Design Of Sampled-data Systems Research Articles

High-gain observer design with sampled measurements: application to inverted pendulum

New results on high-gain observer design for sampled-data systems are presented for a large class of nonlinear uniformly observable systems. It is shown that by using an appropriate Lyapunov function, it is possible to design a continuous high-gain observer coupled with a large class of output predictors. An explicit bound on the maximum allowable sampling interval guaranteeing stability of the observation error is given. This result is illustrated on an experimental setup.

Modified fast-sample/fast-hold approximation and γ-independent H ∞-discretisation for general sampled-data systems by fast-lifting

This article is concerned with the fast-lifting approach to H ∞ analysis and design of sampled-data systems, and extends our preceding study on modified fast-sample/fast-hold (FSFH) approximation, in which the direct feedthrough matrix D 11 from the disturbance w to the controlled output z was assumed to be zero. More precisely, this article removes this assumption and shows that a γ-independent H ∞ discretisation is still possible in a nontrivial fashion by applying what we call quasi-finite-rank approximation of an infinite-rank operator and then the loop-shifting technique. As in the case of D 11 = 0, the modified FSFH approach retains the feature that both the upper and lower bounds of the H ∞-norm or the frequency response gain can be computed, where the gap between the upper and lower bounds can be bounded with the approximation parameter N and is independent of the discrete-time controller. This feature is significant in applying the new method especially to control system design, and this study indeed has a very close relationship to the recent progress in the study of control system analysis/design via noncausal linear periodically time-varying scaling. The significance of a key lemma pertinent to the fast-lifting approach is suggested in connection with such a relationship, and also with its application to time-delay systems.

Linear matrix inequality-based robust H∞ control of sampled-data systems with parametric uncertainties

The problem of robust H∞ controller design for sampled-data systems with time-varying norm-bounded parameter uncertainties in the state matrices is investigated. Attention is focused on the design of a causal sampled-data controller which guarantees the asymptotical stability of the closed-loop system and reduces the effect of the disturbance input on the controlled output to a prescribed H∞ performance bound for all admissible uncertainties. Sufficient condition for the solvability of the problem is in terms of linear matrix inequalities (LMIs) technique. It is shown that the desired H∞ controller can be constructed by solving certain LMIs. An illustrative example is given to demonstrate the effectiveness of the proposed method.

Convergence of Sampled-Data Models in Digital Redesign

This note proposes sufficient conditions that guarantee uniform-in-time convergence, as the sampling period approaches zero, of the control input to and the controlled output of a plant under sampled-data control to those corresponding signals of the same plant under continuous-time control. Sampled-data control systems exhibiting such behavior are formally defined as sampled-data models, which can be very convenient in the analysis and design of sampled-data systems since they can warn the engineer if a known limiting closed-loop behavior is likely to be violated. This practical consideration often occurs in digital redesign, where an analog control law is implemented digitally, with the objective of preventing intersample ripples.

H/sub 2/ optimal linear robust sampled-data filtering design using polynomial approach

A new frequency domain approach to robust multi-input-multi-output (MIMO) linear filter design for sampled-data systems is presented. The system and noise models are assumed to be represented by polynomial forms that are not perfectly known except that they belong to a certain set. The optimal design guarantees that the error variance is kept below an upper bound that is minimized for all admissible uncertainties. The design problem is cast in the context of H/sub 2/ via the polynomial matrix representation of systems with norm bounded unstructured uncertainties. The sampled-data mix of continuous and discrete time systems is handled by means of a lifting technique; however, it does not increase the dimensionality or alter the computational cost of the solution. The setup adopted allows dealing with several filtering problems. A simple deconvolution example illustrates the procedure.

Design of sampled-data systems with large plant uncertainty using quantitative feedback theory

This paper proposes a new quantitative feedback theory (QFT) design framework for dealing with sampled-data systems with large plant uncertainty. After the QFT-based design in the continuous-time domain is completed, the analogue controller can be transformed directly into a rational discrete-time transfer function via approximate Z transform, with the sampling time as a free parameter. The sampling time can therefore be adjusted to make the uncertain sampled-data system robustly stable. In comparison with other approaches, our approach is much more systematic without the solvability problem and yet significant enough to guide the designer to realize the physical controller in which the plant transfer function has prescribed bounds on its parameters. Several examples are used to illustrate the proposed approach and excellent results are obtained.

A new representation of the parameters of lifted systems

Lifting, i.e., discretization with built-in intersample behavior, is an emerging technique for the analysis and design of sampled-data systems. The applicability of the lifting technique, however, is severely limited owing to difficulties in dealing with the parameters of the lifted systems, which are operators over infinite-dimensional spaces rather than finite-dimensional matrices. In this paper, a new representation for the parameters of the lifted systems is proposed. The technical machinery developed in the paper based on this representation simplifies considerably algebraic manipulation over parameters of the lifted systems, thus extending the scope of applicability of the lifting technique. To illustrate the advantages of the proposed approach, the computational issues in the sampled-data H/sup /spl infin// problem are considered.

