Recent developments in computer and communication technologies have led to a new type of large-scale resource-constrained wireless embedded control systems. It is desirable in these systems to limit the sensor and control computation and/or communication to instances when the system needs attention. However, classical sampled-data control is based on performing sensing and actuation periodically rather than when the system needs attention. This paper provides an introduction to event- and self-triggered control systems where sensing and actuation is performed when needed. Event-triggered control is reactive and generates sensor sampling and control actuation when, for instance, the plant state deviates more than a certain threshold from a desired value. Self-triggered control, on the other hand, is proactive and computes the next sampling or actuation instance ahead of time. The basics of these control strategies are introduced together with a discussion on the differences between state feedback and output feedback for event-triggered control. It is also shown how event- and self-triggered control can be implemented using existing wireless communication technology. Some applications to wireless control in process industry are discussed as well.

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An introduction to event-triggered and self-triggered control

Event-triggered control (ETC) is a control strategy that is especially suited for applications where communication resources are scarce. By updating and communicating sensor and actuator data only when needed for stability or performance purposes, ETC is capable of reducing the amount of communications, while still retaining a satisfactory closed-loop performance. In this paper, an ETC strategy is proposed by striking a balance between conventional periodic sampled-data control and ETC, leading to so-called periodic event-triggered control (PETC). In PETC, the event-triggering condition is verified periodically and at every sampling time it is decided whether or not to compute and to transmit new measurements and new control signals. The periodic character of the triggering conditions leads to various implementation benefits, including a minimum inter-event time of (at least) the sampling interval of the event-triggering condition. The PETC strategies developed in this paper apply to both static state-feedback and dynamical output-based controllers, as well as to both centralized and decentralized (periodic) event-triggering conditions. To analyze the stability and the L2-gain properties of the resulting PETC systems, three different approaches will be presented based on 1) impulsive systems, 2) piecewise linear systems, and 3) perturbed linear systems. Moreover, the advantages and disadvantages of each of the three approaches will be discussed and the developed theory will be illustrated using a numerical example.

/pdf/periodic-event-triggered-control-for-nonlinear-systems-4semh9nxhe.pdf

Periodic event-triggered control for nonlinear systems

Brief paper: A state-feedback approach to event-based control

There are many communication imperfections in networked control systems (NCS) such as varying transmission delays, varying sampling/transmission intervals, packet loss, communication constraints and quantization effects. Most of the available literature on NCS focuses on only some of these aspects, while ignoring the others. In this paper we present a general framework that incorporates communication constraints, varying transmission intervals and varying delays. Based on a newly developed NCS model including all these network phenomena, we will provide an explicit construction of a continuum of Lyapunov functions. Based on this continuum of Lyapunov functions we will derive bounds on the maximally allowable transmission interval (MATI) and the maximally allowable delay (MAD) that guarantee stability of the NCS in the presence of communication constraints. The developed theory includes recently improved results for delay-free NCS as a special case. After considering stability, we also study semi-global practical stability (under weaker conditions) and performance of the NCS in terms of Lp gains from disturbance inputs to controlled outputs. The developed results lead to tradeoff curves between MATI, MAD and performance gains that depend on the used protocol. These tradeoff curves provide quantitative information that supports the network designer when selecting appropriate networks and protocols guaranteeing stability and a desirable level of performance, while being robust to specified variations in delays and transmission intervals. The complete design procedure will be illustrated using a benchmark example.

/pdf/networked-control-systems-with-communication-constraints-5ak0mdbgn7.pdf

Networked Control Systems With Communication Constraints: Tradeoffs Between Transmission Intervals, Delays and Performance

Most event-triggered controllers available nowadays are based on static state-feedback controllers. As in many control applications full state measurements are not available for feedback, it is the objective of this paper to propose event-triggered dynamical output-based controllers. The fact that the controller is based on output feedback instead of state feedback does not allow for straightforward extensions of existing event-triggering mechanisms if a minimum time between two subsequent events has to be guaranteed. Furthermore, since sensor and actuator nodes can be physically distributed, centralized event-triggering mechanisms are often prohibitive and, therefore, we will propose a decentralized event-triggering mechanism. This event-triggering mechanism invokes transmission of the outputs in a node when the difference between the current values of the outputs in the node and their previously transmitted values becomes “large” compared to the current values and an additional threshold. For such event-triggering mechanisms, we will study closed-loop stability and L∞-performance and provide bounds on the minimum time between two subsequent events generated by each node, the so-called inter-event time of a node. This enables us to make tradeoffs between closed-loop performance on the one hand and communication load on the other hand, or even between the communication load of individual nodes. In addition, we will model the event-triggered control system using an impulsive model, which truly describes the behavior of the event-triggered control system. As a result, we will be able to guarantee stability and performance for event-triggered controllers with larger minimum inter-event times than the existing results in the literature. We illustrate the developed theory using three numerical examples.

Output-Based Event-Triggered Control With Guaranteed ${\cal L}_{\infty}$ -Gain and Improved and Decentralized Event-Triggering

http://www.dct.tue.nl/New/Heemels/HeeGor_99_CEP.pdf

Asynchronous measurement and control: a case study on motor synchronization

An output-error identification method is used to determine, on-line, the parameters of an induction motor. A key step in the identification procedure is the transformation of measured signals to rotor coordinates. All machine parameters, except the stator resistance, can be identified in rotor coordinates in each operating condition. Taking into account the skin-effect in the identification yields better estimations of the motor parameters. Computer simulations, as well as experimental results from a 45 kW induction motor, demonstrate that the identification scheme's performance is satisfactory over a wide range of operating conditions. >

Skin effect impact on induction motor parameters estimation using an output-error identification method

An identification procedure is presented which estimates, based on measurements of voltages, currents and velocity, the physical parameters of an induction machine. The identifiability of different machine parameters under different steady state operating conditions is investigated. When no velocity measurements are available, the identification method can still be used and yields an estimate of the mechanical velocity and the machine parameters, provide that the input signal contains sufficient information. >

Simultaneous estimation of induction machine parameters and velocity

Parameter estimation for induction machines

Torque and speed of inverter fed squirrel cage induction motors are estimated in this paper, based on just measured voltages and currents Neither shaft sensors nor machine parameters are needed for the presented estimation method When current- and stator terminal flux-vectors are projected onto a rotating reference frame according to the Fish Method, a flux-fish and a current-fish curve of almost identical shapes result Differences between these curves incorporate machine parameter and loading influences A consistent periodic current-fish movement caused by 'slipping-by' rotor-bars is used to determine the shaft speed and relative shaft position relative to the airgap flux >

R.J.A. Gorter

Papers

Asynchronous measurement and control: a case study on motor synchronization

Skin effect impact on induction motor parameters estimation using an output-error identification method

Simultaneous estimation of induction machine parameters and velocity

Parameter estimation for induction machines

Fish Method based state estimation for controlling inverter driven machines