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In the study, a model inversion based two degree-of-freedom (DOF) controller is proposed to achieve optimal robust performance for multi-input-multi-output (MIMO) system with existence of both model and signal uncertainties. The original plant dynamics are modified by a pre-compensator and a post-compensator to obtain a diagonally dominant matrix, where the selected dynamics of the plant are contained within the diagonal entries. The inversion of the diagonal matrix, as a result, reflects the inversion of the plant dynamics within a specified frequency range. The feedback controller is designed using a standard H2 mixed sensitivity approach. The feedforward controller consists of plant inversion and a feedforward filter, which is optimized to balance the trade-off between nominal performance and robust performance under model uncertainty and signal uncertainty. A numerical example is used to demonstrate the improvement of the robust performance when using the optimal feedforward control.

This paper presents a scheme for designing a robust decentralized PI controller for an industrial utility boiler system. First, a new method for designing robust decentralized PI controllers for uncertain LTI MIMO systems is presented. Sufficient conditions for closed-loop stability and diagonal dominance of a multivariable system are given. For each isolated subsystem a first order approximation is obtained. Then, achieving robust stability and closedloop diagonal dominance is formulated as local robust performance problems. It is shown by selecting time constants of the closed-loop isolated subsystems appropriately, these local robust performance problems are solved and the interactions between closed-loop stabilized subsystems are attenuated. The internal model control (IMC) method is used to design local PI controllers. The suggested design strategy is applicable to unstable systems as well. Thereafter, the nonlinear model of an industrial utility boiler is linearized about its operating points and the nonlinearity is modeled as uncertainty for a nominal LTI MIMO system. Using the new proposed method, a decentralized PI controller for the uncertain LTI nominal model is designed. The designed controller is applied to the real system. The simulation results show the effectiveness of the proposed methodology.

In this paper a simple approach is proposed for decentralized control of linear large-scale systems. Sufficient conditions for diagonal dominance of closed-loop large-scale systems are derived. Based on these conditions, the interactions between the subsystems can be considered as external disturbances for each isolated subsystem. Then a previously proposed approach is used to attenuate disturbances via dynamic output compensators based on complete parametric eigenstructure assignment. Through attenuation of the disturbances, the closed-loop poles of the overall system are assigned to the desirable region, by assigning the eigenstructure of each isolated subsystem appropriately. An example is given to show the effectiveness of the proposed method.

The paper considers the problem of stabilizing large scale dynamic systems (LSS) via decentralized controllers based on Variable Structure Systems (VSS) and using the principle of dominant subsystems. The principle and applications for LSS are described and simulation test results on a two- machines power system with nonlinear model are presented.

In an open loop scheme, given a nonsingular, nominal plant and a decoupling, precompensator of It, we find bounds on the size of the uncertaintiIes of the nominal plant for which the condition of diagonal dominance of the overall perturbed system is achived. The main result gives this bounds in terms of the dimensions of the plant.

This paper describes on-line re-estimation formulae for arbitrary hidden Markov models, extending previous work that proposed a recursive formula for re-estimation of a diagonally dominant state transition probability matrix. Simulation experiments show that for some applications the formula described here should be used instead in order to ensure algorithm convergence. Also proposed is a re-estimation formula for online update of non-parametric observation probabilities. Simulation experiments show that these estimates are in general asymptotically biased.

In the INA design technique the key of designing control system is to achieve diagonal dominance by input - output compensators. This paper gives sufficient conditions and necessary conditions for achieving diagonal dominance by a real constant compensator. It is easy to check these conditions with the aid of a computer, and the real constant compensator K can be found at same time. The paper gives two examples which show the practical application of these conditions. If plant has to achieve diagonal dominance by a non - constant compensator K(s), this paper gives analytical expression of K(s). The expression is based on the idea of realizing disturbance decoupling of the system by feedforward philosophy. Our results have improved and developed Rosenbrock’s (1974.) work.

This paper deals with the construction of Lyapunov functions for the finite dimensional linear system ẋ = Ax when the entries of the generating matrix A satisfy various conditions requiring dominance of its diagonal elements and nonnegativity of its off-diagonal elements. The particular case in which the system defines a Markov chain is given special attention and it is shown that the results then imply certain inequalities which have an intuitively appealing information theoretic significance.

