摘要:

An adaptive deadzone inverse approach is developed for control of discrete-time systems with unknown deadzones at the input of linear dynamics. The proposed controller consists of an adaptive deadzone inverse, whose parameters are updated to cancel the effect of the deadzone, and a linear part, which is designed to achieve tracking of a reference signal by the system output. When the linear part of the system is known, its parameters are used to specify the parameters of the linear part of the controller. When the linear part of the plant is unknown, the linear control parameters are adaptively estimated. The control error caused by the adaptive deadzone inverse is expressed as a linearly parametrizable part plus a bounded disturbance. Adaptive laws which employ parameter projection are used to update the controller parameters. They are robust with respect to the bounded disturbance, and they result in parameter estimates needed to implement an adaptive deadzone inverse. We prove the closed-loop signal boundedness, and illustrate by simulations that the system tracking performance is significantly improved.

ISSN:0020-7179    

DOI:10.1080/00207179508921889

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

Four kinds of ℒ2to ℒ∞gains for sampled-data systems are defined and derived in this paper. It turns out that these gains can be expressed by analytical formulae which are easy to compute (only a discrete Lyapunov equation is involved).

ISSN:0020-7179    

DOI:10.1080/00207179508921890

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

In this paper, we deal with single-input single-output systems of the formon a separable Hilbert spaceH, where the operatorAis the generator of an exponentially stable C0-semigroup onH, b ϵ H, C is aA-admissible linear operator andwis an arbitrary constant disturbance vector inH. We propose a low-gain PI-controller which stabilizes and regulates the system such that, for a given reference constantyr, y(t)tends toyrindependently ofwast → + ∞ . Our result generalizes the previous one of Pohjolainen (1982) in that the semigroup is not necessarily holomorphic. A numerical example will be given to illustrate the application of the theory.

ISSN:0020-7179    

DOI:10.1080/00207179508921891

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

A new block-structured Lyapunov sum for partitioned matrices is defined and basic properties are established. It has similar properties to a Lyapunov matrix, but preserves the block structure, and has similar properties to the block Kronecker sum, but with about half the dimension. It is used to solve a maximal stability problem of integral controllability, and is also used to solve for the maximal stability range of singularly perturbed systems. In both cases closed formulae are obtained with lower dimensions than existing formulae.

ISSN:0020-7179    

DOI:10.1080/00207179508921892

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

Given a linear discrete time system, necessary and sufficient conditions for the existence of a linear or nonlinear controller, which satisfies a specified closed-loopH∞norm bound, are stated in terms of the solutions to two uncoupled algebraic discrete Riccati equations of the order of the system. State-space formulae for all the stabilizing controllers, some of the order of the system, which satisfy an achievable bound are also given. In this first part of the paper, new growth and convergence properties of the solution to a time-varying discrete Riccati equation are used to derive the necessary and sufficient conditions for the existence of a solution in the full information case. These properties generalize those of the corresponding discrete Riccati equation related to the LQR problem. In the second part of the paper, a non-standard estimation problem is posed and solved. This problem arises as a novel reinterpretation of theH∞norm objective. Its solution can be used to reduce a partial information to a full information control problem. Our approach to solving theH∞output feedback control problem is based on this result. This approach, the dual of that typically used inH∞control theory, yields significant new insights into theH∞regulation problem. Minimax difference game theory is central to the developments of this paper and it is shown that minimax, not saddle point game theory, provides the proper framework to solve theH∞regulation problem.

