A parametric frequency domain approach to decoupling with coupled rows

This contribution considers the incomplete decoupling of non-minimum phase and non-decouplable systems by static state feedback, where a stable diagonal decoupling is not possible. By introducing a coupled row in the reference transfer matrix, so that one output is affected by several reference inputs, an incompletely decoupled but internally stable closed loop system is obtained. This decoupling problem is solved using a parametric approach to the design of state feedback controllers in the frequency domain. Explicit expressions are derived for the design parameters of the state feedback controller achieving the decoupled reference transfer matrix. A simple example demonstrates the proposed design procedure.     

A precompensator of minimal order for decoupling a linear multi-variable system†

A theorem is proved which gives the minimal order of a precompensator which together with state feedback decouples a given linear time-invariant multi-variable system provided the system is invertible. In addition a design procedure is described by which the parameters of the precompensator are determined by solving a set of linear equations.     

Dynamic decoupling for right-invertible nonlinear systems

It is shown that every system with more inputs than outputs that is right invertible, in the sense of [5], can be decoupled via a dynamic state feedback that can be computed using a given algorithm.This result generalizes the one of [2] and completes the results of [3].     

Structured systems within the transfer matrix approach: application to decoupling

We consider a new approach to structured systems within the transfer matrix framework. We associate with such a structured system a graph which concentrates both knowledge on structural properties of independent subsystems and on their interconnections. The analysis of this associated graph allows to conclude on the decouplability of structured systems.     

Some issues of structure and control for linear time-invariant systems

The objective of this paper is to emphasise the role played by particular structures in the solution of some control problems. The so-called “structural approach” relies on various indicators of dynamical systems such as, for instance, finite and infinite zeros, kernel indices, …. The fundamental invariance properties of these structures under the action of some transformations groups (e.g. feedback) are at the origin of their key role. Structural solutions to “classical” control problems, such as disturbance rejection, model matching and non-interaction are now rather well known: zeros at infinity play a role in the existence of “proper” solutions, while finite (invariant) zeros allow for the characterisation of “fixed poles”, whose location in the complex plane gives answer to pole placement limitations (including stability). Among the recent contributions to this structural approach, a particular attention is here devoted to:

- “Partial” versions of some of these control problems: The control objective only concerns a finite number of (and not necessarily all) the first Markov parameters of the transfer function matrix of the controlled system (e.g. to be zero for disturbance rejection or model matching, to be diagonal for non-interaction). Some interesting new issues in the dual context of failure detection are also sketched.

- Generalised solutions: Based on proportional and derivative feedback laws, with new issues in the context of systems with variable internal structures, and also for systems with delays.

Geometric concepts, such as invariant and almost invariant subspaces, and algebraic counterparts, such as factorisations on some special rings, are intermediary tools which support the characterisations of those particular structures and which allow for a structural treatment of the considered control and/or observation problems.

The results are here presented without proof: references are given to previous published results (in most cases in books and journals which are easily available), and some simple examples are used to illustrate non-standard notions (among which systems with variable internal structure, and time domain left invertibility).

Most of the results here presented rely on long and intensive collaborations between the author and various colleagues.     

On parametrizations for the minimal partial realization problem

The paper considers parametrizations for minimal partial realizations of a finite sequence of Markov parameters. First it is shown that all minimal partial realizations have the same set of input and output Kronecker indices. A parametrization is obtained formulated in terms of a minimal set of extension entries. Then an I/O canonical form is used as a parametrization for the set of minimal partial realizations. It is shown that this allows to define the invariants of the problem. Moreover, the I/O canonical form is shown to contain a set of parameters that can be chosen such that any minimal partial realization can be represented.     

Inverted decoupling internal model control for square stable multivariable time delay systems

This paper presents a new tuning methodology of the main controller of an internal model control structure for n × n stable multivariable processes with multiple time delays based on the centralized inverted decoupling structure. Independently of the system size, very simple general expressions for the controller elements are obtained. The realizability conditions are provided and the specification of the closed-loop requirements is explained. A diagonal filter is added to the proposed control structure in order to improve the disturbance rejection without modifying the nominal set-point response. The effectiveness of the method is illustrated through different simulation examples in comparison with other works.     

The disturbance decoupling problem with stability for switching dynamical systems

The disturbance decoupling problem with stability is dealt with by means of the geometric approach for switching systems. The existence of feedbacks which decouple the disturbance and, at the same time, assure stability is difficult to characterize, since the action of the feedback couples with that of the switching law. Under suitable conditions, it is shown that the above requirement can be dealt with in separate ways and this allows us to state a checkable necessary condition and, on that basis, also a sufficient condition for solvability of the problem.     

Almost disturbance decoupling and pole placement

We revisit here the Almost Disturbance Decoupling Problem (ADDP) (Willems, 1981) by state feedback with the objective to solve ADDP and simultaneously place the maximal number of poles in the closed-loop solution. Indeed, when ADDP is solvable, we show that, whatever be the choice of a particular feedback solution, the obtained closed-loop system always has a set of fixed poles. We characterize these Fixed Poles of ADDP. The other (non-fixed) poles can be placed freely, and we characterize the “optimal” solutions (in terms of ad hoc subspaces and feedbacks) which allow us to solve ADDP with maximal pole placement. From our contribution, which treats the most general case for studying ADDP with maximal, usually partial, pole placement, directly follow the solutions of ADDP with complete pole placement (when there are no ADDP Fixed Poles) and ADDP with internal stability (when all the Fixed Poles of ADDP are stable), without requiring the use of stabilizability subspaces, as in Willems (1981). We extend the concept of Self-Bounded Controlled-Invariant Subspaces (Basile & Marro, 1992) to almost ones. An example is proposed that illustrates our contributions.     