H2 and $H^\infty$ Design of Sampled-Data Systems Using Lifting. Part I: General Framework and Solutions

This paper presents a complete solution to the H2 and $H^\infty$ problems for sampled-data systems. As opposed to previous works in the area, it is assumed here that all or some of the sampling function, the discrete-time controller, and the hold function are available for design. The solution is obtained by transforming the problem to discrete time using the well-known lifting technique. It is then shown that the desired components of the sampled-data controller can be peeled-off from the inherently infinite-dimensional description in the lifted-domain. The procedure for doing this last step is central to the approach in this paper. Both new and revised solutions are presented in this paper. The solution to the H2 problems is completely new. The solution to the $H^\infty$ problems is presented in a unifying framework and is more transparent than the previous existing solutions in the literature. Transparency pays in the form of clearer results. In particular, a separation structure is established between the design of (sub)optimal hold and sampler.

H2and \Hinf Design of Sampled-Data Systems Using Lifting. Part II: Properties of Systems in the Lifted Domain

An important class of sampled-data systems becomes time-invariant when the systems are "lifted" into an appropriate domain. The purpose of the present paper is to study some basic properties of systems represented by state space equations in the lifted domain. Hidden modes, invariant zeros, and Riccati equations are investigated, and the connection between representations in continuous and lifted domains are clarified. The material treated here is important for solving optimal control problems of generalized sampled-data systems.

L/sub 1/ analysis and design of sampled-data systems

The focus of this work is L/sub 1/-optimal control of sampled-data systems. A converging approximation procedure is derived to compute the L/sub infinity /-induced norm of closed-loop finite-dimensional linear time-invariant (LTI) sampled-data systems. An approximation method is developed to synthesize L/sub 1/-optimal sampled-data regulators. Finally, an example is provided that illustrates the L/sub 1/ analysis and design techniques presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Quantitative feedback design for sampled-data systems

In quantitative feedback theory (QFT) the plant uncertainty is defined by a set P = {P} ofpossible plants. The problem is to guarantee that the system response is in a specified acceptable set A, for all P in P. QFT has been developed for large classes of plants imbedded in continuous feedback structures. This paper extends QFT to sampled-data structures. A central problem is to find the minimum sampling frequency (ωs)min needed. The greater the plant uncertainty and the narrower the performance tolerances, the larger must ( ωs)min be. The detailed design procedure parallels very closely that for continuous systems, by using the complex variable w, which maps the unit circle in the z-domain to the imaginary axis in the w-domain.

Robust design of sampled-data systems with application to an electro-hydraulic position controller

Attention is drawn to the importance of the sampling frequency as a design parameter of sampled-data feedback control systems and consideration is given to its implication to the ability of the systems to withstand gross variations of the plant without unacceptable deviation from the desired performance. It is seen that the robustness of a system is intimately related to the sampling frequency as a consequence of the limitations which it imposes on the achievable loop bandwidth. Conversely, for any specified degree of robustness, the minimum frequency of sampling is well defined. However, for plants with high-frequency dynamics such as the electro-hydraulic servo discussed within the paper, time constraints imposed by a dedicated microprocessor add to the restrictions of the sampling process in such a way that it may not be possible to guarantee the existence of a discrete compensator to satisfy the given specifications.

Design of linear multivariable sampled-data systems via polynomial equations

The design of a sampled-data system using output feedback and a digital controller in cascade with the system, is considered. The problems of exact model matching, decoupling, and of minimum settling time are discussed and constraints are derived using polynomial equations. The techniques are illustrated by numerical examples.

Stability-equation method for sampled-data systems

This paper presents a new transformation by which the stability-equation method can be applied for analysis and design of sampled-data systems. New stability criteria applicable to systems with transfer function having both real and complex coefficients are presented. Several kinds of examples are considered with computer results given.

Comments on “An infinite dimensional matrix for the design of sampled-data systems”

Comments on “An infinite dimensional matrix for the design of sampled-data systems”

Application of pole-zero concepts to design of sampled-data systems

This paper relates the pole-zero configuration of an error-sampled control system to the transient and steady-state response in a form amenable to straightforward synthesis procedures. The approximate transient response, as defined by percent overshoot and rise time, is specified for a generalized quadratic model in terms of readily discernable parameters. The steady-state error coefficients are developed in terms of the closed-loop poles and zeros. Several examples are used to illustrate the procedure and indicate certain practical conclusions.

Transient response of sampled-data systems

IT IS KNOWN that the z-transform method <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1−4</sup> can be readily used for analysis and design of sampled-data systems. This method is essentially a Laplace transform technique in which the sampled output is related to the input by system functions in the form of z-transforms. These system functions can be generally regarded to consist of zeros and poles, in the form of rational polynomial in the variable z, where z is defined as ∊ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Ts</sup> and T is the sampling period. The purpose of this digest is to investigate in detail the effect of the locations of the poles and zeros of the transfer function on the transient response of sampled-data systems when subjected to step input.

Extension of continuous-data system design techniques to sampled-data control systems

THE purpose of this paper is to extend the utility of certain synthesis techniques, which have proved useful in the design of continuous feedback systems, to the study of sampled-data systems. In recent publications,1,3,6 the z-transformation has been utilized to advantage in simplifying the analysis of sampled-data systems. However, several useful techniques applicable to the design of continuous-data systems have not been made available for the design of sampled-data systems. In this paper, by means of an extension of the concepts embodied in the z-transformation, the application to sampled-data systems of root-locus plots, asymptotic frequency plots, and Routh's criterion is shown to be feasible. Through the use of these techniques, a digital program giving the desired system compensation is readily synthesized.