Plant Transfer Function Matrix Research Articles

Robust control of water quality in intensive aquaculture using multi‐variable quantitative feedback theory: From an Indian context

AbstractThis paper addresses the problem of controlling turbidity, dissolved oxygen, ammonium‐ion concentration, and water‐temperature to maintain the desired water quality in an intensive aquaculture plant. The research is carried out to fit into the present scenario of intensive aquaculture in India. The plant model along with uncertain parameters are derived using physical laws and the data acquired from an aquaculture pond in Assam, India. A pre‐compensated multi‐variable quantitative feedback theory (QFT)‐based fully populated robust matrix controller is proposed to mitigate the control challenge. A novel method is used to design the pre‐compensator to enhance the diagonal dominance of plant transfer function matrix. The desired robust stability, reference tracking, and sensitivity specifications are fulfilled by the proposed QFT‐based robust controller despite the parametric uncertainty. The effectiveness of the proposed method is validated through numerical simulation. A comparative study against a controller shows that the proposed controller strategy gives a satisfactory performance compared to it.

Control of activated sludge treatment process using pre-compensated multi-variable quantitative feedback theory-based controller

This paper deals with the design of a pre-compensated multi-variable quantitative feedback theory (QFT)-based fully populated matrix controller for an activated sludge treatment process (ASTP) of a waste water treatment plant (WWTP). The regulation of the concentration of biochemical oxygen demand ([Formula: see text]) and ammonium-ion ([Formula: see text]) is the control objective. The plant dynamics are obtained using physical laws available in the literature. The parametric uncertainty is quantified from the measurement data obtained from a real ASTP of an oil refinery. The model is duly cross-validated. A novel technique is proposed to design a pre-compensator that will enhance the diagonal dominance of the plant transfer function matrix. A diagonal controller and a pre-filter, are then designed using a sequential multi-input multi-output (MIMO) QFT-based methodology to meet a set of performance specifications such as relative stability, disturbance rejection, robust tracking and so forth. The simulation results validate the effectiveness of the proposed control scheme. A comparative analysis with reported works shows that the proposed control scheme outperforms some of the reported control strategies.

Design of suboptimal model-matching controllers using squared magnitude function for MIMO linear systems

This paper proposes a novel two-stage method for the design of a suboptimal model-matching controller in an output feedback closed-loop system (OFCLS) using the concept of squared magnitude function (SMF). A streamlined procedure for selection of a reference model, based on a linear quadratic regulator (LQR) with integral action (LQRI) having optimum values for the elements of the weighting matrices and the degree of interaction is proposed. The degrees of the numerator and denominator polynomials of the elements of the OFCLS transfer function matrix (TFM) are obtained from those of the plant and the chosen controller structure. In the first stage of the controller design, taking the LQRI-based closed-loop system (LCLS) as a reference model, the OFCLS is obtained using the approximate model-matching (AMM) technique based on the SMF concept. The approximation method involves a higher-order approximation for stable multiple-input-multiple-output (MIMO) lower-order systems. In the second stage, controller parameters are obtained using the exact model-matching (EMM) method with information about the OFCLS and plant TFMs. The proposed controller design method outperforms the method presented in the literature on integral squared error index. The simulation and experimental results illustrate the effectiveness of the proposed method.

Anti-windup compensator design using Riccati inequality based approach

This paper presents a full-order dynamic anti-windup compensation design scheme for stable LTI systems using a Riccati inequality based approach. The scheme utilizes the Weston-Postlethwaite’s generalized anti-windup configuration and applies right coprime factorization of the plant transfer function matrix to obtain a linear conditioning scheme. The proposed anti-windup scheme ensures the internal stability of the closed-loop control system in presence of actuator saturation and also reduces the performance degradation caused by the saturation phenomena. The Riccati inequality based approach offers a simple and straightforward anti-windup compensator design method which is independent of the design of nominal controller. The effectiveness of the proposed technique is demonstrated through a MIMO example.

Inversion-free decentralised quantitative feedback design of large-scale systems

In this paper, a new method for robust decentralised control of multi-input multi-output (MIMO) systems using quantitative feedback theory (QFT) is suggested. The proposed method does not need inversion of the plant transfer function matrix in the design process. For a given system, an equivalent descriptor system representation is defined. By using this representation, sufficient conditions for closed-loop diagonal dominance over the uncertainty space are obtained. These conditions transform the original MIMO system into a set of isolated multi-input single-output (MISO) subsystems. Then, the local controllers are designed by using the typical MISO QFT technique for each isolated subsystem to satisfy the predefined desired specifications and the closed-loop diagonal dominance sufficient conditions. The proposed technique is less conservative in comparison to the approaches using the over-bounding concept in the design procedure. The effectiveness of the proposed technique is finally assessed on a MIMO Scara robot.

