assignment to more realistic problems, where additional performance and robustness specifications arise. Our aim is to combine time-domain constraints, as reflected by pole location and eigenvector structure, with frequency-domain objectives such as the H₂, H_∞ or Hankel norms. Using pole clustering, we allow poles to move in polydisks of prescribed size around their nominal values, driven by optimisation. Eigenelements, that is poles and eigenvectors, are allowed to move simultaneously and serve as decision variables in a specialised non-smooth optimisation technique. Two aerospace applications illustrate the power of the new method.     

An explicit solution to right factorization with application in eigenstructure assignment

1Proble mfor mulationRight factorization oflinear systems is a basic problemincontrol systems theory,and has important applications inmany analysis and design problems ,such as , robuststabilization [1] ,minimal state space realization [2,3] ,speed servo system design [4] ,synthesis of H_infinitycontrollers [5] ,etc .Furthermore ,it has been shown byDuan and his co_authors that a factorization can be usedtoparameterize all the solutions to a generalized_type ofSylvester matrix equations [6 ~8…     

不确定时滞系统鲁棒镇定的优化方法

对一类含有时滞不确定的线性系统,考虑了鲁棒镇定问题。系统中的不确定性假设满足范数有界备件,通过用改进的Razmikhin-type定理,给出了鲁棒镇定控制器存在的充分条件。通过对Lyapunov矩阵方程的完全参数化求解,得到了鲁棒镇定控制器的参数化形式,鲁棒镇定问题转化为一类优化问题。基于这一条件与参数化特征结构配置结果,得到了状态反馈镇定控制器的设计算法。数值例子说明了该方法的有效性。     

FIR filters for online trajectory planning with time- and frequency-domain specifications

In this paper, the use of FIR (Finite Impulse Response) filters for planning minimum-time trajectories for robots or automatic machines under constraints of velocity, acceleration, etc. is presented and discussed. In particular, the relationship between multi-segment polynomial trajectories, i.e. trajectories composed of several polynomial segments, each one possibly characterized by constraints on one or more specific derivatives (i.e. velocity, acceleration, jerk, etc.), and FIR filters disposed in a cascade configuration is demonstrated and exploited in order to design a digital filter for online trajectory planning. The connection between analytic functions and dynamic filters allows a generalization of these trajectories, usually obtained by second- or third-order polynomial functions (e.g. trapezoidal velocity and double S velocity trajectories), to a generic order with only a modest increase of the complexity. As a matter of fact, the computation of trajectories with higher degree of continuity simply requires additional FIR filters in the chain. Moreover, the modular structure of the planner provides a direct frequency characterization of the motion law. In this way, it is possible to define the trajectories by considering constraints expressed in the frequency-domain besides the classical time-domain specifications, such as bounds on velocity, acceleration, and so on. Two examples illustrate the main features of the proposed trajectory planner, in particular with respect to the problems of multi-point trajectories generation and residual vibrations suppression.     

An eigenstructure assignment approach for constrained linear continuous-time singular systems

This paper establishes necessary and sufficient algebraic conditions for positive invariance of convex polyhedra with respect to some linear continuous-time singular systems. They can be considered as an extension for linear singular systems of the classical positive invariance relations for regular linear systems. For a stabilizable and impulse controllable singular system with constrained inputs, a stabilizing state feedback control guaranteeing the closed-loop positive invariance of some polyhedral sets determined from the feedback matrix is studied. An analysis of the closed-loop positive invariance relations is thus presented in terms of eigenstructure and stability properties. An eigenstructure assignment technique is proposed depending on the number of stable finite poles of the singular system.     

Robust control design using eigenstructure assignment and multi-objective optimization

This paper develops a new approach to multiple objective optimization design for robust multivariable control systems, based on eigenstructure assignment and genetic algorithms. It considers various performance indices (or cost functions) in the objectives, which are individual eigenvalue sensitivity functions, and the sensitivity and the complementary sensitivity functions in the frequency domain, instead of a single performance index for a control system. Based on these performance indices, the robustness criteria are expressed by a set of inequalities. The paper will make full use of the freedom provided by eigenstructure assignment to find a controller to satisfy the robustness criteria. A numerical algorithm for multi-objective optimization using genetic algorithm approaches is developed and applied to the simulation of a distillation column control system design     

Two parametric approaches for eigenstructure assignment in second-order linear systems

