Sampled-data Control Systems Research Articles

Periodic sampled-data-based dynamic model control of switched linear systems

Sampled-data control as an effective mean of digital control has shown its prominent superiority in most practical industries and a zero-order holder (ZOH) is often introduced to maintain continuity of control in the field of sampled-data control system. However, it decreases the control accuracy in a certain extent since the state will be held invariably within each sampling interval. In order to improve the control accuracy, this paper proposes a dynamic model-based control strategy instead of ZOH for a class of switched sampled-data control systems. The model, which is built by abstracting the plant knowledge, is located at the controller side. The controller is set up based on the model state and it provides control input to the switched system. A fixed sampling period is adopted, under which a hybrid-dwell time switching condition is revealed by taking into account asynchronous switching. With reasonable design of switching condition, exponential stability of the closed-loop system can be guaranteed. Finally, advantages of our proposed method are presented through a numerical example by comparing with the result of ZOH-based control.

Stability of Truncated Sampled-Data Control Systems With Impulsive Effects

This article considers the stability problem of truncated sampled-data control systems with impulsive effects. We propose the concept of average sampling interval (ASI), in which the constraint on the lower/upper bound of sampling intervals is removed to handle the sampling intervals from the holistic perspective. Then, in the framework of the input delay method, we transform the addressed system into an equivalent switched time-delay system subject to the impulsive effects that result from the truncated sampled-data control law. Interestingly, it is shown that the truncation of the sampled-data control input, which is an extension of the classical zero-order hold function, can play a stabilizing role in the presence of impulsive effects. Next, based on the ASI concept, the idea of average truncated length is introduced and the corresponding relaxed stability criteria are derived for the truncated sampled-data control systems. Particularly, the potential destabilizing impact of impulsive effects on the stability is theoretically revealed. It is also shown that under certain conditions, a truncated sampled-data system can remain stable if the magnitude of the impulsive effects is sufficiently small. Finally, two illustrative examples are presented to show the validity and also the advantages of the obtained results.

Finite dimensional approximation to muscular response in force-fatigue dynamics using functional electrical stimulation

Recent dynamical models, based on the seminal work of V. Hill, allow to predict the muscular response to functional electrostimulation (FES), in the isometric and non-isometric cases. The physical controls are modeled as Dirac pulses and lead to a sampled-data control system, sampling corresponding to times of the stimulation, where the output is the muscular force response. Such a dynamics is suitable to compute optimized controls aiming to produce a constant force or force strengthening, but is complex for real time applications. The objective of this article is to construct a finite dimensional approximation of this response to provide fast optimizing schemes for the design of a smart electrostimulator for muscular reinforcement or rehabilitation. It is an on-going industrial project based on force-fatigue models, validated by experiments. Moreover it opens the road to application of optimal control to track a reference trajectory in the joint angular variable to produce movement in the non-isometric models.

Stability Criteria for Fuzzy-Based Sampled-Data Control Systems via a Fractional Parameter-Based Refined Looped Lyapunov Functional

This article is concerned with the stability analysis for the fuzzy-based sampled-data control (SDC) systems, which is based on a fractional parameter-based refined looped-Lyapunov functional (RLLF). To do this, with the help of the Takagi–Sugeno fuzzy method, a SDC can be designed. To derive sufficient criteria, a RLLF with information about the sampling period is proposed. In the RLLF, a fractional parameter is introduced and it has more information on the splitted sampling intervals and delayed states with a fractional parameter. The derived criteria guarantee the asymptotic stability of the proposed system with a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> attenuation level. To validate the derived conditions, a state-space model of nonlinear permanent magnet synchronous motor is proposed. Besides, comparison examples are conducted for analyzing the less conservatism of the merit of the proposed methods. Finally, the simulation outcomes are illustrated the superiority of the work.

Practical Prescribed-Time Sampled-Data Control of Linear Systems With Applications to the Air-Bearing Testbed

This article studies the practical prescribed time sampled-data control problem for input-constrained linear time invariant continuous time systems. By using the solution to a parametric Lyapunov equation, a bounded linear time-varying (LTV) sampled-data controller is designed to solve such a problem. In addition, stability analysis and performance analysis of the closed-loop sampled-data control system are presented by using the methodology of scalarization. Finally, the developed LTV sampled-data state controller is utilized to the whole physical simulation system of air-bearing testbed and experimental results verify the effectiveness of the proposed approach.

