Exact Discrete-time Model Research Articles

On the stability of nonlinear sampled-data systems and their continuous-time limits

This work deals with the stability analysis of nonlinear sampled-data systems under nonuniform sampling. It establishes novel relationships between specific stability properties of the exact discrete-time model and stability properties of the continuous-time system that is obtained when the maximum admissible sampling period tends to zero. These results can be used to infer stability properties for the sampled-data system by direct inspection of the stability of the mentioned continuous-time system, a task which is typically easier than the analysis of the closed-loop sampled-data system. Compared to the literature, our results allow to prove stronger (asymptotic) sampled-data stability properties for nonlinear systems in cases for which existing results only guarantee practical stability.

Observer-based control for networked Takagi-Sugeno fuzzy systems with stochastic packet losses

This paper addressed the observer-based control problem for Takagi-Sugeno (T-S) fuzzy systems with stochastic packet losses. More specifically, an sampled-data (SD) control technique is introduced to reduce the burden of the limited bandwidth of the network, a general consecutive packet loss model is used to represent the stochastic packet loss behavior between sensor-to-controller and controller-to-actuator, and an observer scheme based on received SD output information is used to obtain the estimated system states. Based on the above scenarios, an exact discrete-time model approach is developed for stabilizing networked T-S fuzzy systems. First, the considered system with the observer-based control scheme is transformed into its discrete-time model such that subsequent analysis will be carried out in the discrete-time domain. On this basis, stability criteria are derived by fully considering the probability distribution of consecutive packet losses. Furthermore, an observer-based controller is designed by introducing some auxiliary matrices. Finally, the correctness and practicability of the designed controller is demonstrated by a mass-spring-damper system.

Security Control of Sampled-Data T–S Fuzzy Systems Subject to Cyberattacks and Successive Packet Losses

This article investigates the security control problem of sampled-data Takagi–Sugeno (T–S) fuzzy systems subject to cyberattacks and successive packet losses. The cyberattack considered in this article is a stochastic deception attack. The packet losses under consideration occur in the sensor-to-controller and controller-to-actor channels, both of which are modeled as two independent Bernoulli processes. On this basis, a novel successive packet loss modeling method is proposed with some basic assumptions. By the exact discrete-time model approach, a discretized sampled-data T–S fuzzy model is first established by considering the probability characteristic of the deception attacks and successive packet losses in a unified framework. Based on the established mode, the sufficient conditions to guarantee the security degree are derived by the Lyapunov function approach. Furthermore, the fuzzy security controller is designed in view of linear matrix inequalities. Finally, a benchmark example is given to show the validity of the proposed approach.

Event-triggered and consensus-based attitude tracking alignment for discrete-time multiple spacecraft system exploiting interference

This paper presents a discrete-time attitude control strategy with equi-global practical stabilizability for aligning the attitude of multiple spacecraft to a predesigned configuration according to a time-variant reference. By utilizing the interference of the wireless channel, the communication scheme designed in this paper can save communication resources, amount of computation, and energy proportionally to the number of spacecraft. The exact discrete-time model and approximate discrete-time model of the consensus-based spacecraft tracking system are given. Then the framework for the design of an event-triggered control scheme for the exact discrete-time system via its approximate models is developed, which avoids the periodic actuation, and Zeno behavior is proved to be excluded. Furthermore, the control scheme can handle the presence of the unknown fading channel. Finally, simulation results are presented to demonstrate the effectiveness of the control strategy.

On the Realization of Impulse Invariant Low-Rank Volterra Kernels

Volterra models can accurately model numerous nonlinear systems of practical interest, but often at an unacceptable computational cost. If the Volterra kernels of a system have low-rank structure (like, e.g., kernels of bilinear systems), this major drawback can in principle be mitigated. Yet, when one seeks an exact discrete-time model of a mixed-signal chain involving that system, the existing formula that generalizes the impulse invariance principle to Volterra kernels yields discrete-time kernels that do not share the same low rank. At first sight this would seem to seriously complicate the otherwise simple discrete-time realization of low-rank kernels. We show here that this not the case. By defining a cascade operator, the structure of generalized impulse invariance can be unveiled, leading to a realization without an inordinate increase in computational complexity. Finally, we give a numerical example involving a physical system that shows the relevance of our proposal.