The design method proposed here is a frequency-domain method and uses acertain class of generalized Gershgor in bands mapped on the gain-phase plane, which are referred to as GG-pseudo-bands. Its main advantages are that the GG-pseudo-bands have a same width for all loops which is in variant under the changes of the diagonal compensator and the unit systems, that no diagonal dominance is required at high frequencies, and that a quantitative guide line for pseudo diagonalization is given based on the interaction index which is a satisfactory scalor measure of the cross intreaction

Through a couple of naive examples the control theorists are invited to reexamine the role of modeling in the study of large scale dynamic systems. Instead of assuming the existence of “N diagonally dominant blocks, ”they should identify one strongly coupled slow core and N weakly coupled fast subsystems.This structure is exhibited with a physically meaningful choice of state variables. The controls are introduced following the recent concept of multimodeling.

Nonlinear feedback systems with many loops are not well understood, in spite of the fact that deceptively simple changes to single-loop theorems can result in predictions valid for multiple-loop systems. A case in point is stability: the circle criterion used in single-loop systems is based on a “small-gain” theorem which is very general; indeed, the feedback signal may be infinite-dimensional, so there is no problem with the finite-dimensional vectors of multiple-loop feedback systems. The difficulty is that the small gain theorem involves checking a norm inequality. The circle criterion amounts to an ingenious way of checking the inequality for a single-loop system, but for multiple-loop systems there has been no construction of comparable power except in special cases. This paper presents two graphical tests for the norm inequality. The first is somewhat less elegant than the circle criterion but does not require the linear part to have special properties such as normality. Like all criteria based on a small gain theorem, this one is only sufficient for stability but it is shown that the predictions are less conservative than those of other available criteria such as those based on diagonal dominance. The second test is a direct analogue of the circle criterion. It measures the departure from normality of the linear part of the system and when the linear part is normal it is equivalent to (and simpler than) the first test. As the linear part departs from normality the second test becomes more conservative but is still attractive because it is easy to use. It is argued that in any case, near-normality is a requirement for good design. A useful bonus is that it is now possible to explain the failure of some previous attempts to generalise the circle criterion.

A new approach to the design of multivariable control systems using the inverse Nyquist array method is proposed. The technique utilizes a conjugate direction function minimization algorithm to achieve dominance over a specified frequency range by minimizing the ratio of the moduli of the off-diagonal terms to the moduli of the diagonal term of the inverse open loop transfer function matrix. The technique is easily implemented in either a batch or interactive computer mode and will yield diagonalization when previously suggested methods fail. The proposed method has been successfully applied to design a control system for a sixteenth order state model of the F-100 turbofan engine with three inputs.

This paper describes a new method to evaluate diagonal dominance in a transfer matrix for a unilateral decoupled system. Three basic decoupling methods are discussed. The control systems designed with these methods have been used in three units with once-through boilers and have good control qualities. Finally the ways to improve the availability of control systems are discussed.

Decentralised stabilisability problem of 2-D linear time discrete large scale systems (LSS) is considered. Sufficient conditions for existence and an algorithm for finding of local static state feedbacks stabilising robustly the 2-D LSS are given. These conditions are based on new notions of robust separability and generalized block diagonally dominant 2-D LSS.

The Jacobi Eigenvalue criterion is a recently developed, steady state, scaling independent tool for the selection of variable pairing for multiloop control systems (Mijares et al., 1986). This criterion is based on the Jacobi Iteration method for solving sets of linear equations or obtaining the inverse of a matrix. A dynamic extension of the Jacobi Eigenvalue criterion which consists in evaluating the spectral radius of the Jacobi Iteration matrix in the frequency range of interest is presented. The Jacobi Eigenvalue criterion is inherently a diagonal dominance measure, and as such, is readily applied to develop an extension of Rosenbrock's Nyquist stability theorem. The extended Jacobi Eigenvalue criterion is then compared to different interaction and weak coupling measures used for design of decentralized control structures which are based on conditions for generalized diagonal dominance and H-matrices. Two examples are used to illustrate the use of the Jacobi Eigenvalue criterion and its relationship with the other weak coupling measures.

It is shown that the stability of a class of linear multivariable control systems with delays can be determined by checking the stabilities of single-loop systems if the systems possess a diagonal dominance property. It is further shown that the stability result leads to a method of synthesizing decentralized stabilizing servo controllers for a class of large scale systems with time-delays.