Stability of Zeros for Sampled-Data Models with Triangle Sample and Hold Implemented by Zero-Order Hold

This paper deals with the stability characteristics of zeros for sampled-data models with a class of triangle sample and hold realized by a traditional zero-order hold. For any controlled models in the modern industrial system, using a digital control strategy has been shown to provide the means to achieve the assigned objectives. In this process, one must utilize the sample and hold device to obtain the sampled-data models. Previous studies have shown that the triangle sample and hold can improve the stability properties of zeros of a sampled-data control system compared with zero-order hold. However, it is difficult to use triangle sample and hold in practice. In this paper, an approximated method of using triangle sample and hold is proposed. More importantly, on the basis of that method, we explicitly derive the corresponding accurate sampled-data model of controlled models. In addition, we also provide the expression for sampling zeros and the theorem for the stability of a linear control system in the fast sampling process. The results of this paper show that the proposed method has the same advantages as the accurate one. Finally, theoretical findings are validated through numerical simulations with different considerations.

Exponential stability of sampled-data control systems with enhanced average sampling interval

The stabilisation of the sampled-data control systems is addressed to tolerate large sampling intervals that tend to destroy the system's stability. A new sampling sequence is constructed from two sequences with two different sampling time intervals, where the short one corresponds to a stable system, while the long one produces an unstable system. The decay rate of the state trajectory of the former is utilised to overcome the growth rate of the latter, such that the resulting system with mixed sampling intervals is globally exponentially stable. A sufficient condition for stabilisation is given. It is applicable to the system with a single sampling interval under the missing data scenario. The examples are given to illustrate the proposed results.

Sampled-Data Model Predictive Control

This paper focus on model predictive control (MPC) design in the context of sampled-data control systems with full-state measurements. It is shown that recent results on this area can be successfully generalized to cope with sampled-data MPC. The open-loop plant is subjected to polytopic parameter uncertainty and at sampling times a controlled output variable satisfies a set of convex constraints. A guaranteed H2 performance index with infinity horizon is minimized such as the feedback control preserves asymptotic stability and feasibility. The design conditions are expressed though differential linear matrix inequalities (DLMIs). Continuous-time systems are treated with no kind of discrete-time modeling approximation. Comparisons with classical methods from the literature dealing with continuous-time systems are presented and discussed. Examples are included for illustration.

Add-On Type Data-Driven Ripple-Free Dual-Rate Control Design Based on the Null Space of Steady-State Step Responses

In the present study, a data-driven ripple-free design is proposed for a dual-rate sampled-data control system in which the sampling interval of the plant output is longer than the holding interval of the control input. The objective of the present study is to improve the steady-state intersample response without changing the sampled response and without using the plant model. To achieve the objective directly from controlled data, an add-on input based on the null space of steady-state step responses to an existing control system is used. The open-loop or closed-loop system to obtain the step response is assumed to be stable. In the present study, a two-degree-of-freedom design is given that redesigns the intersample output response independently of the steady-state sampled output response. In a numerical example, the proposed method is applied to a linear time-invariant single-input single-output stable system, where intersample ripples are eliminated using the add-on input that is independent of the existing sample output response in steady state.

Delay-Dependent Stability Improvement for Networked Control Systems: a Sampled Data Approach

This paper concerns the stability conditions and controller design for sampled-data networked control systems (NCSs) model subject to network communication delays, the main objective is to guarantee the maximum allowable upper bounds of network-induced time-varying delays that keep the NCSs stable. First, Lyapunov-Krasovskii functional with simple and double-integral terms is constructed considering both upper and lower bounds of network delay. Then, less conservative Linear Matrix Inequalities (LMIs) stability conditions are established using null terms to introduce free weighting matrices based on the Leibniz-Newton formula. Furthermore, Finsler's lemma is used for the relaxation of the obtained LMI's stability conditions using slack decision variables. It is also used to decouple Lyapunov-Krasovskii matrices from the system ones. The application of the proposed approach for different NCSs gives higher upper delay bounds compared with other methods.

