Sampling Instants Research Articles

On the Asymptotic Hyperstability of Linear Time-Invariant Continuous-Time Systems under a Class of Controllers Satisfying Discrete-Time Popov’s Inequality

This paper is concerned with the property of asymptotic hyperstability of a continuous-time linear system under a class of continuous-time nonlinear and perhaps time-varying feedback controllers belonging to a certain class with two main characteristics; namely, (a) it satisfies discrete-type Popov’s inequality at sampling instants and (b) the control law within the intersample period is generated based on its value at sampling instants being modulated by two design weighting auxiliary functions. The closed-loop continuous-time system is proved to be asymptotically hyperstable, under some explicit conditions on such weighting functions, provided that the discrete feed-forward transfer function is strictly positive real.

Periodic event-triggered robust output feedback control for nonlinear uncertain systems with time-varying disturbance

This paper investigates the periodic event-triggered robust output feedback control problem for a class of nonlinear uncertain systems subject to time-varying disturbance. By means of the feedback domination approach and disturbance compensation technique, a new framework of periodic event-triggered robust control strategy is developed in the form of output feedback, which encompasses a discrete-time event-triggering transmission scheme that is only intermittently monitored at sampling instants and a discrete-time output feedback controller consisting of a set of linear difference equations. The proposed robust method may reduce the communication resource utilization as compared to the non-event triggering schemes while maintaining a desirable closed-loop system performance even in the presence of a general class of time-varying disturbance and nonlinear uncertainties. The closed-loop system under the proposed control scheme is actually modeled as a hybrid system, and it is shown that the global practical stability of the closed-loop hybrid system is guaranteed by selecting a sufficiently large scaling gain and a sufficiently small sampling period. Finally, the experimental results on a DC–DC buck power converter are presented to illustrate the effectiveness of the proposed control approaches.

Non-uniform Multi-rate Estimator based Periodic Event-Triggered Control for resource saving

This paper proposes a systematic non-uniform multi-rate estimation and control framework for a periodic event-triggered system which is subject to external disturbance and sensor noise. When the disturbance dynamic model is available, and in order to efficiently estimate the state variable and disturbance from non-uniform slow-rate measurements, a time-varying Kalman filter is designed. When the disturbance dynamic model is not available, a disturbance observer is proposed as an alternative approach. Both the Kalman filter and the disturbance observer are proposed in a non-uniform multi-rate format. Such disturbance estimation enables faster controller updating in spite of slower measurement. Interlacing techniques are used in the control system to uniformly distribute the computational load at each fast sampling instance. Compared to the conventional time-triggered sampling paradigm, the control solution is able to reduce the resource utilization, while maintaining a satisfactory control performance. The proposed control solution will reduce the number of transmissions among devices, which enhances the energy and computational efficiency. Simulation results are provided to validate the effectiveness and benefits of the proposed control algorithms.

Periodic event-triggered control of nonlinear systems using overapproximation techniques

In event-triggered control, the control task consisting of sampling the plant’s output and updating the control input is executed whenever a certain event function exceeds a given threshold. The event function typically needs to be monitored continuously, which is difficult to realize in digital implementations. This has led to the development of periodic event-triggered control (PETC), in which the event function is only evaluated periodically. In this paper, we consider general nonlinear continuous event-triggered control (CETC) systems, and present a method to transform the CETC system into a PETC system. In particular, we provide an explicit sampling period at which the event function is evaluated and we present a constructive procedure to redesign the triggering condition. The latter is obtained by upper-bounding the evolution of the event function of the CETC system between two successive sampling instants by a linear time-invariant system and then by using convex overapproximation techniques. Using this approach, we are able to preserve the control performance guarantees (e.g., asymptotic stability with a certain decay rate) of the original CETC system.

Networked control of a power system: A non-uniform sampling approach

This article deals with the damping of low-frequency power systems oscillations using a networked controller on a smart grid. We assume that the network channel is band-limited and has random communication delay whose probability distribution can be found. To mitigate the effect of delay on control system performance, the measurements from the system are sampled at a random and non-uniform period but the inputs are updated at a faster and constant rate. This makes the closed-loop control system a stochastic switching system. A framework to analyze the mean square stability of the closed-loop system is developed and a switching observer-based controller is designed to ensure the stability of the system at random sampling instants. A case study has been performed using the Western-System-Coordinating-Council (WSCC) 3-machines, 9-bus system for verification of the technique. The contribution of the paper is a bandwidth efficient delay compensation technique and its application to power systems stability enhancement in a smart grid.

