Multi-input Multi-output Plants Research Articles

Approximate local output regulation for nonlinear distributed parameter systems

Output regulation for a class of nonlinear infinite-dimensional systems, called regular nonlinear systems (RNS), is the subject of this work. For the plants in this class, the linearization at the origin is an exponentially stable regular linear system (RLS). The plants are driven by a control input and a disturbance signal. Well-posedness of the plants for small initial states, control inputs and disturbance signals is established and it is shown that if the control input and the disturbance signal for a plant are T-periodic, then so are its state and output (asymptotically). On the basis of this characterization, an approximate local output regulator problem for multi-input multi-output (MIMO) plants in the RNS class is addressed. Given a plant, the regulation objective is to ensure that a finite number of harmonics of a T-periodic reference signal and the plant output are identical whenever the reference signal, the T-periodic disturbance signal for this plant and the initial state are small. An internal model based output feedback control scheme is proposed for an exponentially stable RLS for tracking reference signals, which are a finite sum of functions that are a product of a sinusoid and a polynomial in time. This scheme merely uses the transfer function gains of the RLS at the poles of the Laplace transform of the reference signal and practically requires no other data. Using the proposed control scheme, a linear finite-dimensional controller is designed for a MIMO nonlinear plant in the RNS class using minimal plant information. The resulting closed-loop system is rigorously analyzed to establish that the controller achieves the regulation objective. The efficacy of the control design is illustrated numerically using the model of a cable coupled to a point mass via a nonlinear spring.

Quantitative feedback control for multivariable model matching and disturbance rejection

Summary This article extends two recent contributions in the field of quantitative feedback theory to the multivariable case. They concern the model matching and the measured disturbance rejection problems. The model matching problem is a tracking control problem with specifications given as acceptable deviations from an ideal response. The measured disturbance rejection problem balances feedback and feedforward actions to reject disturbances. Both perspectives present advantages over classical quantitative feedback theory techniques in certain situations. This paper develops the necessary tools to solve both control problems in the case of multi-input multi-output plants. In particular, it shows how to derive nonconservative controller bounds for each of the single-input single-output control problems in which the overall multivariable problem is divided. The result is a systematic controller design methodology for multi-input multi-output plants with structured uncertainty. The application of the technique to the well-known quadruple-tank process illustrates the benefits of the method. Copyright © 2016 John Wiley & Sons, Ltd.

Intelligent computationally efficient modelling of multi-input multi-output non-linear dynamical process plants: An industrial steam generator case study

Most of the process plants have intrinsic non-linear, time-varying, non-minimum phase and coupling characteristics that result in a highly time-consuming and tedious task to derive complicated non-linear dynamic equations governing on such types of processes. On the other hand, even though such equations can be analytically extracted, they have not worked out in most cases yet. To find a simple fix that can address these hurdles associated with analytical modelling, two types of non-analytical models, namely, simulator and predictor, are proposed based on a computationally efficient technique so-called locally linear neuro-fuzzy modelling. That is, a simulator model as well as a specially structured long-term predictor model that is built based on a sequential arrangement of single-stage predictor models is presented for multi-input multi-output non-linear dynamical process plants and feasibly applied to a real water-tube steam generator for the first time. An adaptive evolving algorithm named linear model tree contributes to estimate the parameters of neuro-fuzzy simulator and predictor models. Furthermore, an order selection method based on Lipschitz theory, whose merit is being totally independent from developing any model prior to commencing tedious modelling trials, is also proposed for the first time by defining a modified Lipschitz index to remedy the order determination problem within the very first steps of black-box non-linear system identification. The blend of such a fully modelling-independent order selection algorithm and a unique type of computationally inexpensive non-linear neuro-fuzzy model lessens the overall computational burden of modelling procedure that represents a great concern in a black-box system identification approach. The recorded data from a real water-tube steam generator operating at Abbot Power plant unit of Champaign, IL, were exploited to carry out experimental modelling in order to reveal the pros and cons of the presented models.

