Multivariable Continuous-time Systems Research Articles

A New Optimal Tracking Controller of Linear Strongly Coupled Systems and Its Applications

In this brief, for a class of continuous-time multivariable linear systems with strong coupling property, a new optimal tracking controller is proposed, which can simultaneously decouple the closed-loop system in its dynamic, and provide optimal performance. Firstly, a new quadratic performance index considering decoupling design is introduced, and then the optimal tracking controller is derived by minimizing the new index according to the minimum principle. Finally, the weighting matrices are provided, by using which decoupling and tracking can both be realized. Experiments on a Coupled-Tank are conducted, whose results show the superiority of the proposed method comparing with the conventional linear quadratic tracking (LQT) controller.

Robust Functional Interval Observer for Multivariable Linear Systems

The study of a continuous-time multivariable linear system may not need the knowledge of the entire internal state vector, but only of a linear function of it. In this case, instead of designing a complete observer, only a functional (also called reduced order) observer is used. In this field of research, this paper focuses on robust functional cooperative interval observers. Such an observer is proposed and its properties (in particular, its convergence) are established. Then, a design procedure is given for practical use. Finally, the theoretical contributions are illustrated in examples.

Output feedback adaptive stabilization and command following for minimum phase dynamical systems with unmatched uncertainties and disturbances

In this article, we develop an output feedback adaptive control framework for continuous-time minimum phase multivariable dynamical systems for output stabilisation and command following. The approach is based on a nonminimal state-space realisation that generates an expanded set of states using the filtered inputs and filtered outputs and their derivatives of the original system. Specifically, a direct adaptive controller for the nonminimal state-space model is constructed using the expanded states of the nonminimal realisation and is shown to be effective for multi-input, multi-output linear dynamical systems with unmatched disturbances, unmatched uncertainties and unstable dynamics. The proposed adaptive control architecture requires only knowledge of the open-loop system's relative degree as well as a bound on the system's order. Several illustrative numerical examples are provided to demonstrate the efficacy of the proposed approach.

Non-minimal state variable feedback decoupling control for multivariable continuous-time systems

Most research into non-minimal state variable feedback control, in which the state vector is implemented directly from the measured input and output signals of the controlled process, has considered discrete-time systems represented using either the backward shift or delta operator. However, mechanistic models with physically meaningful parameters are often expressed in terms of differential equations, represented using the Laplace transform or s-operator, and this article is concerned with multivariable design for such models. The controllability conditions are developed and it is shown how the introduction of a diagonal polynomial matrix for filtering yields a control system that is immediately realisable in practice. Worked examples include optimal control with multi-objective optimisation and pole assignment design with analytical multivariable decoupling, with the latter illustrated by its application to a nonlinear wind turbine simulation.

Identification of Multivariable Continuous-time Systems via Projection Type Iterative Learning

Identification of Multivariable Continuous-time Systems via Projection Type Iterative Learning

GMV control of non-linear continuous-time systems including common delays and state-space models

A non-linear generalized minimum variance control law is proposed for the control of non-linear continuous-time multivariable systems with common delays on input and output channels. The quadratic cost index involves both error and control signal costing terms. The solution for the control law is obtained using a non-linear operator representation of the plant and a linear state-equation model for the disturbance and reference models. The reference and disturbance models are represented by linear subsystems. However, the plant model can be in a very general non-linear operator form, which could involve state-space, transfer operators or non-linear function look up tables. The structure of the system and criterion is chosen so that a simple controller structure and solution is obtained. The controller obtained is simple to implement, particularly in one form, which might be considered to be a state-space version of a non-linear Smith predictor. The results are related to those for discrete-time systems but the presence of the transport delay terms complicates the solution rather more in the continuous-time case.

On MIMO model reduction by the weighted equation–error approach

The paper deals with the problem of approximating a stable continuous-time multivariable system by minimizing the L2-norm of a weighted equation error. Necessary and sufficient conditions of optimality are derived, and the main properties of the optimal reduced-order models are presented. Based on these conditions and properties, two efficient procedures for generating approximants that retain different numbers of Markov parameters and time moments are suggested and applied to benchmark examples. The results show that both the transient and the steady-state behaviour of the original systems are reproduced satisfactorily.