Sampled-Data Stabilization of a Class of Stochastic Nonlinear Markov Switching System with Indistinguishable Modes Based on the Approximate Discrete-Time Models

This paper investigates the stabilization issue for a class of sampled-data nonlinear Markov switching system with indistinguishable modes. In order to handle indistinguishable modes, the authors reconstruct the original mode space by mode clustering method, forming a new merged Markov switching system. By specifying the difference between the Euler-Maruyama (EM) approximate discrete-time model of the merged system and the exact discrete-time model of the original Markov switching system, the authors prove that the sampled-data controller, designed for the merged system based on its EM approximation, can exponentially stabilize the original system in mean square sense. Finally, a numerical example is given to illustrate the effectiveness of the method.

Characteristic model-based adaptive control for cryogenic wind tunnels

With the increasing requirement of Reynolds number simulation in wind tunnel tests, the cryogenic wind tunnel is considered as a feasible method to realize high Reynolds number. Characteristic model-based adaptive controller design method is introduced to flow field control problem of the cryogenic wind tunnel. A class of nonlinear multi-input multi-output (MIMO) system is given for theoretical research that is related to flow field control of the cryogenic wind tunnel. The characteristic model in the form of second-order time-varying difference equations is provided to represent the system. A characteristic model-based adaptive controller is also designed correspondingly. The stability analysis of the closed loop system composed of the characteristic model or the exact discrete-time model and the proposed controller is investigated respectively. Numerical simulation is presented to illustrate the effectiveness of this control method. The modeling and control problem based on characteristic model method for a class of MIMO system are studied and first applied to the cryogenic wind tunnel control field.

Linear Feedback Dead-Beat Control for Modular Multilevel Converters: Validation Under Faults Grid Operation Mode

The cascaded control approach is widely used to control the modular multilevel converter (MMC). Such approach allows to manage all MMC state variables in a decoupling manner based on modes separation. This separation introduces conditions related to control objectives response time resulting in slow dynamics. This will limit the use of the potential of MMC energy that is considered as a freedom for ac and dc grids ancillary services. On another side, robustness properties for a given control are also of a great interest when considering unmodeled uncertainties and disturbances. Starting from these requirements, a linear feedback dead-beat control is proposed in this article to accelerate the inner loops and consequently the outer ones (control objectives). The proposed control, based on exact discrete-time model of the MMC in which the sampling period is considered a priory in the control design, is synthetized by taking into account the control outputs saturation. The stability proof of the control and the robustness analysis as well as experimental results under fault grid operations highlighted on small-scale MMC will be presented in this article. The comparison with a continuous-time sliding mode control shows the advantage of the proposed control regarding the response time and undesired oscillation reduction.

Identification of continuous-time systems utilising Kautz basis functions from sampled-data

In this paper we address the problem of identifying a continuous-time deterministic system utilising sampled-data with instantaneous sampling. We develop an identification algorithm based on Maximum Likelihood. The exact discrete-time model is obtained for two cases: i) known continuous-time model structure and ii) using Kautz basis functions to approximate the continuous-time transfer function. The contribution of this paper is threefold: i) we show that, in general, the discretisation of continuous-time deterministic systems leads to several local optima in the likelihood function, phenomenon termed as aliasing, ii) we discretise Kautz basis functions and obtain a recursive algorithm for constructing their equivalent discrete-time transfer functions, and iii) we show that the utilisation of Kautz basis functions to approximate the true continuous-time deterministic system results in convex log-likelihood functions. We illustrate the benefits of our proposal via numerical examples.

Experimental validation of the Newton observer for a nonlinear flux-controlled AMB system operated with zero-bias flux

ABSTRACT The paper presents the results of experimental validation of the Newton observer for estimation of the magnetic flux within the feedback control of a nonlinear active magnetic bearing (AMB) system. In the preliminary work the Newton observer was adapted for the exact discrete-time model of the simplified one-degree-of-freedom AMB system, operated with zero-bias flux and under the voltage switching strategy, and showed good results in case of numerical simulations. The objective of this paper is to confirm these results on the basis of experimentation. The experiments were conducted on the AMB test rig, developed and manufactured at Bialystok University of Technology.