The disturbance decoupling problem in decentralized linear multi-variable systems by local dynamic feedback

Following the works of Hu and Zheng [7] on the problem of disturbance decoupling in decentralized systems with non-dynamic feedback (DDPP), this paper studies the problem of disturbance decoupling in decentralized linear multi-variable systems with one or two local dynamic feedbacks (abbreviated as DDDPDC1 or DDDPDC2 respectively). A counter-example is given to indicate that the main results of Cury [1] are incorrect. Developing the concepts such as structure subspace pair and structure subspace vector, the necessary and sufficient conditions of DDDPDC1 and DDDPDC2 using low order compensators is derived.     

实现系统解耦的预补偿阵设计新方法

本文提出一种实现多变量系统解耦的预补偿器常数阵的设计方法,即从传递函数阵G(s)导出一个复常阵C,通过C求得预补偿阵Kp.文中还论述了这种方法的原理,同时给出了应用实例,结果令人满意.     

Multiple models and neural networks based decoupling control of ball mill coal-pulverizing systems

Using a ball mill coal-pulverizing system as a motivating/application example, a class of complex industrial processes is investigated in this paper, which has strong couplings among loops, high nonlinearities and time-varying dynamics under different operation conditions. Focusing on such processes, an intelligent decoupling control method is developed, where the effects of nonlinearities are dealt with by neural network compensations and coupling effects are handled by specifically designed decoupling compensators, while the effect of time-varying dynamics is treated by a switching mechanism among multiple models. The stability and convergence of the closed-loop system are analyzed. The proposed method has been applied to the ball mill coal-pulverizing systems of 200 MW units in a heat power plant in China. Application results show that the system outputs are maintained in desired scopes, the electric energy consumption per unit coal has been reduced by 10.3%, and the production rate has been increased by 8%.     

板带钢平整机张力-速度解耦控制

分析平整机产品质量存在的问题。从张力一速度系统的耦合动力学模型入手，提出基于极点配置的解耦控制策略，详细介绍解耦控制器设计的原理及实现方法。理论分析、计算机仿真和工业实验都表明，该控制方法能实现对平整机前张力、后张力和工作辊速度的解耦控制，降低了它们之间的相互耦合程度，改善了系统的控制效果，有利于提高带材产品的质量。     

An extended approach of inverted decoupling

This paper presents an extension of the inverted decoupling approach that allows for more flexibility in choosing the transfer functions of the decoupled apparent process. In addition, the expressions of the inverted decoupling are presented for general n × n processes, highlighting that the complexity of the decoupler elements is independent of the system size. The realizability conditions are stated in order to select a proper configuration, and the different possible cases for each configuration are shown. Comparisons with other works demonstrate the effectiveness of this methodology, through the use of several simulation examples and an experimental lab process.     

The solution of diagonal decoupling problem by dynamic outputfeedback and constant precompensator: the general case

In this paper, the solution to diagonal decoupling problem via dynamic output feedback and constant precompensator is presented in the general case. The literature contains a number of particular solutions for this problem. These solutions are valid, for instance, for square transfer matrices or they employ restricted dynamic output feedback schemes. Here, we start with a nonsquare transfer matrix and consider a dynamic output feedback scheme where there is a proper compensator in the feedback loop accompanied by a constant gain (precompensator) in the feedforward path. In this respect, the problem being considered is the dynamic output feedback version of the well-known Morgan's problem. The approach taken involves the characterization of open-loop diagonalizers which admit a dynamic output feedback realization. The key concepts involved in the solution are the generalized version of diagonal causality degree dominance and the set of attainable infinite zero orders. An example is also included to illustrate the main result     

混合励磁电机系统输入输出解耦和线性化

讨论混合励磁电机系统的输入输出解耦和线性化问题.根据机电动力学原理,导出了混合励磁电机系统在与转子同步旋转的d-q坐标系中的动态方程.应用非线性系统几何理论,通过非线性状态反馈和坐标变换,实现了混合励磁电机系统的输入输出解耦控制和完全线性化.将原系统分解为3个线性子系统：d轴磁链子系统、q轴磁链子系统和转速子系统.仿真结果表明,基于输入输出线性化控制设计的混合励磁电机控制系统具有良好的动态性能.     

Transfer matrix approach to the triangular block decoupling problem

The triangular block decoupling problem for linear multivariable systems is studied via the transfer matrix approach. This approach clearly separates the problem of admissible control laws from the one of desired decoupled system specifications. Necessary and sufficient triangular decoupling conditions are given for various control laws. These conditions are expressed in a very simple way in terms of linear dependance among the transfer matrix rows. It turns out that when the problem is solvable, this can be done by static state feedback on a minimal realization of the system. Furthermore it is shown that whenever triangular block decoupling is possible, it is also attainable with stability.     

Disturbance decoupling in fault detection of linear periodic systems

This paper studies fault detection problems of linear discrete-time periodic systems. The aim is to design residual generators, which deliver a residual signal fully decoupled from unknown disturbances. First, a periodic parity relation based full decoupling residual generator with a periodically varying parity vector is established. Then, the relation between periodic parity vectors and periodic observer-based residual generators is investigated. It is shown that a periodic observer-based full decoupling residual generator can be obtained from a periodic full decoupling parity vector. Finally, the condition of disturbance decoupling is discussed and an example is given to illustrate the proposed approaches.