Path tracking design based on Davidson–Cole prefilter using a centralized CRONE controller applied to multivariable systems

To perfectly govern MIMO (Multi-Input Multi-Output) processes, a fully populated matrix controller has been developed due to its flexibility. Taking into account the plant uncertainties, the CRONE (Commande Robuste d’Ordre Non Entier) control approach is used with the non-diagonal quantitative feedback theory (QFT) procedure. The MIMO-QFT robust synthesis methodology has been used in order to generate the appropriate equivalent MISO (Multi-Input Single-Output) system structure from the MIMO plant. For each MISO structure, the CRONE control approach based on third-generation CRONE methodology is used to find the diagonal elements of the controller of the plant while considering the plant uncertainties. The non-diagonal part of the controller is determined to reach the aim of minimizing the coupling effects. After that, a fractional prefilter synthesis approach is developed to find the non-integer prefilter expression satisfying the tracking specifications. A SCARA robot manipulator has been used to verify the designed controller performances.

Low order integral-action controller synthesis

A simple controller synthesis method is developed for certain classes of linear, time-invariant, multi-input multi-output plants. The number of poles in each entry of these controllers depends on the number of right-half plane plant zeros, and is independent of the number of poles of the plant to be stabilized. Furthermore, these controllers have integral-action so that they achieve asymptotic tracking of step input references with zero steady-state error. The designed controller’s poles and zeros are all in the stable region with the exception of one pole at the origin for the integral-action design requirement. The freedom available in the design parameters may be used for additional performance objectives, although the only goal here is stabilization and tracking of constant references.

Strong Stabilization of a Class of MIMO Systems

Stabilization of finite dimensional linear, time-invariant, multi-input multi-output plants by stable feedback controllers, known as the strong stabilization problem, is considered for a class of plants with restrictions on the zeros in the right-half complex plane. The plant class under consideration has no restrictions on the poles, or on the zeros in the open left-half complex plane, or on the zeros at the origin or at infinity; but only one finite positive real zero is allowed. A systematic strongly stabilizing controller design procedure is proposed. The freedom available in the design parameters may be used for additional performance objectives although the only goal here is strong stabilization. In the special case of single-input single-output plants within the class considered, the proposed stable controllers have order one less than the order of the plant.

Simultaneous and strong simultaneous stabilisation of some classes of MIMO systems

Sufficient conditions are derived for simultaneous stabilisability of any finite number of linear, time-invariant, multi-input multi-output (MIMO) systems. Four general MIMO plant classes with arbitrary finite number of plants are shown to be simultaneously stabilisable using simple proportional + derivative controllers. For some of these plant classes it is also possible to achieve simultaneous stabilisation and asymptotic tracking of step-input references with zero steady-state error by using integral-action controllers. Three of these general MIMO plant classes are shown to be strongly simultaneously stabilisable.

Operator-based robust nonlinear control system design for MIMO nonlinear plants with unknown coupling effects

In this article, operator-based robust nonlinear control system design for multi-input multi-output (MIMO) plants with unknown coupling effects is considered. That is, by using operator-based robust nonlinear control design, coupling effects existing in the MIMO nonlinear plants can be decoupled based on a feedback design and robust right coprime factorisation approach, the coupling effects caused by controllers and plant outputs can be stabilised by using definition of Lipschitz operator and contraction mapping theorem, and output tracking performance can be realised by a tracking design scheme. Finally, a simulation example about temperature control process of 3-input/3-output aluminum plate is given to support the theoretical analysis.

Reliable decentralised control of delayed MIMO plants

Reliable decentralised proportional–integral–derivative controller synthesis methods are presented for closed-loop stabilisation of linear time-invariant plants with two multi-input, multi-output (MIMO) channels subject to time delays. The finite-dimensional part of plants in the classes considered here are either stable or they have at most two poles in the unstable region. Closed-loop stability is maintained with only one of the two controllers when the other controller is turned off and taken out of service.

On the density of stabilizable plants in the class of unstabilizable plants: The real symmetric disk algebra case

Abstract Let A R denote the set of functions from the disk algebra having real Fourier coefficients. Generalizing a result of Quadrat we show that every unstabilizable multi-input multi-output plant is as close as we want to a stabilizable multi-input multi-output plant in the product topology.