Isolation of parametric faults in continuous-time multivariable systems: a sampled data-based approach

A novel approach is proposed towards on-line and real-time detection and isolation of parametric faults in a multivariable linear continuous-time (CT) system. The problem of fault detection and isolation (FDI) is formulated in terms of a CT state space model. Since parameters in a CT model usually have simple relationships with physical parameters of the system, isolating parametric faults in the CT model can lead to the isolation of undesired changes in the physical parameters. Isolating parametric faults is very challenging, because even in a linear time-invariant system, the fault model can be time-varying and random. To obtain a constant fault model, many existing parametric FDI schemes have to make unrealistical assumptions. Our proposed FDI approach can generate an optimal primary residual vector (PRV), in which the fault model is constant without making any assumptions. To isolate faults, the PRV is transformed into a set of structured residual vectors (SRVs), where one SRV is made insensitive to a specified subset of faults, but most sensitive to other faults. The proposed approach is successfully applied to detection and isolation of undesired changes in the physical parameters of a simulated continuously stirred tank process.

Control of lti systems subject to unanticipated extreme perturbations using self-tuning 3-term switching controllers

In the design of conventional control systems for a multivariable system, using robust/adaptive control techniques, the motivation is to design a controller which "works satisfactorily" in the presence of plant uncertainty. Unfortunately, however, if large unanticipated structural changes subsequently occur in the system, severe limitations in practical performance may occur, since such conventional control schemes usually do not have the ability to control systems which are subject to unplanned extreme changes. Moreover, for the realistic situation when control input constraints exist, few results for continuous time multivariable systems are available. In this paper, a new class of self-tuning proportional-integral-derivative switching controllers, which is an extension of the self-tuning integral controller of Miller and Davison, is described, and has the property that it is robust to unplanned extreme changes in the plant and satisfies any feasible control signal input constraints. Results of this self-tuning controller when applied to an experimental multivariable system also are described.

純虚数零点をもつ多入出力連続時間系に対する離散化モデルの零点

純虚数零点をもつ多入出力連続時間系に対する離散化モデルの零点

STATE-SPACE SELF-TUNING CONTROL FOR NONLINEAR STOCHASTIC AND CHAOTIC HYBRID SYSTEMS

This paper presents a new state-space self-tuning control scheme for adaptive digital control of continuous-time multivariable nonlinear stochastic and chaotic systems, which have unknown system parameters, system and measurement noises, and inaccessible system states. Instead of using the moving average (MA)-based noise model commonly used for adaptive digital control of linear discrete-time stochastic systems in the literature, an adjustable auto-regressive moving average (ARMA)-based noise model with estimated states is constructed for state-space self-tuning control of nonlinear continuous-time stochastic systems. By taking advantage of a digital redesign methodology, which converts a predesigned high-gain analog tracker/observer into a practically implementable low-gain digital tracker/observer, and by taking the non-negligible computation time delay and a relatively longer sampling period into consideration, a digitally redesigned predictive tracker/observer has been newly developed in this paper for adaptive chaotic orbit tracking. The proposed method enables the development of a digitally implementable advanced control algorithm for nonlinear stochastic and chaotic hybrid systems.

Design of Lifted Dual-Rate Digital Controllers for X-38 Vehicle

A new state-matching digital redesign method to Ž nd the lifted dual-rate pulse-amplitude-modulated (PAM) and pulse-width-modulated (PWM) digital controllers from a predesigned, state-feedback, continuous-time controller is presented. The proposed method provides close matching of the states of the continuous-time controlled analog system with those of the digitally redesigned system (including intersample behavior). The redesigned lifted dual-rate controller enables the digitally controlled X-38 vehicle to track the desired trajectory while remaining insensitive to modeling parameters, initial conditions, and exogenous disturbances for larger sample times than existing methods. The X-38 will require a PAM controller for commanding the electromechanical actuators that operate its aerodynamic surfaces for  ight in the atmosphere. PWM control will be used to command the reaction control jets during orbital operations. The proposed method provides a new alternative for indirect digital design of state-feedback multivariable continuous-time systems.

An iterative learning control method for continuous-time systems based on 2-D system theory

This work presents a two-dimensional (2-D) system theory based iterative learning control (ILC) method for linear continuous-time multivariable systems. We demonstrate that a 2-D continuous-discrete model can be successfully applied to describe both the dynamics of the control system and the behavior of the learning process. We successfully exploited the 2-D continuous-discrete Roesser's linear model by extending the ILC technique from discrete control systems to continuous control systems. Three learning rules for ILC are derived. Necessary and sufficient conditions are given for convergence of the proposed learning rules. Compared to the learning rule suggested by Arimoto et al. (1984), our developed learning rules are less restrictive and have wider applications. The third learning rule proposed ensures the reference output trajectory can be accurately tracked after only one learning trial. Three numerical examples are used to illustrate the proposed control procedures.