Characterization of semiglobal stability properties for discrete-time models of non-uniformly sampled nonlinear systems

Discrete-time models of non-uniformly sampled nonlinear systems under zero-order hold relate the next state sample to the current state sample, (constant) input value, and sampling interval. The exact discrete-time model, that is, the discrete-time model whose state matches that of the continuous-time nonlinear system at the sampling instants may be difficult or even impossible to obtain. In this context, one approach to the analysis of stability is based on the use of an approximate discrete-time model and a bound on the mismatch between the exact and approximate models. This approach requires three conceptually different tasks: (i) ensure the stability of the (approximate) discrete-time model, (ii) ensure that the stability of the approximate model carries over to the exact model, (iii) if necessary, bound intersample behaviour. Existing conditions for ensuring the stability of a discrete-time model as per task (i) have some or all of the following drawbacks: are only sufficient but not necessary; do not allow for varying sampling rate; cannot be applied in the presence of state-measurement or actuation errors. In this paper, we overcome these drawbacks by providing characterizations of, i.e. necessary and sufficient conditions for, two stability properties: semiglobal asymptotic stability, robustly with respect to bounded disturbances, and semiglobal input-to-state stability, where the (disturbance) input may successfully represent state-measurement or actuation errors. Our results can be applied when sampling is not necessarily uniform.

Stabilization Analysis for a Class of Nonlinear Systems Based on Characteristic Model

This paper studies the characteristic modeling problem for a class of single input single output (SISO) nonlinear systems with a relative degree of two. Firstly, to deal with the complexities of high-order nonlinear systems, we provide a class of low order and slowly time-varying linear systems to represent the original systems. Secondly, based on the characteristic model, we propose a linear controller by using coefficients obtained from system online identification. Through the above two steps, we solve the stabilization problem of closed-loop system composed of the characteristic model and the linear controller. Furthermore, the stability analysis of the closed-loop system composed of an exact discrete-time model and a linear controller is given. Finally, two simulation examples are given to show the effectiveness of the proposed design.

Robust sensitive fault detection and estimation for single-rate and multirate nonlinear sampled-data systems

This paper investigates the problem of fault detection and estimation for nonlinear sampled-data systems in the presence of unknown exogenous inputs. Both cases of single-rate and multirate sampling are treated and general observer-based frameworks are provided using discrete-time approximation to estimate fault signals of any sources. We show that these frameworks are input-to-error stable with respect to the estimation error and can simultaneously enhance robustness against unknown inputs and sensitivity to faults in a mixed H−∕H∞ sense for the unknown exact discrete-time model of the plant. Our results are then applied to a class of Lipschitz nonlinear systems with a refined Euler approximate model to derive sampled-data fault estimation techniques where stability and H−∕H∞ optimization are ensured using linear matrix inequalities (LMIs). Simulation results of a flexible joint robot illustrate the effectiveness of the proposed methodologies.

Integral versions of input-to-state stability for dual-rate nonlinear sampled-data systems

This paper presents versions of integral input-to-state stability and integral input-to-integral-state stability for nonlinear sampled-data systems, under the low measurement rate constraint. In particular, we compensate the lack of measurements using an estimator approximately reconstructing the current state. Interestingly, under certain checkable conditions, we establish that a controller that semiglobally practically integral input-to-(integral-)state stabilizes an approximate discrete-time model of a single-rate nonlinear sampled-data system, also stabilizes the exact discrete-time model of the nonlinear sampled-data system in the same sense implemented in a dual-rate setting. Numerical simulations are given to illustrate the effectiveness of our results.