ISSN:0020-7179    

DOI:10.1080/00207179508921893

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

The minimal dimension of a linear-quadratic-gaussian (LQG) compensator is almost always equal to the dimension of the design plant. This deficiency can lead to implementation problems when considering control design for high-order systems such as flexible structures and has led to the development of methodologies for the design of optimal (or near optimal) controllers whose dimension is less than that of the design plant. This paper presents a new (gradient-based) homotopy algorithm for the design of reduced-order,H2optimal controllers. An important result is the development of an efficient methodology for computation of the cost functional hessian which is required by the algorithm. The optimal controller is represented by a parameter vector and various parametrizations of the optimal controller are considered to reduce the algorithm dimensionality. The algorithm has been implemented in MAT-LAB and the results are illustrated using a benchmark, non-collocated flexible structural control problem. It is seen that the choice of a particular controller parametrization often introduces numerical ill-conditioning in the algorithm implementation.

ISSN:0020-7179    

DOI:10.1080/00207179508921894

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

This paper presents a controller design methodology for a class of uncertain, multivariable, regulating systems required to maintain operating conditions within small tolerances despite a vector step disturbance. Furthermore, each control effort is limited by its hardware, namely the actuator outputs are limited in magnitude and response speed. The design methodology is a frequency domain approach and is based on single loop design. A Gauss elimination technique facilitates the various design steps. The specific class of systems addressed are those which can be modelled as square, multivariable systems with structured (i.e. parametric) and/or unstructured uncertainty. One restriction imposed on the system is that it must be invertible for all plant parameter combinations. The key features of this methodology include (i) the role played by loop interaction in achieving overall system performance; (ii) the ability to accommodate both parametric and unstructured uncertainty; (iii) the explicit consideration of transmission zeros; and (iv) the incorporation of controller constraints. As will be seen, focusing the design efforts on the loop interactions at a local level will allow individual bandwidths to be specified thereby providing an economical design.

ISSN:0020-7179    

DOI:10.1080/00207179508921895

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

A scheme is presented in the paper for the digital identification of a continuous-time system. The proposed identifier operates on a sampled data system but generates an estimate of the unknown continuous-time system directly. Convergence results are obtained and are independent of the sampling rate and the knowledge of input-output signals between sampling instants. Also discussed in the paper are some related problems. In particular, the convergence of the identifier requires the persistent excitation (PE) condition on certain signals, and that PE condition is reduced to the controllability and observability of the sampled system of an unknown continuous-time system. Moreover, results are derived concerning the controllability and observability of the sampled data system for an unknown continuous-time system.

ISSN:0020-7179    

DOI:10.1080/00207179508921896

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

This paper considers the robust implementation of a class of predictive control methods represented by GPC. Such controllers are in two-degrees-of-freedom form where there are dynamics in both the forward and the feedback paths. The ‘tuning knobs’ of predictive controllers determine the characteristic polynomialPC, and for a givenPCthe observer or prefiltering polynomialTin the feedback path determines the robustness of the closed loop. Previous intuitive guidelines on the selection ofTare shown to be limited in their effectiveness. For an open-loop stable plant, a simple criterion is provided which allows the feedback dynamics to be specified so as to enhance robustness. TheTpolynomial is then chosen to satisfy this criterion. In addition, robust design throughTis related to anH∞-optimal control scheme using the so-calledQ-parametrization. Despite its simplicity, the new proposed approach to the design ofTis seen to result in robustness comparable with that obtained from theH∞method.

ISSN:0020-7179    

DOI:10.1080/00207179508921897

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

A generalized predictive controller (GPC) is derived based on a general state-space model. The equivalence of the predictive control problem to a perturbation problem is revealed. In the case of a small perturbation, the closed-loop poles are calculated with high accuracy. For the case of a general perturbation, an upper bound on the permissible perturbation norm is derived assuming an open-loop stable system. Both the plant-model match and plant-model mismatch cases are analysed. The controller is proven to be robust and an adaptive implementation is motivated. For open-loop stable systems, the convergence and stability of the control scheme are ensured by proper tuning of the control weight and prediction horizon. The results are applicable to a wide range of predictive controllers. The main contribution of this paper is not a new control algorithm, but new techniques to analyse the GPC as well as new stability and convergence results.

ISSN:0020-7179    

DOI:10.1080/00207179508921898

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor