Showing papers by "Wpmh Maurice Heemels published in 2012"

An introduction to event-triggered and self-triggered control

Abstract: 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.

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

Abstract: 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.

Dynamic programming formulation of periodic event-triggered control: Performance Guarantees and co-design

Abstract: While potential benefits of choosing the transmissions times in a networked control system based on state or event information have been advocated in the literature, few general methods are available that guarantee closed-loop improvements over traditional periodic transmission strategies. In this paper, we propose event-triggered controllers that guarantee better quadratic discounted cost performance than periodic control strategies using the same average transmission rate. Moreover, we show that the performance of a method in the line of previous Lyapunov based approaches is within a multiplicative factor of periodic control performance, while using less transmissions. Our approach is based on a dynamic programming formulation for the co-design problem of choosing both transmission decisions and control inputs in the context of periodic event-triggered control for linear systems. A numerical example illustrates the advantages of the proposed method over traditional periodic control.

FPGA Implementations of Piecewise Affine Functions Based on Multi-Resolution Hyperrectangular Partitions

Abstract: In this paper we propose a digital architecture suited for fast, low-power and small-size electronic implementation of PieceWise Affine (PWA) functions defined over n-dimensional domains partitioned into multi-resolution hyperrectangles. The point location problem, which requires most of the computational effort, is solved through an orthogonal search tree, which is easily and efficiently implementable. In the case of domains partitioned into single-resolution hyperrectangles, a simpler and even faster architecture is proposed. After introducing the new architectures, their key features are discussed and compared to previous architectures implementing PWA functions with domains partitioned into different types of polytopes. Case studies concerning the FPGA implementation of so-called explicit Model Predictive Control (MPC) laws for constrained linear systems are used as benchmarks to compare the different architectures.

Scheduling measurements and controls over networks — Part I: Rollout strategies for protocol design

Abstract: We consider networked control systems where nodes (sensors, actuators, and controller) are connected via a communication network that allows only one user to transmit at a given time. We tackle the scheduling problem of deciding which node should access the network at each transmission time so as to optimize a quadratic performance objective. Using the framework of dynamic programming, we propose a rollout strategy by which the node elected to transmit at each step is the one that leads to optimal performance over a lookahead horizon assuming that from then on nodes transmit in a periodic order. The proposed strategy leads to a protocol in which a conic state partition determines which node transmits at each step and which can outperform any given periodic protocol. Moreover, we show that some of the protocols previously proposed in the literature, such as the Maximum Error First and the dynamic protocols, can be viewed as rollout strategies for a certain dynamic programming problem. The advantages of using rollout strategies are illustrated by a numerical example.

Approximation of explicit model predictive control using regular piecewise affine functions : an input-to-state stability approach

Abstract: Piecewise affine (PWA) feedback control laws defined on general polytopic partitions, as for instance obtained by explicit model predictive control, will often be prohibitively complex for fast systems. In this work the authors study the problem of approximating these high-complexity controllers by low-complexity PWA control laws defined on more regular partitions, facilitating faster on-line evaluation. The approach is based on the concept of input-to-state stability (ISS). In particular, the existence of an ISS Lyapunov function (LF) is exploited to obtain a priori conditions that guarantee asymptotic stability and constraint satisfaction of the approximate low-complexity controller. These conditions can be expressed as local semidefinite programs or linear programs, in case of 2-norm or 1, ∞-norm-based ISS, respectively, and apply to PWA plants. In addition, as ISS is a prerequisite for our approximation method, the authors provide two tractable computational methods for deriving the necessary ISS inequalities from nominal stability. A numerical example is provided that illustrates the main results.

Scheduling measurements and controls over networks — Part II: Rollout strategies for simultaneous protocol and controller design

Abstract: We consider a networked control system where a plant is connected to a remote controller via a shared network that allows only one user to transmit at a given time. At each transmission time, the controller decides between sampling one of the plant's sensors or transmitting control data to the plant. We tackle the problem of simultaneously designing a policy for scheduling decisions and a policy for control inputs so as to optimize a quadratic objective. Using the framework of dynamic programming, we propose a rollout strategy by which the scheduling and control decisions are determined at each transmission time as the ones that lead to optimal performance over a given horizon assuming that from then on controller and sensors transmit in a periodic order and the control law is a standard optimal law for periodic systems. We show that this rollout strategy results in a protocol where scheduling decisions are based on the state estimate and error covariance matrix of a Kalman estimator, and must be determined on-line. We contrast the solution to this problem with the solution to the seemingly similar sensor scheduling problem where optimal scheduling decisions can be determined off-line. We highlight how the protocol obtained from the rollout algorithm can be implemented in a distributed way in broadcast networks. Moreover, it follows by construction of rollout algorithms that our proposed scheduling method can outperform any periodic scheduling of transmissions.

Tracking control of mechanical systems with a unilateral position constraint inducing dissipative impacts

Abstract: In this paper, the tracking control problem is considered for mechanical systems with unilateral constraints with dissipative impacts. In these systems, impacts are triggered at the exact moment when the constraint becomes active. Typically, a small time mismatch is introduced between the impacts of the plant and the reference, even if this trajectory is arbitrarily close to the reference. Consequently, the Euclidean tracking error cannot behave stable in the sense of Lyapunov, such that standard tracking control approaches are unfeasible. However, desirable tracking behaviour does not imply that the Euclidean error vanishes asymptotically over time. We design continuous-time controllers that can handle the impact time mismatch and achieve accurate tracking of reference trajectories containing dissipative impacts for mechanical systems with a unilateral constraint. The behaviour of the resulting closed-loop dynamical system is illustrated with an exemplary bouncing ball system.