Model reference robust control for MIMO systems

Model reference robust control (M RRC) of single-input single-output (SISO) systems was introduced as a new means of designing I/O robust control (Qu et al. 1994). This I/O design is an extension of the recursive backstepping design in the sense that a nonlinear dynamic control (not static) is generated recursively. Backstepping entails the design of fictitious controls starting with the output state-space equation and backstepping until one arrives at the input state-space equation where the actual control can be designed. At each step the system is transformed and a fictitious control is designed to stabilize the transformed state (Naik and Kumar 1992). It is shown in this paper that M RRC of multiple input multiple output (MIMO) systems is an extension of model reference control (M RC) of MIMO systems and M RRC of SISO systems. Unwanted coupling exists in many physical MIMO systems. It is shown that M RRC decouples MIMO systems using only input and output measurements rather than state feedback. This is a very desirable property, because in many instances state information is not available. A diagonal transfer function matrix is strictly positive real (SPR) if and only if each element on the diagonal is SPR. The fact that complicates the development of robust control laws is that the recursive backstepping procedure used in non-SPR SISO systems cannot be directly applied to diagonal MIMO non-SPR systems without the introduction of the augmented matrix or a pre-compensator. MRC of systems where one has perfect plant knowledge is reviewed. Assumptions are listed for the application of model reference robust control for MIMO systems. Model selection is presented as the right Hermite normal form of the plant transfer function matrix. M RRC is derived for MIMO systems that have a right Hermite normal form which is SPR and diagonal, and then for systems whose right Hermite normal form is diagonal but not SPR. Robust control laws are generated for achieving stability using Lyapunov's second method. Future research will focus on MIMO systems which are not diagonal.

Specification framework for robust control of a run-of-mine ore milling circuit

It is difficult in run-of-mine (ROM) milling circuits to control the particle size of the product and other important variables because the ore fed to the mill also acts as the main grinding medium. This results in significant uncontrolled disturbances and uncertainties. Before the μ-controller synthesis and analysis methodology can be applied to this multivariable control problem it is necessary to formalize the uncertainties and specifications in terms of a suitable general framework. The uncertainty description for an industrial milling circuit obtained from plant perturbation tests is used to motivate the choice and location of uncertainty weights within the plant transfer function matrix structure. The choice of performance weights based on their economic and plant-related importance is also discussed. The ROM milling circuit model with its uncertainty and performance weights is then cast into a general synthesis and analysis framework.

A near-decoupling design of multivariable feedback systems with the V-canonical compensator

In this paper a practical procedure is proposed for the decoupling design of multivariable feedback systems. The so-called V-canonical compensator is used to remove the need for inversion of the plant transfer function matrix. The cross-coupling in the plant is first expressed in terms of the equivalent disturbance. Then a strictly-decoupling formula is established to reduce this equivalent disturbance. Ultimately, nearly-decoupling control is concerned with the design of a realizable compensator.

Feedback Design of a Canonical Multivariable System With Application to Shape Control in Sendzimir Mills

The shape control problem, for a Sendzimir Cold Rolling Mill, is multivariable. The plant transfer function matrix, however, has the special form: G(s) = g(s)Gm, where g(s) is a scalar transfer function and Gm a square matrix of constant gains. The control philosophy presented exploits this structure by diagonalising the system using an eigenvector/eigenvalue decomposition resulting in a scalar frequency response design problem. An important consideration in shape control systems is the robustness of the design due to the wide range of materials rolled, reflected in changes in the elements of Gm. Therefore, a development is included which represents the robustness of the design, with respect to errors in Gm, in terms of a set of strict inequalities.

Robustness of multivariable smith predictors

Stability and stability robustness of multivariable Smith predictors are analysed by viewing Smith predictors as instances of internal model control. This allows a much simpler development than appears in previous analyses, and the way that delays enter the plant transfer function matrix is unrestricted. it is shown that robustness to additive plant perturbations can be predicted during design, on the basis of a model of the rational part of the plant alone. A design example based on the Shell control problem is included.

Robust Controller Design for a Run-of-Mine Milling Circuit

A new approach to the problem of designing a control system for an industrial run-of-mine (ROM) mining circuit is described. This problem is formalized in terms of a general linear system synthesis and analysis framework to which the µ-Methodology is applied. Correlations of plant parameter uncertainties and the choice of the location of uncertainty weights within the plant transfer function matrix structure, are discussed. The choice of performance weights is discussed with regard to the economic and process-related importance of plant outputs. A µ-controller is obtained which provides robust performance in the face of significant model uncertainties.

