Absolute stability analysis of sampled-data scaled bilateral teleoperation systems

Stability of a bilateral teleoperation system may be jeopardized by controller discretization, which has been shown to involve energy leaks. This paper proposes a novel approach to analyzing the absolute stability of sampled-data bilateral teleoperation systems consisting of discrete-time controllers and continuous-time master, slave, operator, and environment. The proposed stability analysis permits scaling and delay in the master and the slave positions and forces. The absolute stability conditions reported here impose bounds on the gains of the discrete-time controller, the damping terms of the master and the slave, and the sampling time. A design-related application of these results is in proper selection of various control parameters and the sampling rate for stable teleoperation under discrete-time control. To explore the trade-off between the control gains and the sampling time, it is studied that how large sampling times, which require low control gains for maintaining stability, can lead to unacceptable teleoperation transparency and human task performance in a teleoperated switching task. This shows that the effect of sampling time must be taken into account because neglecting it (as in the absolute stability literature) undermines both stability and transparency of teleoperation. The resulting absolute stability condition has been verified via experiments with two Phantom Omni robots.     

Stability analysis of bilinear systems under aperiodic sampled-data control

This note considers the problem of local stability of bilinear systems with aperiodic sampled-data linear state feedback control. The sampling intervals are time-varying and upper bounded. It is shown that the feasibility of some linear matrix inequalities (LMIs), implies the local asymptotic stability of the sampled-data system in an ellipsoidal region containing the equilibrium. The method is based on the analysis of contractive invariant sets, and it is inspired by the dissipativity theory. The results are illustrated by means of numerical examples.     

Stability of sampled-data piecewise affine systems: A time-delay approach

This paper addresses the stability analysis of sampled-data piecewise-affine (PWA) systems consisting of a continuous-time plant in feedback connection with a discrete-time emulation of a continuous-time state feedback controller. The sampled-data system is first considered as a continuous-time system with a variable time delay. Conditions under which the trajectories of the sampled-data closed-loop system will converge to an attracting invariant set are then presented. It is also shown that when the sampling period converges to zero, these conditions coincide with sufficient conditions for non-fragility of the stabilizing continuous-time PWA state feedback controller. The results are successfully applied to a helicopter example.     

Randomized algorithms for quadratic stability of quantized sampled-data systems

In this paper, we present a novel development of randomized algorithms for quadratic stability analysis of sampled-data systems with memoryless quantizers. The specific randomized algorithm employed generates a quadratic Lyapunov function and leads to realistic bounds on the performance of such systems. A key feature of this method is that the characteristics of quantizers are exploited to make the algorithm computationally efficient.     

Polynomial-time probabilistic observability analysis of sampled-data piecewise affine systems

This paper proposes a polynomial-time probabilistic approach to solve the observability problem of sampled-data piecewise affine systems. First, an algebraic characterization for the system to be observable is derived. Next, based on the characterization, we propose a randomized algorithm that can determine if the system is observable in a probabilistic sense or the system is not observable in a deterministic sense. Finally, it is shown with some examples, for which it is hopeless to check the observability in a deterministic way, that the proposed algorithm is very useful.     

Conic sectors for sampled-data feedback systems

A multivariable analog system can be controlled by a sampled-data compensator. A conic sector that can be used to analyze the closed-loop stability and robustness of this feedback system is presented in this letter.     

Control of sampled-data systems with variable sampling rate

This paper addresses stability and performance of sampled-data systems with variable sampling rate, where the change between sampling rates is decided by a scheduler. A motivational example is presented, where a stable continuous time system is controlled with two sampling rates. It is shown that the resulting system could be unstable when the sampling changes between these two rates, although each individual closed-loop system is stable under the designed controller that minimizes the same continuous loss function. Two solutions are presented in this paper. The first solution is to impose restrictions on switching sequences such that only stable sequences are chosen. The second solution presented is more general, where a piecewise constant state feedback control law is designed which guarantees stability for all possible variations of sampling rate. Furthermore, the performance defined by a continuous time quadratic cost function for the sampled-data system with variable sampling rate can be optimized using the proposed synthesis method.     

New conic sectors for sampled-data feedback systems

New conic sectors are presented which can be used to analyze sampled-data feedback systems. First, a cone is constructed which contains just the sampler. Next, by using conic sector results for interconnected systems, the cone is propagated to the entire sampled-data operator. The new cone result is less conservative (has a smaller radius) and removes the restriction of an open-loop stable sampled-data compensator.     