Reliable decentralized PID controller synthesis for two-channel MIMO processes

Reliable stabilization and regulation of two-channel decentralized multi-input multi-output (MIMO) control systems is considered. The system has integral-action due to using proportional + integral + derivative (PID) controllers. Closed-loop stability and asymptotic tracking of step-input references are achieved at each output channel when all controllers are operational. Stability is maintained when one of the controllers fails completely and is set to zero. Controller synthesis procedures are proposed for stable MIMO plants and for several unstable MIMO plant classes that admit PID controllers. These synthesis procedures are applied to various examples of process systems to illustrate the design methodology.

Feedback Linearization Based Nonlinear Control Strategy of VSC-HVDC

The model of Voltage Source Converter (VSC) based HVDC in the synchronous dq reference frame is presented in this paper. The model includes the DC link model and the VSC models. The feedback linearization principle for Multi-input Multi-output plants is analyzed. Based on the analysis, nonlinear decoupling control strategies for the two VSCs are proposed. For one VSC, the proposed nonlinear control strategy enables it to decouple DC voltage and reactive power control, and for the other one, the strategy guarantees the control of active power and that of reactive power independently. Simulation was conducted with MATLAB/Simulink software to verify the proposed control strategies. The simulation results prove that the nonlinear decoupling control strategies are able to provide good performance.

A QFT/EEAS Design of Multivariable Robust Adaptive Controllers

Abstract This paper presents a robust adaptive control design methodology for multi-input multi-output (MIMO) plants based on Quantitative Feedback Theory (QFT) and Externally Excited Adaptive System (EEAS), both of which are the novel ideas of Horowitz. Self Oscillating Adaptive Systems (SOAS) are proposed to mainly overcome the problem of large gain variations, which is important in certain applications. To further improve the SOAS design, the idea of EEAS was developed. Finally, combined QFT and EEAS proposed a robust adaptive controller for SISO uncertain plants. However, due to the complex design nature of the proposed combined methodology and the difficulty of an optimal design, this line of Horowitz's research was not followed further. In this paper, to overcome the above mentioned problems the design procedure is reformulated as a set of cost functions and constraints. Genetic Algorithms are then used to solve the optimal design. Also, QFT/EEAS design is extended to multivariable uncertain plants. Sufficient conditions are derived to assure the achievement of given off-diagonal performance. Then, the given main channel performance could be achieved by using SISO QFT/EEAS method. Simulation studies indicate the effective performance of the proposed QFT/EEAS MIMO design methodology. It is shown that the proposed approach can handle large plant parameter uncertainties with lower loop bandwidths.

Simultaneous stabilization of MIMO systems with integral action controllers

Simultaneous stabilization with asymptotic tracking of step-input references is explored for linear, time-invariant, multi-input multi-output stable plants. Necessary conditions are presented for existence of simultaneous integral-action controllers and existence of simultaneous PID-controllers. A systematic simultaneous PID-controller synthesis method is proposed under a sufficient condition.

An observer based switching control strategy for the stabilization of uncertain multi-input–multi-output plants

The paper proposes a stabilizing dynamic output switching control policy, based on variable structure control, which extends recently published results to a wider class of systems, and further improves the controller performances in terms of transient duration. It is worthy of note that the proposed observer based variable structure controller, exploiting the features of the coupled switching control, is based on less restrictive conditions with respect to those traditionally assumed. The proposed controller has been tested by simulation on IFAC benchmark problem no. #90-09.

PID controller synthesis for a class of unstable MIMO plants with I/O delays

Conditions are presented for closed-loop stabilizability of linear time-invariant (LTI) multi-input, multi-output (MIMO) plants with I/O delays (time delays in the input and/or output channels) using PID ( Proportional + Integral + Derivative ) controllers. We show that systems with at most two unstable poles can be stabilized by PID controllers provided a small gain condition is satisfied. For systems with only one unstable pole, this condition is equivalent to having sufficiently small delay-unstable pole product. Our method of synthesis of such controllers identify some free parameters that can be used to satisfy further design criteria than stability.