Leader-Following Consensus of Multi-Agent Systems With Switching Networks and Event-Triggered Control

This paper addresses the event-based leader-following consensus of a class of multi-agent systems with switching networks. Fully distributed event-triggered functions are proposed to select the sampling instants automatically. Detailed algorithms are given to design the feedback gains and coupling strength. The positive lower bound of the sampling intervals is captured to exclude Zeno behaviours. Finally, simulations are also carried out to verify the effectiveness of the event-triggered control scheme.

Simultaneous three-wavelength unwrapping using external digital holographic multiplexing module.

We present an external interferometric setup that is able to simultaneously acquire three wavelengths of the same sample instance without scanning or multiple exposures. This setup projects onto the monochrome digital camera three off-axis holograms with rotated fringe orientations, each from a different wavelength channel, without overlap in the spatial-frequency domain, and thus allows the full reconstruction of the three complex wavefronts from the three wavelength channels. We use this new setup for three-wavelength phase unwrapping, allowing phase imaging of thicker objects than possible with a single wavelength, but without the increased level of noise. We demonstrate the proposed technique for micro-channel profiling and label-free cell imaging.

Further Results on Stabilization of Chaotic Systems Based on Fuzzy Memory Sampled-Data Control

This note investigates sampled-data control for chaotic systems. A memory sampled-data control scheme that involves a constant signal transmission delay is employed for the first time to tackle the stabilization problem for Takagi–Sugeno fuzzy systems. The advantage of the constructed Lyapunov functional lies in the fact that it is neither necessarily positive on sampling intervals nor necessarily continuous at sampling instants. By introducing a modified Lyapunov functional that involves the state of a constant signal transmission delay, a delay-dependent stability criterion is derived so that the closed-loop system is asymptotically stable. The desired sampled-data controller can be achieved by solving a set of linear matrix inequalities. Compared with the existing results, a larger sampling period is obtained by this new approach. A simulation example is presented to illustrate the effectiveness and conservatism reduction of the proposed scheme.

An improved fragmentation approach to sampled-data synchronization of chaotic Lur’e systems

This paper considers the sampled-data synchronization problem for two identical chaotic Lur’e systems. Under aperiodic samplings, the output of the chaotic Lur’e systems is available only at sampling instants. An improved fragmentation approach addresses a system description of the fragmented state located between the last sampling instant and present time. The sampled output of the fragmented state system is updated only at sampling instants, like the identical chaotic Lur’e systems. Thus, utilizing the additional information on the fragmented state system helps in handling the sampling interval. In the looped-functional framework, a sampled-data synchronization criterion is proposed for stability analysis and control synthesis about stabilization in terms of linear matrix inequalities. Simulation results show the effectiveness of the proposed criterion.

Stochastic self-triggered model predictive control for linear systems with probabilistic constraints

A stochastic self-triggered model predictive control (SSMPC) algorithm is proposed for linear systems subject to exogenous disturbances and probabilistic constraints. The main idea behind the self-triggered framework is that at each sampling instant, an optimization problem is solved to determine both the next sampling instant and the control inputs to be applied between the two sampling instants. Although the self-triggered implementation achieves communication reduction, the control commands are necessarily applied in open-loop between sampling instants. To guarantee probabilistic constraint satisfaction, necessary and sufficient conditions are derived on the nominal systems by using the information on the distribution of the disturbances explicitly. Moreover, based on a tailored terminal set, a multi-step open-loop MPC optimization problem with infinite prediction horizon is transformed into a tractable quadratic programming problem with guaranteed recursive feasibility. The closed-loop system is shown to be stable. Numerical examples illustrate the efficacy of the proposed scheme in terms of performance, constraint satisfaction, and reduction of both control updates and communications with a conventional time-triggered scheme.