On designing filters for uncertain sampled-data nonlinear systems

This paper is concerned with the problem of nonlinear filtering for sampled-data systems with nonlinear time-varying parameter uncertainty. The aim is to design a digital filter such that the ratio between the energy of the estimation errors and the energy of the exogenous inputs is minimised or guaranteed to be less or equal to a prescribed value for all admissible uncertainties. A nonlinear bounded real lemma for sampled-data systems with nonlinear time-varying parameter uncertainty is provided. Based on this nonlinear bounded real lemma, the robust filtering problem is solved in terms of both continuous and discrete Hamilton–Jacobi equations.     

State-dependent parameter modelling and identification of stochastic non-linear sampled-data systems

State-dependent parameter representations of stochastic non-linear sampled-data systems are studied. Velocity-based linearization is used to construct state-dependent parameter models which have a nominally linear structure but whose parameters can be characterized as functions of past outputs and inputs. For stochastic systems state-dependent parameter ARMAX (quasi-ARMAX) representations are obtained. The models are identified from input–output data using feedforward neural networks to represent the model parameters as functions of past inputs and outputs. Simulated examples are presented to illustrate the usefulness of the proposed approach for the modelling and identification of non-linear stochastic sampled-data systems.     

Stability of sampled-data piecewise-affine systems under state feedback

This paper addresses stability of sampled-data piecewise-affine (PWA) systems consisting of a continuous-time plant and a discrete-time emulation of a continuous-time state feedback controller. The paper presents conditions under which the trajectories of the sampled-data closed-loop system will exponentially converge to a neighborhood of the origin. Moreover, the size of this neighborhood will be related to bounds on perturbation parameters related to the sampling procedure, in particular, related to the sampling period. Finally, it will be shown that when the sampling period converges to zero the performance of the stabilizing continuous-time PWA state feedback controller can be recovered by the emulated controller.     

Robust backstepping for the Euler approximate model of sampled-data strict-feedback systems

Stabilization of uncertain sampled-data strict-feedback systems is addressed. The stability study is carried out on the Euler approximation of the exact discretized model of the plant. Firstly, a class of state-feedback controllers is developed that guarantees an input-to-state stability property for the closed-loop system. Additionally, assuming some hypotheses on the uncertain terms hold, a practical asymptotic stability property is ensured by designing an appropriate class of controllers.     

Robust sampled-data control for Markovian jump linear systems

In this paper, we consider the problem of robust control for uncertain sampled-data systems that possess random jumping parameters which is described by a finite-state Markov process. The conditions for the existence of a stabilizing control and optimal control for the underlying systems are obtained. The desired controllers are designed which are in terms of matrix inequalities. Finally, a numerical example is given to show the potential of the proposed techniques.     

Convex conditions for robust stability analysis and stabilization of linear aperiodic impulsive and sampled-data systems under dwell-time constraints

Stability analysis and control of linear impulsive systems is addressed in a hybrid framework, through the use of continuous-time time-varying discontinuous Lyapunov functions. Necessary and sufficient conditions for stability of impulsive systems with periodic impulses are first provided in order to set up the main ideas. Extensions to the stability of aperiodic systems under minimum, maximum and ranged dwell-times are then derived. By exploiting further the particular structure of the stability conditions, the results are non-conservatively extended to quadratic stability analysis of linear uncertain impulsive systems. These stability criteria are, in turn, losslessly extended to stabilization using a particular, yet broad enough, class of state-feedback controllers, providing then a convex solution to the open problem of robust dwell-time stabilization of impulsive systems using hybrid stability criteria. Relying finally on the representability of sampled-data systems as impulsive systems, the problems of robust stability analysis and robust stabilization of periodic and aperiodic uncertain sampled-data systems are straightforwardly solved using the same ideas. Several examples are discussed in order to show the effectiveness and reduced complexity of the proposed approach.     

Quadratic stabilization of sampled-data systems with quantization

A design method of memoryless quantizers in sampled-data systems is proposed. The design objective is quadratic stability in the continuous-time domain, and thus the decay rate between sampling times is guaranteed. Our general treatment enables us to look for quantizers efficient in terms of data rate.     