Decentralized Resilient $H_{\infty}$ Load Frequency Control for Cyber-Physical Power Systems Under DoS Attacks

This paper designs a decentralized resilient H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> load frequency control (LFC) scheme for multi-area cyber-physical power systems (CPPSs). Under the network-based control framework, the sampled measurements are transmitted through the communication networks, which may be attacked by energy-limited denial-of-service (DoS) attacks with a characterization of the maximum count of continuous data losses (resilience index). Each area is controlled in a decentralized mode, and the impacts on one area from other areas via their interconnections are regarded as the additional load disturbance of this area. Then, the closed-loop LFC system of each area under DoS attacks is modeled as an aperiodic sampled-data control system with external disturbances. Under this modeling, a decentralized resilient H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> scheme is presented to design the state-feedback controllers with guaranteed H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance and resilience index based on a novel transmission interval-dependent loop functional method. When given the controllers, the proposed scheme can obtain a less conservative H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance and resilience index that the LFC system can tolerate. The effectiveness of the proposed LFC scheme is evaluated on a one-area CPPS and two three-area CPPSs under DoS attacks.

Hidden Markov model-based asynchronous quantized sampled-data control for fuzzy nonlinear Markov jump systems

This paper investigates the problem of asynchronous control for nonlinear Markov jump systems on the basis of fuzzy quantized sampled-data controller. The modes of the designed fuzzy controller and the modes of the original system are asynchronously operational, which has been widely used in the real world and expressed by a hidden Markov model. Based on the mode-dependent Lyapunov-Krasovskii functional (LKF) approach and some improved inequalities, a novel criterion is established to ensure the stochastic stability of fuzzy nonlinear Markov jump systems. As a particular case, with the help of novel LKF and new integral inequalities, new stability condition with less conservatism and low computational complexity for nonlinear quantized sampled-data control systems is obtained. Finally, the validity and merits of the developed method are shown by two numerical examples.

Exponential stability for nonlinear fractional order sampled-data control systems with its applications

This paper investigates some topics about fractional order nonlinear systems with sampled-data. First, according to comparison principle and Laplacian transform method, sufficient conditions are derived to guarantee that the fractional order sampled-data control systems are globally and exponentially stable. Then, based on the stability results above and some properties of fractional order integral and derivative, the sampled-data controller is designed for the fractional order neural networks. Furthermore, the synchronization criteria of fractional order dynamical networks with sampled-data communications are obtained based on matrix technique and above analysis methods. Finally, three numerical examples are provided to illustrate the effectiveness of the derived results.

An Input Delay Approach to Interval Type-2 Fuzzy Exponential Stabilization for Nonlinear Unreliable Networked Sampled-Data Control Systems

This paper is devoted to the interval type-2 (IT2) fuzzy exponential stability for nonlinear networked sampled-data control systems with random communication links. By using the input delay approach, the designed networked IT2 fuzzy sampled-data controller can be applied in the continuous-time controlled plant, and the continuous-time Lyapunov-Krasovskii functional (LKF) is constructed. Based on the LKF theory, the stability analysis is conducted in the sense of mathematical expectation, and the sufficient conditions are determined in terms of the linear matrix inequalities. Then, the IT2 fuzzy networked controller is developed such that the networked closed-loop control system is exponentially stable. Finally, the simulation results are used to demonstrate the efficiency of the proposed design. The merits of the proposed algorithm are also shown by some comparative results.