Robust Sampled-Data Bilateral Teleoperation: Single-Rate and Multirate Stabilization

This paper investigates robust sampled-data control design strategies for nonlinear bilateral teleoperators exposed to communication constraints, using discrete-time approximate models of the master and slave robots and assuming both single-rate and multirate sampling. The single-rate design guarantees input-to-state stability of the (unknown) exact discrete-time model in a semiglobal practical sense, in spite of norm-bounded channel uncertainties. Then imposing different sampling rates on positions/velocities or torque inputs in each side of the system, a multirate scheme is proposed and shown to maintain similar stability properties under a well-known Nyquist frequency assumption on control torques. Simulation results verify the advantages of our direct sampled-data design. The example also shows that the multirate controller successfully stabilizes the teleoperation system even when the single-rate bilateral setup is ineffective in the presence of different sampling rates.

Discrete-Time Observer Design for Sensorless Synchronous Motor Drives

This paper deals with the speed and position estimation of interior permanent-magnet synchronous motor (IPM) and synchronous reluctance motor (SyRM) drives. A speed-adaptive full-order observer is designed and analyzed in the discrete-time domain. The observer design is based on the exact discrete-time motor model, which inherently takes the delays in the control system into account. The proposed observer is experimentally evaluated using a 6.7-kW SyRM drive. The analysis and experimental results indicate that major performance improvements can be obtained with the direct discrete-time design, especially if the sampling frequency is relatively low compared with the fundamental frequency. The ratio below 10 between the sampling and fundamental frequencies is achieved in experiments with the proposed discrete-time design.

Sufficient conditions to stabilize time-varying nonlinear sampled-data systems via approximation

Summary This paper investigates the problem of stabilizing a time-varying nonlinear sampled-data system based on its approximate models. Given a time-varying nonlinear sampled-data system, we make use of the approximate models of the system at each sampling instant to build a time-varying approximate model with which an appropriate controller is designed. This paper provides some sufficient conditions under which a controller stabilizing the approximate models can also stabilize the exact sampled-data system under any sufficiently small sampling period. With this method, we do not need to compute the complicated exact discrete-time model of the concerned system and significantly simplify the controller design. The major contribution of this method lies in extending the available results regarding the time-invariant sampled-data systems to the time-varying case. Moreover, this method enables us to analyze the influence of the precision of approximate models on the system performance. Copyright © 2016 John Wiley & Sons, Ltd.

Input-to-error stable observer for nonlinear sampled-data systems with application to one-sided Lipschitz systems

In this paper the design of sampled-data state observers for nonlinear plants is investigated under the effect of system and measurement disturbance signals. We establish general design principles using the standard approaches of (i) direct discrete-time design via approximation and (ii) discretization of a continuous-time observer (emulation). By interpreting the disturbances as exogenous inputs affecting the error dynamics, sufficient conditions are derived which ensure the input-to-state stability (ISS) of the observer error system in a semiglobal practical sense for the unknown exact discrete-time model. Next, we focus on systems whose vector fields are one-sided Lipschitz to develop constructive design techniques via linear matrix inequalities (LMIs). Numerical simulations of an academic example and a chaotic attractor corroborate the effectiveness of the proposed sampled-data estimators.

Discretización exacta de un robot móvil con retardo de transporte

En este trabajo se presenta la obtención del modelo exacto en tiempo discreto de un robot móvil tipo (2,0), bajo la consideración de la existencia de retardos de transporte en la señal de control, producidos por la propagación de las señales entre los sensores y actuadores del robot y el control remoto. El modelo obtenido es evaluado mediante simulación, comparando su desempeño con un modelo discreto aproximado que incluye también retardos de transporte y con el modelo en tiempo continuo del mismo sistema.

Sampled-data [formula omitted] fault detection and isolation for nonlinear systems in T–S form: An approximate model approach

A direct discrete-time design methodology for the sampled-data fault detection and isolation (FDI) problem is proposed for a nonlinear system in Takagi–Sugeno form. The generalized observer scheme is adopted, accompanied by a bank of the sensors' number of observers. A sufficient condition to find observer and residual gains, based on an accessible approximate—rather than unavailable exact—discrete-time model is proposed in terms of matrix inequalities so that it exhibits H−/H∞ performance and asymptotic stability. An algorithm involving a convex optimization is presented using the cone complementary linearization technique. We show that the FDI observer ensures (modified) H−/H∞ performance and Lagrange stability, when it is connected to the actual nonlinear system.