On the Lyapunov-based adaptive control redesign for a class of nonlinear sampled-data systems

Stabilization of the exact discrete-time models of a class of nonlinear sampled-data systems, with an unknown parameter, is addressed. Given a Lyapunov-based continuous-time adaptive controller that ensures some stability properties for the closed-loop system, a sufficient condition for the design of high order discrete-time controllers is given. The stability analysis is carried out considering the truncated Fliess series of the Lyapunov difference equation. Due to the appearance of power terms of the unknown parameter, the problem is reparameterized in a convex-like form and an estimation law for the new unknown parameter is derived with no need of overparametrization or projection techniques. Then, assuming appropriate conditions hold, high order controllers can be designed. The boundedness of the extended state vector is ensured under some conditions, for a sufficiently small sampling period. It is shown how increasing the controller order can improve system performance.     

Implementation of algebraic controllers for non-conventional sampled-data systems

Nowadays, in industrial control applications, is rather usual to sample and update different variables at different rates, although it is common to consider all these activities equally and regularly spaced on time. These applications are implemented on real-time operating systems by decomposing them into several tasks in such a way that pre-emption and blocking may appear due to task priorities and resource sharing. This could imply the presence of delays, leading to a non-regular periodic behaviour and, as a result, the control performance can be degraded. In order to undertake this problem, a solution based on a modelling methodology for non-conventional sampled-data systems is proposed. This technique permits the consideration of any cyclic sampling pattern. Thus, these delays can be considered in the modelling step, and later on, a non-conventional controller based on this model can be designed. In this way, if the considered non-conventional control system is implemented assuming a real-time operating system (Tornado-VxWorks, in this case), a clear performance improvement can be observed. ángel Cuenca was born in Valencia (Spain) in 1974. He received his M.Sc. degree in Computer Science in 1998 and his Ph.D. in Control Engineering in 2004, from the Polytechnic University of Valencia. He is with the department of Systems Engineering and Control at the Polytechnic University of Valencia. He has been teaching courses on systems theory, programmable logic controllers and multi-rate sampled-data systems. His research interests include non-conventionally sampled-data systems and networked based control systems. He has taken part in several national and European research projects. Julian Salt was born in Valencia, Spain in 1960. He received his M.Sc. degree in industrial engineering in 1986 and his Ph.D. in Control Engineering in 1992, from Valencia Polytechnic University. His current position is as Professor of Automatic Control (2000-), Valencia Polytechnic University (UPV), teaching a wide range of subjects in the area from continuous and discrete simulation to automation and programmable logic controllers applications. His research interests include non-conventionally sampled control systems and networked based control systems. He has taken part in research projects funded by local industries, government and the European Science Foundation. He has also been involved in educational projects and currently is Head of the Systems Engineering and Control Department at UPV. He has been director of 8 PhD thesis and coauthor of about 60 technical papers in journals and technical meetings. Pedro Albertos, full Professor since 1975, currently at the Dept of Systems Engineering and Control at the Polytechnic University of Valencia, Spain. He has been Director from 1979 to 1995 and in 1998. He has been teaching courses on Advanced Control Systems, Intelligent Control Systems and Systems Theory. He is Honorary Profesor at the Northwestern University, Senhyang, China and Doctor Honoris Causa at the Universities of Oulu (Finland) and Polytechnic of Bucarest (Rumania). Invited Professor in more than 20 Universities, all around the world, he has delivered seminars in more than 30 universities and research centres. Authored more than 300 papers, book chapters and congress communications, he is co-editor of 7 books and co-author of Multivariable Control Systems (Springer 2004). He has directed 16 PhD thesis, and he is the coordinator of the PhD Program on Automatica and Industrial Informatics, which has been implemented in Spain, Mexico, Columbia and Venezuela. He has participated in many national and international research projects. Currently is involved in the ARTIST2 Node of Excellence on Embedded Control Systems. He is associated editor of Control Engineering Practice and Automatica and editor in chief of the journal Revista RIAI (Revista Iberoamericana de Automática e Informática Industrial). In the period 1999–2002 he was the IFAC President.     

Dual-rate sampled-data systems. Some interesting consequences from its frequency response analysis

The main goal of this contribution is to introduce a new procedure in order to analyse properly SISO dual-rate systems (DRS) and to provide straightforward answers to some common general questions about this kind of systems. Frequency response analysis based on DRS lifting modelling can lead to interesting results about stability margins or performance prediction. As a novelty, it is explained how to understand DRS frequency response and how to handle it for an easy computation of magnitude and phase margins keeping classical frequency domain methods. There are also some repetitive questions about DRS that can be analysed and answered properly using the results from this contribution: what the optimum relation between sampling periods is or what effects does delay have in a DRS. Every step is illustrated with examples that should clarify the understanding of the text.