Showing papers by "Wpmh Maurice Heemels published in 2008"

Analysis of event-driven controllers for linear systems

Abstract: Most research in control engineering considers periodic or time-triggered control systems with equidistant sample intervals. However, practical cases abound in which it is of interest to consider event-driven control in which the sampling is event-triggered. Although there are various benefits of using event-driven control like reducing resource utilization (e.g., processor and communication load), their application in practice is hampered by the lack of a system theory for event-driven control systems. To provide a first step in developing an event-driven system theory, this paper considers an event-driven control scheme for perturbed linear systems. The event-driven control scheme triggers the control update only when the (tracking or stabilization) error is large. In this manner, the average processor and/or communication load can be reduced significantly. The analysis in this paper is aimed at the control performance in terms of practical stability (ultimate boundedness). Several examples illustrate t...

Algebraic Necessary and Sufficient Conditions for the Controllability of Conewise Linear Systems

Abstract: The problem of checking certain controllability properties of even very simple piecewise linear systems is known to be undecidable. This paper focuses on conewise linear systems, i.e., systems for which the state space is partitioned into conical regions and a linear dynamics is active on each of these regions. For this class of systems, we present algebraic necessary and sufficient conditions for controllability. We also show that the classical results of controllability of linear systems and input-constrained linear systems can be recovered from our main result. Our treatment employs tools both from geometric control theory and mathematical programming.

Input-to-state stabilizing sub-optimal NMPC with an application to DC–DC converters

Abstract: This article focuses on the synthesis of computationally friendly sub-optimal nonlinear model predictive control (NMPC) algorithms with guaranteed robust stability. To analyse the robustness of the MPC closed-loop system, we employ the input-to-state stability (ISS) framework. To design ISS sub-optimal NMPC schemes, a new Lyapunov-based method is proposed. ISS is ensured via a set of constraints, which can be specified as a finite number of linear inequalities for input affine nonlinear systems. Furthermore, the method allows for online optimization over the ISS gain of the resulting closed-loop system. The potential of the developed theory for the control of fast nonlinear systems, with sampling periods below 1 ms, is illustrated by applying it to control a Buck-Boost DC–DC converter. Copyright © 2007 John Wiley & Sons, Ltd.

Observer Designs for Experimental Non-Smooth and Discontinuous Systems

Abstract: This brief presents the design and implementation of observer design strategies for experimental non-smooth continuous and discontinuous systems. First, a piece-wise linear observer is implemented for an experimental setup consisting of a harmonically excited flexible steel beam with a one-sided support which can be considered as a benchmark for a class of flexible mechanical systems with one-sided restoring characteristics. Second, an observer is developed for an experimental setup that describes a dynamic rotor system which is a benchmark for motion systems with friction and flexibility. In both cases, the implemented observers guarantee global asymptotic stability of the estimation error dynamic in theory. Simulation and experimental results are presented to demonstrate the performance of the observers in practice. These results support the use of (switched) observers to achieve state reconstruction for such non-smooth and discontinuous mechanical systems.

Stabilization of Networked Control Systems with large delays and packet dropouts

Abstract: We consider the stabilization problem for networked control systems (NCSs) with uncertain, time-varying network-induced delays and a bounded number of subsequent packet dropouts. A discrete-time model, describing a NCS with packet dropouts and time-varying delays, that can be both smaller and larger than the sampling interval, is presented. Based on this NCS model sufficient LMI conditions are proposed for the stability analysis and controller synthesis problem for two different controllers, i.e. a feedback controller that depends on both the state and the past control inputs and a state-feedback controller. The applicability of both controllers is compared. Moreover, the stability and controller synthesis LMIs allow for a performance analysis in terms of a lower bound for the transient decay rate of the response. The results are illustrated by application to a typical motion control example.

Optimized input-to-state stabilization of discrete-time nonlinear systems with bounded inputs

Abstract: In the problem of input-to-state stabilization of nonlinear systems, synthesis of input-to-state stabilizing feedback laws is usually carried out off-line. This results in a constant input-to-state stability (ISS) gain, which is guaranteed for the closed-loop system. As an alternative, we propose a finite dimensional optimization problem that allows for the simultaneous on-line computation of an ISS control action, and minimization of the ISS gain of the closed-loop system. The advantages of the developed controller are: ISS is guaranteed for any (feasible) solution of the optimization problem, constraints can be explicitly accounted for and feedback to disturbances is provided actively, on-line. The control scheme also has favorable computational properties for nonlinear systems affine in control. In this case the optimization problem can be formulated as a single quadratic or linear program.

Reconfigurable control of PWA systems with actuator and sensor faults: Stability

Abstract: A new approach to the reconfigurable control of piecewise affine (PWA) systems after actuator and sensor faults is presented. The approach extends the concept of virtual actuators and virtual sensors from linear to PWA systems on the basis of the fault-hiding principle. The weak fault-hiding goal is introduced as a relaxation of the asymptotic fault-hiding goal. Sufficient linear matrix inequality conditions for the existence of input-to-state stabilizing virtual actuators and sensors are given that lead to a tractable computational algorithm. The stability of the reconfigured closed-loop system is verified. The approach is evaluated using a system of interconnected tanks.

Null controllability of discrete-time linear systems with input and state constraints

Abstract: This paper presents necessary and sufficient conditions for null controllability of discrete-time linear systems subject to both input and state constraints. The classical results for linear systems without constraints by Kalman and Hautus and for linear systems with only input constraints by Evans, Nguyen and Sontag can be obtained from our main result as particular cases.

Observer-based control of discrete-time piecewise affine systems: Exploiting continuity twice

Abstract: Output-based feedback control of discrete-time hybrid systems is an important problem, as in practice it is rarely the case that the full state variable is available for feedback. A typical approach for output-based feedback design for linear and smooth nonlinear systems is to use certainty equivalence control, in which an observer and a state feedback controller (using the observer state) are combined. Although for linear systems and some classes of nonlinear systems, separation principles exist to justify this approach, for hybrid systems this is not the case. In this paper, we isolate a class of hybrid systems for which a systematic design procedure for certainty equivalence controllers including a separation principle will be presented. This class consists of discrete-time piecewise-affine (PWA) systems with continuous dynamics. In the design procedure, we will exploit the continuity of the PWA dynamics twice. Firstly, it will be used to establish input-to-state stability (ISS) w.r.t. measurement errors from ISS w.r.t. additive disturbances. This is a crucial step as the latter problem is much easier to tackle than the former. Secondly, continuity will be used in the observer design procedure to obtain a significantly simplified set of LMIs with respect to existing observer design approaches for PWA systems. All the design conditions will be formulated in term of LMIs, which can be solved efficiently, as is also illustrated by a numerical example.

Further results on "Robust MPC using Linear Matrix Inequalities"

Abstract: This paper presents a novelmethod for designing the terminal cost and the auxiliary control law (ACL) for robust MPC of uncertain linear systems, such that ISS is a priori guaranteed for the closed-loop system. The method is based on the solution of a set of LMIs. An explicit relation is established between the proposed method and \(\mathcal{H}_\infty\) control design. This relation shows that the LMI-based optimal solution of the \(\mathcal{H}_\infty\) synthesis problem solves the terminal cost and ACL problem in inf-sup MPC, for a particular choice of the stage cost. This result, which was somehow missing in the MPC literature, is of general interest as it connects well known linear control problems to robust MPC design.

An LMI-based L 2 gain performance analysis for reset control systems

Abstract: In this paper we present a general LMI-based analysis method to determine an upperbound on the L2 gain performance of a reset control system These computable sufficient conditions for L2 stability, based on piecewise quadratic Lyapunov functions, are suitable for all LTI plants and linear-based reset controllers, thereby generalizing the results available in literature Our results furthermore extend the existing literature by including tracking and measurement noise problems by using strictly proper input filters We illustrate the approach by a numerical example

Output-feedback control of Lur’e-type systems with set-valued nonlinearities: A Popov-criterion approach

Abstract: This paper presents an output-feedback controller design for Lur'e-type systems with set-valued nonlinearities in the feedback loop based on a generalization of a Popov-like criterion. Hereto, we introduce the concept of absolute input-to-state stability (ISS) that generalizes the well-known absolute stability property. The latter concept is used to design a state-feedback controller that renders the closed-loop system absolutely ISS and, therewith, robust to uncertainties in the nonlinearities and disturbances, such as measurement noise. Furthermore, an output-feedback controller design is constructed by exploiting the ISS property, where a model- based observer is used to estimate the system state. The control strategy is applied to a mechanical motion system with non-collocation of actuation and dry friction for which well-known strategies such as direct friction compensation fail. The effectiveness of the proposed output-feedback control strategy is shown in simulations.

Reference governors for controlled belt restraint systems

Abstract: This paper presents a novel control strategy for real-time controlled restraint systems. Todaypsilas restraint systems typically include a number of airbags, and a three-point seat belt with load limiter and pretensioner. In the class of realtime controlled restraint systems, the restraint actuator settings are continuously manipulated during the crash. The control strategy developed here is based on reference management, in which a nonlinear device - a reference governor - is added to a primal closed loop controlled system. This governor determines an optimal setpoint in terms of injury reduction and constraint satisfaction by solving a constrained optimization problem. Prediction of the vehicle motion, required to predict future constraint violation, is included in the design and is based on linear regression of past crash data. Simulation results with a MADYMO model show that a significant injury reduction is possible, without prior knowledge of the crash. Furthermore, it is shown that the algorithms are sufficiently fast to be implemented on-line.

Switching control in active vibration isolation

Abstract: In this paper, a switching control approach is studied with applications to active vibration isolation. The control design is based on the concept of input-to-state stability of the resulting discontinuous feedback system with respect to disturbances. The switching control strategy demonstrates improved disturbance rejection under feedback combined with a small sensitivity to noise in the absence of such feedback. Herein the control effort needed to achieve improved performance is substantially reduced. To access the performance of the closed-loop system, the control scheme is tested on a commercially available isolation system.

Tracking control for piecewise linear systems using an error space approach: A case-study in sheet control

Abstract: This paper presents the design of tracking controllers for piecewise linear systems, with application to sheet control in a printer paper path. The approach that we will take is based upon an error space approach, which is derived from linear systems theory. We will show that due to the discontinuity in the piecewise linear system, the resulting model in error space consists of both flow conditions, describing the dynamics in each regime, and jump conditions, describing the error dynamics at the switching boundaries. Two types of controllers are proposed that result in either full or partial linearization of the closed-loop error dynamics. To show the effectiveness of the control design approach in practice, the sheet controllers are implemented on an experimental paper path setup.