Robust multi-tracking of heterogeneous multi-agent systems with uncertain nonlinearities and disturbances

A robust multi-tracking problem is solved for heterogeneous multi-agent systems with uncertain nonlinearities and disturbances. The nonlinear function satisfies a Lipschitz condition with a time-varying gain, the integral of which is bounded by a linear function. A distributed impulsive protocol is proposed, where the position data and velocity data of desired trajectories are needed only at sampling instants. Based on the system decomposition technique, the error dynamic system of achieving multi-tracking is decomposed into two impulsive dynamic systems with vanishing perturbation and nonvanishing perturbation, respectively. Constructing a nominal model, then the multi-tracking problem is converted into the stability of impulsive dynamic system with nonvanishing perturbation under some conditions. It is proved that the proposed impulsive protocol is robust enough to solve the multi-tracking problem. Numerical examples are presented to illustrate the effectiveness of our theoretical results.

Low-Noise Isolated Digital Shunt for Precision Class-D Power Amplifiers

Power electronic converters regularly employ isolated analog-to-digital converters (ADCs) for the acquisition of voltage/current signals that are required for their digital control systems. In precision power converters, such as those required in nanometer-accuracy positioning systems for integrated circuit manufacturing, the noise content of the measured signals is critical since it leads to undesired noise in the power converter output signals due to the feedback system's high sensor noise sensitivity. This letter illustrates how sampling jitter, i.e., stochastic deviations of the ADC's sampling instants from their ideal occurrences, which is mainly caused by the digital signal isolators used to isolate the ADC control signals, introduces a measurement error and critically influences the signal to noise ratio (SNR) of an isolated current measurement at the output of a half-bridge. Jitter figures of commonly used digital signal isolators are measured, as these values are rarely available in the literature. It is revealed that RMS jitter varies significantly between the analyzed devices, from 13 ps up to 250 ps, even among those that utilize similar isolation techniques. Thus, in a second step, it is analytically derived how the half-bridge inductor, and the related half-bridge current ripple, directly influences the SNR of the current measurement. Using the resulting simple design equations, which are also verified with numeric simulations, the half-bridge inductor can be designed to significantly reduce the half-bridge current measurement noise, by a factor of up to $\approx$ 0.6 in common measurement configurations.

Nonlinear discrete-time multirate adaptive control of non-linear vibrations of smart beams

The nonlinear adaptive digital control of a smart piezoelectric beam is considered. It is shown that in the case of a sampled-data context, a multirate control strategy provides an appropriate framework in order to achieve vibration regulation, ensuring the stability of the whole control system. Under parametric uncertainties in the model parameters (damping ratios, frequencies, levels of non linearities and cross coupling, control input parameters), the scheme is completed with an adaptation law deduced from hyperstability concepts. This results in the asymptotic satisfaction of the control objectives at the sampling instants. Simulation results are presented.

An Asynchronous Operation Approach to Event-Triggered Control for Fuzzy Markovian Jump Systems With General Switching Policies

This paper investigates the problem of event-triggered control for a class of fuzzy Markov jump systems with general switching policies. A novel event-triggered scheme is proposed to improve the transmission efficiency at each sampling instance. Each transition rate allows to be unknown, known, or only its uncertain domains value is known. With the help of a tailored technique to bind the uncertain terms and an asynchronous operation approach to tackle the fuzzy system and fuzzy controller, sufficient conditions for the resulting fuzzy Markovian jump systems are established in terms of coupled linear matrix inequalities. Finally, an example is given to illustrate the validity of the developed technique.

Aperiodic sampled-data control for LPV systems under input saturation

Abstract This paper addresses the problem of aperiodic sampled-data control of linear parameter varying (LPV) systems under input saturation. It is explicitly assumed that plant scheduling parameter can continuously vary between two sampling instants, while the control signal is computed using the measurement of this parameter only at the sampling instants. Assuming an affine parameter dependence, conditions based on the use of a parameter dependent (PD) looped-functional and a PD generalized sector approach, are proposed to compute a sampled-data LPV state feedback control law that ensures the regional asymptotic stability of the closed-loop system. LMI-based optimization procedures to maximize an estimate of the region of attraction of the origin or the allowable bound on the intersampling interval for a guaranteed region of stability are proposed.