Decentralized static output-feedback control via networked communication

Abstract: This paper provides an approach to the design of decentralized switched output-feedback controllers for large-scale linear plants where the controllers, sensors and actuators are connected via a shared communication network subject to time-varying transmission intervals and delays. Due to the communication medium being shared, it is impossible to transmit all control commands and measurement data simultaneously over the communication network. As a consequence, a protocol is needed to orchestrate what data is sent over the network at each transmission instant. To effectively deal with the shared communication medium using static controllers, we adopt a switched controller structure that switches based on available control inputs at each transmission time. By taking a discrete-time switched linear system perspective, we are able to derive a general model that captures all these networked and decentralized control aspects. The proposed synthesis method is based on decomposing the closed-loop model into a multi-gain switched static output-feedback form. This decomposition allows for the formulation of linear matrix inequality based synthesis conditions which, if satisfied, provide stabilizing switched controllers, which are both decentralized and robust to network effects. A numerical example illustrates the aforementioned developed theory.

Nonlinear control for stabilization of small neoclassical tearing modes in ITER

Abstract: In this paper, the feasibility of feedback stabilization of neoclassical tearing modes at small island sizes, corresponding to otherwise unstable island sizes in ITER scenario 2, is demonstrated. The islands are stabilized by application of electron cyclotron resonance heating and current drive in a regime where the application of current drive in open loop normally results in a complete suppression of the island. By applying current drive in closed loop with feedback of real-time measurements of the island width, complete suppression is avoided and the island is stabilized at a specific reduced size. In contrast to complete suppression, control of islands at a specific size will allow the manipulation of a plasma's current density profile in hybrid scenarios. Three conceptual (non-)linear feedback controllers with varying complexity, performance, robustness and required model knowledge are introduced. Simulations show the theoretical feasibility of small island stabilization at a specific reduced width. The controllers are applied to the generalized Rutherford equation, which governs the island evolution subject to electron cyclotron current drive. A strategy for the gradual implementation of the controllers is suggested. Stabilization of small islands by feedback control will allow the use of system identification to extend the model knowledge on the evolution of small islands, and in addition will extend the operational regime.

Extension and evaluation of model-based periodic event-triggered control

Abstract: Periodic event-triggered control (PETC) is a control strategy that combines ideas from conventional periodic sampled-data control and event-triggered control. By communicating periodically sampled sensor and controller data only when needed to guarantee stability and performance properties, PETC is capable of reducing the number of transmissions significantly, while still retaining a satisfactory closed-loop behavior. In this paper, we provide an extension of an existing model-based PETC strategy for linear systems by including an (approximate) disturbance model. This extension can further enhance communication savings in the presence of disturbances. In addition, we evaluate the extended model-based PETC strategy by comparing this strategy to the standard model-based PETC and to a model-based periodic time-triggered control (PTTC) strategy. In this PTTC strategy, data is transmitted at fixed sampling times. For the evaluation, we present techniques for stability and ℓ2-gain performance analysis for both the PETC strategy and the PTTC strategy. Finally, the advantage of the (extended) PETC strategy over the PTTC strategy will be demonstrated by providing numerical examples.

Compensation-based control for lossy communication networks

Abstract: In this paper we are concerned with the stability analysis and the design of stabilizing compensation-based control algorithms for networked control systems (NCSs) that exhibit packet dropouts. We propose a new type of model-based dropout compensator, which depends on the local dropout history, and we provide LMI-based conditions for their synthesis. The analysis and design framework includes stochastic models to describe the packet dropout behavior in both the sensor-to-controller and controller-to-actuator channel. Via examples we demonstrate the significantly improved robustness with respect to packet dropouts using the proposed dropout compensator, compared to using the zero strategy and the hold strategy.

Emulation-based tracking solutions for nonlinear networked control systems

Abstract: We investigate emulation-based tracking control for nonlinear networked control systems (NCS) affected by disturbances We consider a general scenario in which the network is used to ensure the communication between the controller, the plant and the reference system generating the desired trajectory to be tracked The communication constraints induce nonvanishing errors (in general) on the feedforward term and the output of the reference system These network-induced errors affect the convergence of the tracking error As a consequence, available results on the stabilization of equilibrium points for NCS are not applicable Therefore, we develop an appropriate hybrid model and we give sufficient conditions on the closed-loop system, the communication protocol and an explicit bound on the maximum allowable transmission interval (MATI) guaranteeing that the tracking error converges to the origin up to some errors due to both the external disturbances and the aforementioned non-vanishing network-induced errors Our results cover a large class of the so-called uniformly globally asymptotically stable protocols which include the well-known round-robin and try-once-discard protocols We also introduce a new dynamic protocol suitable for tracking control

Tracking control of mechanical systems with impacts

Abstract: In this paper controllers are designed such that the state trajectories of mechanical systems with impacts converge to a reference trajectory that contains impacts. The impact times of the plant will typically not coincide with those of the reference, such that the Euclidean tracking error intrinsically behaves in an unstable manner. Therefore, an alternative approach is needed and we propose to study the convergence of a non-Euclidean tracking error measure that corresponds to the intuitive notion of tracking: impact times of the plant converge to those of the reference, and the plant follows the reference away from the impacts. Sufficient conditions for asymptotic stability in terms of this tracking error are presented, and the results are illustrated with a bouncing ball example.