Multivariable pi-sharing theory and its application on the Lur'e problem

The pi-sharing theory developed by Lawrence and Johnson (1986) is extended to handle square multivariable continuous-time systems, and for the most essential part of finding usable pi-coefficients, LMI formulations are utilized such that for any finite-dimensional LTI systems, time-invariant pi-coefficients can be obtained easily. Furthermore, pi-coefficients are derived for sector-bounded nonlinearities, and the extended pi-sharing theory is applied to the multivariable Lur'e problem. With this approach, not only can a Lur'e system with known sector bounds on nonlinearities be checked for stability, but also the maximal bounds ensuring stability can be found under some conditions.

Static Output Feedback Controllers for Continuous-Time and Discrete-Time Systems with Input Non-Linearities

In this paper we develop a static output feedback controller synthesis framework for continuous-time and discrete-time multivariable linear time-invariant systems subject to input time-varying non-linearities. The proposed framework directly accounts for robust stability and robust performance over the class of input non-linearities. Specifically, using a Riccati equation approach we develop a controller synthesis framework for constructing feedback controllers with a guaranteed domain of attraction for systems with input saturation non-linearities. The proposed design approach provides a systematic procedure for loop shaping and hence can account for classical design objectives within a modern multivariable control-system design framework. Several illustrative numerical examples are presented to demonstrate the effectiveness of the proposed approach.

Weighted Least Squares Method for Model Order Reduction of Multivariable Plants

This paper presents a frequency-shaped model order reduction for continuous-time multivariable systems with application to closed-loop model order reduction. The problem is first given an algebraic form by the means of the A-transform - a transformation based on the Chebyshev series expansion - and then solved through the least squares approach. The salient feature of the proposed method is the implicit weighting due to both the A-transform method and the particular implementation of the least squares procedure.

Sensitivity integrals for multivariable discrete-time systems

The purpose of this paper is to develop integral formulae for singular values of the sensitivity function to express design constraints in multivariable discrete-time systems. We present extensions to both the classical Poisson integral and Bode's sensitivity integral formulae. The main utility of these results is that they can be used to quantify design limitations that arise in multivariable discrete-time systems, due to such system characteristics as open-loop unstable poles and nonminimum-phase zeros, and to such design requirements as stability and bandwidth constraints. These formulae are similar to those for multivariable continuous-time systems obtained elsewhere, and they reveal that feedback design limitations depend on directionality properties of the sensitivity function, and on those of unstable poles and nonminimum-phase zeros in the open loop transfer function.

Robust performance of decentralized control systems by expanding sequential designs

This paper considers designs of decentralized controllers for continuous-time linear time-invariant multivariable control systems. The purpose is to show how to attain robust stability and robust performance of decentralized control systems by sequential design procedure. Compared with independent designs in which each controller block is designed independently of others, sequential designs can reduce conservatism associated with the controller design since they can exploit information about the other loops which have been already designed. A novel method of sequential designs for the robust performance are proposed. Moreover, an approach to a kind of failure tolerance is considered. The proposed sequential design procedure is based on expanding construction of decentralized control systems, so that the proposed methods can deal with extension of subsystems.

An Adaptive VSS Regulator for Multivariable Nonminimum-Phase Systems Based on Doubly Coprime Factorization

An adaptive regulator problem for continuous-time multivariable nonminimum-phase systems of unknown order is considered using the idea of the sliding mode control method. Introducing the state variable filters of the input and the output with auxiliary inputs additively superimposed and appealing to the doubly coprime factorization associated with the transfer matrix, an adaptive state feedback control law is derived that drives the state variables to the subspace defined by the intersection of the two sliding hyperplanes on which the state variables decay to the origin exponentially quickly. The global asymptotic stability of the proposed adaptive regulator is established under the assumptions that the number of the input is equal to the number of the output and the upper bound of the controllability indices is known.

Hysteresis switching adaptive control of linear multivariable systems

This paper presents a model reference adaptive control scheme for deterministic continuous-time multivariable systems represented by square, strictly proper, minimum-phase transfer function matrices. A typical requirement of existing algorithms is to assume that the zero structure at infinity and the high-frequency gain matrix are fully (or at least partially) known. It is well known that these requirements may be very restrictive, since, in general, both the zero structure at infinity and the high-frequency gain matrix depend on plant parameters. In this paper we show that these restrictive assumptions may be considerably weakened using Morse et al.'s hysteresis switching control strategy (1992). The strategy entails running a finite number of parameter estimators in parallel and using a switching algorithm to select between candidate estimators based on their associated prediction errors. Hysteresis in the switching algorithm precludes switching arbitrarily rapidly between estimators, and all switching ceases within a finite time. The results represent a significant step forward in understanding the minimal amount of prior knowledge necessary to design a stabilizing controller for a linear multivariable system.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>