On a generalization of the Youla–Kučera parametrization. Part II: the lattice approach to MIMO systems

Within the lattice approach to analysis and synthesis problems recently developed in Quadrat (Signal Syst, to appear), we obtain a general parametrization of all stabilizing controllers for internally stabilizable multi input multi output (MIMO) plants which do not necessarily admit doubly coprime factorizations. This parametrization is a linear fractional transformation of free parameters and the set of arbitrary parameters is characterized. This parametrization generalizes for MIMO plants the parametrization obtained in Quadrat (Syst Control Lett 50:135–148, 2003) for single input single output plants. It is named general Q-parametrization of all stabilizing controllers as we show that some ideas developed in this paper can be traced back to the pioneering work of Zames and Francis (IEEE Trans Automat control 28:585-601, 1983) on H ∞-control. Finally, if the plant admits a doubly coprime factorization, we then prove that the general Q-parametrization becomes the well-known Youla-Kucera parametrization of all stabilizing controllers (Desoer et al. IEEE Trans Automat control 25:399–412, 1980; Vidyasagar, Control system synthesis: a factorization approach MIT Press, Cambridge 1985).

Adaptive control for a class of large scale non-linear systems

The design of stabilizing controllers for multi-input multi-output (MIMO) non-linear plants with unknown non-linearities is a challenging problem. The inability to identify the non-linearities on-line or off-line accurately motivates the design of stabilizing controllers based on approximations or on approximate estimates of the plant non-linearities. However, the design of a centralized controller for large scale non-linear systems is often complex due to the high dimensionality and difficulty to implement in real time. In this paper a decentralized-like non-linear adaptive control algorithm is designed and analysed for a class of large scale non-linear systems with unknown non-linearities. The controller guarantees closed loop semi-global stability and convergence of the tracking error to a small residual set whose size can be specified a priori provided the neglected in the control design non-linear interconnections are small relative to the modelled non-linear parts. A procedure for choosing the various design parameters to guarantee that the tracking error bound will converge to within the specified a priori bound is presented. Even though the proposed controller is not purely decentralized it does reduce computations and makes the control design easier than a corresponding centralized approach.

Output feedback model reference adaptive control for multi-input–multi-output plants with state delay

Two new output feedback adaptive control schemes based on Model Reference Adaptive Control (MRAC) and adaptive laws for updating the controller parameters are developed for a class of linear multi-input–multi-output (MIMO) systems with state delay. An effective controller structure established on a new error equation parametrization is proposed to achieve tracking with the error tending to zero asymptotically. To achieve exact asymptotical tracking, we introduce, in the standard MRAC structure for plants without delay, a new additional adaptive feedforward control component as an output of a dynamical system driven by the reference signal. Adaptive laws are developed using the SPR-Lyapunov design approach and two assumptions regarding the prior knowledge of the high-frequency matrix K p . This work is the first asymptotic exact zero tracking results for this class of systems in the framework of the certainty equivalence approach.

Robust adaptive control of uncertain MIMO non-linear systems — feedforward Takagi–Sugeno fuzzy approximation based approach

This paper proposes a robust adaptive controller using a feedforward Takagi-Sugeno (T-S) fuzzy approximator for a class of multi-input multi-output (MIMO) non-linear plants that is highly unknown. Different to typical fuzzy approximation approaches, the desired commands are taken as input variables of a T-S fuzzy system. Meanwhile, the unknown feedforward terms required during steady state are adaptively approximated and compensated. This allows a simpler architecture during implementation and drops the typical boundedness assumption on fuzzy universal approximation errors. Furthermore, according to H/sup /spl infin// control techniques, non-linear damping design, and sliding mode control, the controllers are synthesised to assure either only the disturbance attenuation, the attenuation of both disturbances and estimated fuzzy parameter errors, or globally asymptotic stable tracking. A linear matrix inequality (LMI) technique then provides a straightforward gain design. Finally, numerical simulations are carried out on a two-link robot to illustrate the expected performance.