Direct reduced order discretization of continuous-time controller

Anderson, Brian D. O.; Chongsrid, K.; Limebeer, D.J.N.; Hara, Shinji

doi:10.1002/(sici)1099-1239(199903)9:3<143::aid-rnc397>3.0.co;2-o

Cited by 8 publications

(4 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This hybrid nature of the system requires a special treatment to guarantee a better performance and to increase the accuracy in the description of the model. Therefore, over the past few years, different methods to synthesize controllers for hybrid systems have emerged in the continuous-time domain and in the discrete-time domain [4][5][6][7][8]. In the context of the techniques developed in the discrete-time domain, most of the approaches aim to satisfy two main requirements: (1) to yield a discrete-time model that accurately represents the dynamics of the continuous-time 2300 M. F. BRAGA ET AL.…”

Section: Introductionmentioning

confidence: 99%

Linear quadratic networked control of uncertain polytopic systems

Braga

Morais

Tognetti

et al. 2015

Intl J Robust & Nonlinear

View full text Add to dashboard Cite

SUMMARYThis paper investigates the problem of designing robust linear quadratic regulators for uncertain polytopic continuous-time systems over networks subject to delays. The main contribution is to provide a procedure to determine a discrete-time representation of the weighting matrices associated to the quadratic criterion and an accurate discretized model, in such a way that a robust state feedback gain computed in the discretetime domain assures a guaranteed quadratic cost to the closed-loop continuous-time system. The obtained discretized model has matrices with polynomial dependence on the uncertain parameters and an additive norm-bounded term representing the approximation residual error. A strategy based on linear matrix inequality relaxations is proposed to synthesize, in the discrete-time domain, a digital robust state feedback control law that stabilizes the original continuous-time system assuring an upper bound to the quadratic cost of the closed-loop system. The applicability of the proposed design method is illustrated through a numerical experiment.

show abstract

Section: Introductionmentioning

confidence: 99%

Linear quadratic networked control of uncertain polytopic systems

Braga

Morais

Tognetti

et al. 2015

Intl J Robust & Nonlinear

View full text Add to dashboard Cite

show abstract

“…In the present paper, a discretization method of continuous-time controllers based on frequency response matching such as the loop transfer function or a continuous-time controller is proposed. A number of frequency response based methods have already been proposed [1], [6], [8]- [11]. The methods proposed by Keller, et al [1], Anderson, et al [11], Mori, et al [9], Rafee, et al [5] and Cantoni, et al [12] are norm-based methods and the reference functions are closed-loop systems.…”

Section: Introductionmentioning

confidence: 99%

“…A number of frequency response based methods have already been proposed [1], [6], [8]- [11]. The methods proposed by Keller, et al [1], Anderson, et al [11], Mori, et al [9], Rafee, et al [5] and Cantoni, et al [12] are norm-based methods and the reference functions are closed-loop systems. Norm-based methods sometimes provide high-order controllers if additional frequency dependent weighting functions are used in order to match the frequency response span over several decades.…”

Section: Introductionmentioning

confidence: 99%

Discretization Method of Continuous-Time Controllers Based on Frequency Response Fitting

Chida

Nishimura

2008

SICE Journal of Control, Measurement, and System Integration

View full text Add to dashboard Cite

: In the present paper, a digital redesign problem that converts continuous-time controllers into digital controllers is considered. A new discretization method based on matching of the frequency response of a continuous-time control system is proposed. The frequency response is matched using the least squares method based on data of discrete frequency points. The matching problem is described using an LMI, and the stability condition of the closed-loop system and the redesigned controller are described as additional conditions of LMIs. An optimizing problem described by some LMI conditions is solved by an iterative procedure. Examples are presented that prove the superior performance of the proposed method.

show abstract

“…Such a procedure is justified and well understood in the context of linear systems (see for example [1,2,10] and the references therein); however there is relatively little theoretical justification for this approximation in the context of nonlinear controllers and plants.…”

Section: Introductionmentioning

confidence: 99%

General fast sampling theorems for nonlinear systems

Bian

French

2005

Systems & Control Letters

View full text Add to dashboard Cite

This paper is concerned with the gap metric approach to controller discretisation problems for continuous-time nonlinear systems with disturbances in both input and output channels. The principal idea is to construct a discrete controller based on a given stabilizing continuous time controller via a fast sampling and hold procedure and to calculate the gap between the two controllers. It is expected that, under general conditions, the computed gap depends on the discrete sample size and the faster the sample rate, the smaller the gap and, therefore, existing gap metric robust stability theorems can be applied to obtain both stability and performance results for the appropriately discretised controller. This is shown for the case of memoryless controllers and for a more general class of controllers specified by stable, causal operators. In both cases, both regional and global results are obtained under respective local and global incremental stability assumptions on the controllers.

show abstract

Direct reduced order discretization of continuous-time controller

Cited by 8 publications

References 13 publications

Linear quadratic networked control of uncertain polytopic systems

Linear quadratic networked control of uncertain polytopic systems

Discretization Method of Continuous-Time Controllers Based on Frequency Response Fitting

General fast sampling theorems for nonlinear systems

Contact Info

Product

Resources

About