Intersample optimization in a sampled-data control system using the redundancy of a dual-rate system

The present study discusses the design method for controlling a single-input/single-output linear time-invariant dual-rate system, where the sampling interval of the plant output is longer than the holding interval of the control input. In such a dual-rate system, the intersample output might oscillate even when the sampled output converges to the reference input in the steady state. In a conventional ripple-free method, an existing control law is extended by introducing an exogenous variable, which is independent of the discrete-time sampled response, and the exogenous variable is designed for eliminating the steady-state intersample ripples without changing the existing sampled response. In another method, since a control law is designed such that the intersample performance is optimized, the intersample ripples are eliminated in the transient as well as steady states. However, the preservation of an existing sampled response is not taken into account. The present study proposes a new design method for eliminating the intersample ripples subject to the existing sampled response. In the proposed method, the continuous-time index is optimized subject to the existing discrete-time response. As a result, the intersample ripples are eliminated in the transient as well as steady states, and the existing discrete-time sampled response is maintained. The proposed method is compared to the conventional dual-rate design methods in numerical examples, and the effectiveness of the method is demonstrated.

Stability Analysis of Sampled-Data Load Frequency Control Systems With Multiple Delays

The load frequency control (LFC) system equipped with communication networks includes both sampled-data and time-delay characteristics. How to consider both characteristics effectively in stability analysis is of great importance to obtain accurate results. In this brief, we investigate the delay-dependent stability of sampled-data systems with multiple delays by separately considering the effects of sampling and delays. We first build a discrete-time model for an LFC system with both conventional units and energy storage systems, where the effect of time-varying delays is modeled as matrix uncertainty. Based on this model, we propose a stability criterion for delay margin computation using the region-division technique. A heuristic algorithm is further developed to enhance the computational efficiency and accuracy of the proposed criterion. Case studies are carried out to show the effectiveness and advantages of the proposed method.

Stability and Stabilization of Aperiodic Sampled-Data Systems Subject to Control Input Saturation: A Set Invariant Approach

This article proposes a new method to deal with the stability analysis and stabilization of aperiodic sampled-data control systems subject to input saturation. An impulsive system representation is employed, with a linear flow and a nonlinear jump dynamics, such that the evolution of the system at the sampling instants can be modeled by a difference inclusion defined by two set-valued maps. We show that to ensure the asymptotic stability it is sufficient to verify that a Lyapunov function decreases by a certain amount only at a grid of possible values for the sampling interval, as long as the increase of the function in continuous-time is conveniently bounded. Simulation results compare our approach with other ones.

Continuous-time synthesizing robust sampled-data dynamic output-feedback controllers for uncertain nonlinear systems in Takagi–Sugeno form: A descriptor representation approach

This paper discusses controller design techniques for robust sampled-data dynamic output-feedback (DOF) for nonlinear systems in the Takagi–Sugeno (T–S) fuzzy form with parametric uncertainties and L2/L∞ disturbances. We perform the sampled-data syntheses in a continuous-time domain based on an augmented sampled-data closed-loop model in descriptor form. Hence, the investigation does not require any (approximate) discrete-time model of a T–S fuzzy system, which is a significant obstacle in nonlinear sampled-data control system designs. Moreover, various cross-product terms among system matrices, to-be-designed DOF controller matrices, and other decision variables are reduced, yielding single-stage linear matrix inequality-based design conditions.

Improved Stabilization Criteria for Sampled-Data Control Systems via a Less Conservative Looped-Functional Method

Improved Stabilization Criteria for Sampled-Data Control Systems via a Less Conservative Looped-Functional Method

Integrated stabilisation policy over multipath routing‐enabled network

In this study, a sampled-data networked control system over a multipath routing-enabled network is investigated, where each delivered signal in a path suffers a random delay. For such a system, the mean square stabilisation problem is considered under the joint design of the event-driven strategy on the actuator side and the control policy on the decision-maker side. The contributions of this study are twofold. First, by pre-defining an application time as an event-triggering parameter, the sampled-data system is transformed into a stochastic form with input delay and packet dropout. When the probability distribution F ( ⋅ ) of random delay is known a priori, the close form of packet dropout rate is proposed and a set of necessary and sufficient stabilisation conditions are developed simultaneously. When F ( ⋅ ) is unknown, the reduced system is an uncertain dynamic system. Utilising matrix polynomials, a verifiable criterion is derived for stabilising the uncertain system, which is also necessary and sufficient. Second, for the scalar system, the close form of allowable sampling period bound is developed in terms of F ( ⋅ ) and system parameters.