Networked control systems in the presence of scheduling protocols and communication delays

This paper develops the time-delay approach to Networked Control Systems (NCSs) in the presence of variable transmission delays, sampling intervals and communication constraints. The system sensor nodes are supposed to be distributed over a network. Due to communication constraints only one node output is transmitted through the communication channel at once. The scheduling of sensor information towards the controller is ruled by a weighted Try-Once-Discard (TOD) or by Round-Robin (RR) protocols. Differently from the existing results on NCSs in the presence of scheduling protocols (in the frameworks of hybrid and discrete-time systems), we allow the communication delays to be greater than the sampling intervals. A novel hybrid system model for the closed-loop system is presented that contains {\it time-varying delays in the continuous dynamics and in the reset conditions}. A new Lyapunov-Krasovskii method, which is based on discontinuous in time Lyapunov functionals is introduced for the stability analysis of the delayed hybrid systems. Polytopic type uncertainties in the system model can be easily included in the analysis. The efficiency of the time-delay approach is illustrated on the examples of uncertain cart-pendulum and of batch reactor

Model Reduction for Aperiodically Sampled Data Systems

Two approaches to moment matching based model reduction of aperiodically sampled data systems are given. The term "aperiodic sampling" is used in the paper to indicate that the time between two consecutive sampling instants can take its value from a pre-specified finite set of allowed sampling intervals. Such systems can be represented by discrete-time linear switched (LS) state space (SS) models. One of the approaches investigated in the paper is to apply model reduction by moment matching on the linear time-invariant (LTI) plant model, then compare the responses of the LS SS models acquired from the original and reduced order LTI plants. The second approach is to apply a moment matching based model reduction method on the LS SS model acquired from the original LTI plant, and then compare the responses of the original and reduced LS SS models. It is proven that for both methods, as long as the original LTI plant is stable, the resulting reduced order LS SS model of the sampled data system is quadratically stable. The results from two approaches are compared with numerical examples

Permanent Magnet Synchronous Motor control via Parameter Dependent Relay Control

International audienceThe article presents a novel control strategy for the control of Permanent Magnet Synchronous Motor (PMSM). The approach is motivated by the fact that PMSM are usually controlled by relays and thus only a finite set of control inputs is available. However in classical control design the use of Pulse-Width Modulation (PWM) ignores the relay nature of the actuators. Here we propose a direct relay control. As PMSM may be modeled as Linear Parameter Varying (LPV) systems, we propose a Parameter Dependent Relay (PDR) control. A design based on Linear Matrix Inequalities (LMI) allows to derive the switching surfaces, which depend on the motor position. The theory described is illustrated by simulations results

Observer analysis and synthesis for perturbed Lipschitz systems under noisy time-varying measurements

International audienceIn this paper the observer synthesis problem is studied for nonlinear Lipschitz systems with noisy time-varying sampling and bounded state perturbations. To establish criteria for robust convergence of the observer, we model the impact of sampling by a reset integrator operator. First, generic conditions for the input-to-state stability of a sampled-data system are presented. Second, it is shown how to derive a tractable numerical criterion for the synthesis of a sampled-data Luenberger observer. Then, new conditions for robustness analysis of a known observation gain are given

On Finite-time Stabilization via Relay Feedback Control

International audience— The problem of finite-time stabilization of multi-input linear system by means of relay feedback is considered. A new control design procedure, which combines convex embedding technique with implicit Lyapunov function method, is developed. The issues of practical implementation of the obtained implicit relay feedback are discussed. Theoretical result is supported by numerical simulation

Observer synthesis under time-varying sampling for Lipschitz nonlinear systems

International audienceIn this work, the problem of observation of continuous-time nonlinear Lipschitz systems under time-varying discrete measurements is considered. This class of systems naturally occurs when continuous processes are observed through digital sensors and information is sent via a network to a computer for state estimation. Since the network introduces variations in the sampling time, the observer must be designed so that it takes them into account. Here impulsive observers, which make instantaneous correction when information is received, are investigated. Moreover, we consider time-varying observer gains adapting to the varying sampling interval. In order to deal with both continuous-time and discrete-time dynamics, a new hybrid model is used to state the problem and establish the convergence of the proposed observer. First, generic conditions are provided using a hybrid Lyapunov function. Then, a restriction of the generic Lyapunov function is used to establish tractable conditions that allows the analysis and synthesis of an impulsive gain

Design of robust structurally constrained controllers for MIMO plants with time-delays

International audience— The structurally constrained controller design problem for linear time invariant neutral and retarded time-delay systems (TDS) is considered in this paper. The closed-loop system of the plant and structurally constrained controller is modelled by a system of delay differential algebraic equations (DDAEs). A robust controller design approach using the existing spectrum based stabilisation and the H-infinity norm optimisation of DDAEs has been proposed. A MATLAB based tool has been made available to realise this approach. This tool allows the designer to select the sub-controller input-output interactions and fix their orders. The results obtained while stabilising and optimising two TDS using structurally constrained (decentralised and overlapping) controllers have been presented in this paper

Discrete and intersample analysis of systems with aperiodic sampling

International audienceThis article addresses the stability analysis of linear time invariant systems with aperiodic sampled-data control. Adopting a difference inclusion formalism, we show that necessary and sufficient stability conditions are given by the existence of discrete-time quasi-quadratic Lyapunov functions. A constructive method for computing such functions is provided from the approximation of the necessary and sufficient conditions. In practice, this leads to sufficient stability criteria under LMI form. The inter-sampling behavior is discussed there: based on differential inclusions, we provide continuous-time methods that use the advantages of the discrete-time approach. The results are illustrated by numerical examples that indicate the improvement with regard to the existing literature

Vector Lyapunov Function based Stability for a Class of Impulsive Systems

International audienceThis paper contributes to the exponential stability analysis for impulsive dynamical systems based on a vector Lyapunov function and its divergence operator. The method relies on a 2D time domain representation. The results are applied to analyze the exponential stability of linear impulsive systems based on LMIs. Some examples illustrate the feasibility of the proposed approach

Observer-based Control for Linear Sampled-Data Systems: An Impulsive System Approach

International audienceThis paper deals with the sampled-data control problem based on state estimation for linear sampled-data systems. An impulsive system approach is proposed based on a vector Lyapunov function method. Observer-based control design conditions are expressed in terms of LMIs. Some examples illustrate the feasibility of the proposed approach