This paper considers eigenstructure assignment in second-order linear systems via proportional plus derivative feedback . It is shown that the problem is closely related to a type of so-called second-order Sylvester matrix equations. Through establishing two general parametric solutions to this type of matrix equations, two complete parametric methods for the proposed eigenstructure assignment problem are presented. Both methods give simple complete parametric expressions for the feedback gains and the closed-loop eigenvector matrices. The first one mainly depends on a series of singular value decompositions, and is thus numerically simple and reliable; the second one utilizes the right factorization of the system, and allows the closed-loop eigenvalues to be set undetermined and sought via certain optimization procedures. An example shows the effectiveness of the proposed approaches.     

Robust door assignment in less-than-truckload terminals

The assignment of incoming trailers to strip doors is one of the critical decisions that affect the performance of cross docking operations in less-than-truckload terminals. This paper introduces a mixed integer quadratic model with the objective of generating trailer-to-door assignments that equally distribute idle times at doors to accommodate operational level uncertainty encountered in truck arrival times. A door assignment heuristic is presented. The performance of the heuristic is compared with optimal solutions to small problems. The effectiveness of the proposed heuristic is studied under a variety of circumstances and terminal sizes. The simulation results show that the proposed heuristic is applicable to realistic-size terminals, and it is effective when variability in truck arrival and service times is considered.     

基于混合灵敏度优化的鲁棒特征结构配置

将H_∞理论的混合灵敏度指标融入到特征结构配置中, 将混合灵敏度指标转换为特征结构设计参数的函数关系, 建立了特征结构配置的频率域指标约束. 这两种方法的结合各自利用了其在时域和频率域的设计优势. 通过优化算法所获得的鲁棒特征结构配置, 既保证了闭环特征值/特征向量, 又使反馈回路具有一定的频率域特性. 计算实例表明这种综合设计方法的有效性.     

具有圆盘极点约束的不确定切换系统的鲁棒控制

本文研究了一类具有圆盘极点约束的不确定线性切换系统的鲁棒镇定问题．对此类系统设计了状态反馈控制器,使得闭环系统的所有极点均位于一个给定的圆盘中,并得到了一个基于LMI的充分条件．通过求解线性矩阵不等式,可以构造一个具有较小反馈增益参数的状态反馈控制器．最后的仿真算例证明了本文结果的有效性。     

Robust pole assignment in systems subject to structured perturbations

The problem of robust pole assignment by feedback in a linear, multivariable, time-invariant system which is subject to structured perturbations is investigated. A measure of robustness, or sensitivity, of the poles to a given class of perturbations is derived, and a reliable and efficient computational algorithm is presented for constructing a feedback which assigns the prescribed poles and optimizes the robustness measure.     

An explicit solution to polynomial matrix right coprime factorization with application in eigenstructure assignment

In this paper, an explicit solution to polynomial matrix right coprime factorization of input-state transfer function is obtained in terms of the Krylov matrix and the Pseudo-controllability indices of the pair of coefficient matrices. The proposed approach only needs to solve a series of linear equations. Applications of this solution to a type of generalized Sylvester matrix equations and the problem of parametric eigenstructure assignment by state feedback are investigated. These new solutions are simple, they possess better structural properties and are very convenient to use. An example shows the effect of the proposed results.     

Robust performance of linear parametrically varying systems using parametrically-dependent linear feedback

In this paper a parameter-dependent control problem for linear parametrically varying (LPV) systems is presented. Sufficient conditions are given that guarantee an LPV system is exponentially stable and achieves an induced L₂-norm performance objective from the disturbance to error signals. The usefulness of parameter-dependent controllers is motivated from a gain-scheduling viewpoint. The resulting synthesis problem is reformulated into a convex optimization problem, which can be solved using efficient new algorithms.     

Adaptive tuning to frequency response specifications

The paper describes a procedure to design adpative controllers when the specifications are given in terms of a number of points of a desired closed-loop frequency response. The key idea is the use of a bank of ‘band-compensators’, each one of which is intended to act on its corresponding frequency band. The compensator parameters are updated based on a finite impulse response on-line interpolation of the plant frequency response. The latter is carried out using a bank of filters and independent processing of the complex valued gain of each band. This frequency-domain approach obviates the need of parametric representations for both, plant and reference model, and inherits the robustness properties of frequency response designs.