On-line frequency-and time-domain identification of a linear multivariable system

Abstract A method for the on-line identification of a linear multivariable plant subject to both deterministic and stochastic disturbances is proposed. The identification scheme rests on the use of a sum of sinusoids of distinct frequencies as probing-signal inputs and on the employment of linear time-varying filters to filter the plant inputs and the plant outputs. The time-varying filters are essentially banks of narrow-band filters tuned to the probing-signal frequencies. The filtered plant inputs and the filtered plant outputs yield an estimate of the plant transfer function matrix at the probing-signal frequencies. The filtered data are further processed using a recursive least-squares algorithm and a time-domain model estimate is obtained in terms of the coefficients of the difference equation relating each input-output pair. The identification algorithm is decoupled in the sense that the estimate of the transfer function or difference equation between the ith input and jth output is unaffected by other inputs or outputs. Simulation results on the performance of the time-varying filter and the identification scheme are given.

Perfect and subperfect regulation in linear multivariable control systems

This paper is concerned with the synthesis of a high-gain feedback control, called perfect regulation (p.r.), for linear multivariable systems with external signals. The existence condition for p.r. is derived, in which the minimum phase property plays an essential role. The use of an observer is discussed for achieving p.r. under restricted state observation. Some asymptotically ideal feedback properties are demonstrated, such as the complete desensitization, the complete servo performance with decoupling and the complete disturbance rejection, which formulate the loop-tightness for multivariable systems. A design method for applying p.r. to non-minimum phase systems, called subperfect regulation (s.p.r.), is proposed based on the factorization of the plant transfer function matrix into the minimum phase part and the totally non-minimum phase part. It is a multivariable extension of a well-known design technique for scalar systems to overcome the difficulty of phase non-minimality. Computational procedures for p.r. and s.p.r. are discussed. An illustrative example is shown.

A Modified Direct-Decoupling Method for Multivariable Control System Designs

A design method, which decouples an interactive system by using a compensator obtained from the plant inverse matrix, which is often called the direct-decoupling method is modified in this paper. The modified direct-decoupling method uses the adjoint matrix instead of the inverse of the plant matrix to construct the compensator. The method uses a frequency-domain model-reduction method to simplify the degree of the given plant transfer function matrix and the obtained compensator. For an open-loop stable multivariable system, the proposed method gives a simple, practical, and realizable controller without using an unstable pole-zero cancellation approach.

Triangularization technique for the design of multivariable control systems

This paper presents a novel technique for the design of multivariable control systems. A stable and proper precompensator is to be determined for a multivariable plant such that the compensated plant transfer function matrix is tringular and diagonally dominnnt in a non-standard way. As a consequence of the triangular-diagonal-dominance property, only the diagonal elements need to be considered in an overall closed-loop design. In effect, the technique provides a systematic procedure to reduce a multivariable design problem to independent scalar design problems.

An approach to multivariable system identification

Two prototype identifiable structures are presented which make possible the identification via an equation-error model reference adaptive system of linear plants with rational transfer function matrices. The structures include as specialisations many of the particular structures presented hitherto in the literature. Convergence properties are also discussed, and several modes of convergence are distinguished: model output to plant output, model transfer function matrix to plant transfer function matrix, and model parameters to plant parameters. Conditions are presented for exponentially fast convergence in the absence of noise.

Dyadic expansion for the analysis of linear multivariable systems

In a practical situation, the control engineer may have experience with his system and have some insight into its dynamic behaviour. This paper suggests a theoretical method for making use of this background knowledge in the feedback-control design process by manipulating the frequency-response information available in the plant transfer-function matrix H(s) into a form suitable for physical interpretation. The approach used is that of dyadic expansion of H(s). The technique represents an extension of the dyadic-approximation method used in the analysis of nuclear-reactor spatial control systems to include a description of interactions in a general case in terms of the matrix H(s)H−1(s). However, the representation given in this paper is exact. As the aim is to enable frequency-response data to be interpreted physically, the method described does not generate a complete design technique. An example indicates, however, that, if used with physical intuition, the procedure can provide guidelines to practical controller structures for highly interacting systems.

Dyadic approximation method for multivariable control-systems analysis with a nuclear-reactor application

A method is developed for the approximation of an N×N plant transfer-function matrix by a transfer-function matrix consisting of the linear sum of N frequency-independent dyads with scalar transfer-function coefficients. The use of the approximation method in the design of failsafe feedback-control systems for the plant is described, and an application is suggested in the stabilisation of the radial spatial modes of a thermal nuclear power reactor.

Multivariable Adaptive Control System

A multivariable control system in which the parameters of the plant transfer function matrix are unknown functions of time is described in this paper. It is a sequel to a previous one1 dealing with a single variable control system. A scheme is presented here in which the parameters of the plant transfer function are tracked and the controller transfer function matrix is adjusted in such a way as to keep the overall system optimized. The system may be realized in terms of ordinary analog computer elements. Information is given in a form which may be readily inserted into a controller for realization of a general type of adaptive control system.