Unified Approach to the Analysis and Performance Evaluation of Sampled-Data Control Applied to Nonlinear Systems

Abstract This paper presents a general and unified approach to the stability and performance analysis of Markov jump nonlinear systems governed by a state feedback sampled-data control law, where the sampling instants are evenly spaced. Initially, the closed-loop system is equivalently described as a hybrid system. Then, mean square stability and performance optimization of the general nonlinear hybrid system are addressed. This study is based on the existence of a solution of a Two-Point Boundary Value Problem (TPBVP) composed by a Hamilton-Jacobi-Bellman Equation (HJBE) and defined in the time interval corresponding to two consecutive sampling instants. Solving this TPBVP implies that the performance index of interest is exactly evaluated. Additionally, a numerical method is proposed to cope with the H2 framework. In this case, a guaranteed upper bound to the referred index is obtained. Examples illustrates the proposed theoretical results.

Sampled-Data Based State and Parameter Estimation for State-Affine Systems with Uncertain Output Equation

The problem of sampled-data observer design is addressed for a class of state- and parameter-affine nonlinear systems. The main novelty in this class lies in the fact that the unknown parameters enter the output equation and the associated regressor is nonlinear in the output. Wiener systems belong to this class. The difficulty with this class of systems comes from the fact that output measurements are only available at sampling times causing the loss of the parameter-affine nature of the model (except at the sampling instants). This makes existing adaptive observers inapplicable to this class of systems. In this paper, a new sampled-data adaptive observer is designed for these systems and shown to be exponentially convergent under specific persistent excitation (PE) conditions that ensure system observability and identifiability. The new observer involves an inter-sample output predictor that is different from those in existing observers and features continuous trajectories of the state and parameter estimates.

New CO2 Concentration Predictions and Spectral Estimation Applied to the Vostok Ice Core

The Vostok ice core provides measurements of the CO2 concentration during the last $414\times 10^{3}$ years (yr). Estimations of power spectra show peaks, with the strongest one corresponding to a time period of around $100\times 10^{3}$ yr. In this paper, a new reconstruction method from irregular sampling is used, allowing more accurate estimation of spectral peaks. This method intrinsically decomposes the analyzed signal as a sum of sines, providing amplitudes but also phase measurements of periodic tendencies (due to the nature of the studied phenomena). This decomposition can be conducted with noisy and inaccurate measurements of the sampling instants and the concentrations. The widely used Vostok data were chosen as an example, but the method could also be applied to data from other places (e.g., dome C, Antarctica) or to study other phenomena as nitrogen dioxide NO2, methane CH4, oxygen isotope 18O (closely linked to temperature), deuterium 2H, or dust concentrations.

Demodulation Approach for Slowly Sampled Sensorless Field-Oriented Control Systems Enabling Multiple-Frequency Injections

This paper describes a demodulation approach based on the least squares method for a saliency-based position estimation in slowly sampled field-oriented control systems. The proposed approach focuses on the sensorless control of electrical drives in which the sample rate of the control task chosen is slower than both the maximum possible update rate of the phase voltages and the maximum possible sample rate of the phase current measurement by a multiple. Under those conditions, it is possible to inject multiple-frequency carrier signals between two successive control sampling instances without affecting the control. Furthermore, a combined demodulation of these signals is enabled by exploiting the constant manipulated variables of the field-oriented control system during the injection sequence. With the proposed method, the signal-to-noise-ratio of the calculated rotor position as well as the acoustic noise produced by signal injections can be optimized. The approach is implemented in a field-oriented control for permanent magnet synchronous machines and is verified in experiments.

Cascade observer design for a class of uncertain nonlinear systems with delayed outputs

This paper proposes a state observer with a cascade structure for a class of nonlinear systems in the presence of uncertainties in the state equations and an arbitrarily long delay in the outputs. The design of the observer is achieved under an appropriate set of assumptions allowing to establish the ultimate boundedness of the observation error. Indeed, a suitable expression of the asymptotic observation error, involving the delay, the bound of the uncertainties and the Lipschitz constant of the system nonlinearities, is derived. Besides, it is shown that this ultimate bound is a decreasing function of the cascade length and is equal to zero in the uncertainty-free case. The observer design is first carried out in the case where the output measurements are continuously available and subsequently extended to the case where the outputs are available only at (non equally spaced) sampling instants. The performance of the proposed observer and its main properties are highlighted through illustrative simulation results involving an academic example.