Showing papers by "Wpmh Maurice Heemels published in 2006"

Stabilizing Model Predictive Control of Hybrid Systems

Abstract: In this note, we investigate the stability of hybrid systems in closed-loop with model predictive controllers (MPC). A priori sufficient conditions for Lyapunov asymptotic stability and exponential stability are derived in the terminal cost and constraint set fashion, while allowing for discontinuous system dynamics and discontinuous MPC value functions. For constrained piecewise affine (PWA) systems as prediction models, we present novel techniques for computing a terminal cost and a terminal constraint set that satisfy the developed stabilization conditions. For quadratic MPC costs, these conditions translate into a linear matrix inequality while, for MPC costs based on 1, infin-norms, they are obtained as norm inequalities. New ways for calculating low complexity piecewise polyhedral positively invariant sets for PWA systems are also presented. An example illustrates the developed theory

A multi-disciplinary and model-based design methodology for high-tech systems

Abstract: System architecting for high-tech machines is currently performed by highly experienced individuals, who often use an intuitive approach to their craft. In order to allow better cooperation, and to enable the dissemination of experience and knowledge, a framework is needed in which the methods, modelling formalisms, techniques and tools used by system architects are captured. In this paper, such a framework is proposed. Different steps in a system architecting process are given, with appropriate techniques. Examples are given from a large scale research project investigating the design of a high-speed copier. Finally, the abstract framework is mapped to a dynamic workflow model closely resembling industrial practice.

Input-to-state stabilizing sub-optimal nonlinear MPC algorithms with an application to DC-DC converters

Abstract: This paper focuses on the synthesis of computationally friendly sub-optimal nonlinear Model Predictive Control (MPC) algorithms with guaranteed robust stability. The input-to-state stability framework is employed to analyze the robustness of the resulting MPC closed-loop systems. Two new sub-optimal nonlinear MPC schemes are proposed, based on a contraction argument and an artificial Lyapunov function, respectively. The developed theory is illustrated by applying it to control a Buck-Boost DC-DC converter. Copyright c ∞2006 IFAC

Analysis and experimental validation of processor load for event-driven controllers

Abstract: Event-driven controllers differ from the standard digital controllers as their sample times are generally not periodic (time equidistant). In literature several proposals for event-driven controllers are made in order to reduce the number of control updates and consequently the processor load needed for its implementation. This is possible without deteriorating the control performance significantly. However, experimental validation has not been presented in literature. This paper aims at filling this gap. Simulations, as well as experiments on a copier paper path test setup, show that a reduction in the number of control updates indeed results in a considerable reduction of the processor load, with only a small decrease of control performance. Furthermore, we present a method to predict the processor load very accurately, without having to implement the controller on a test setup.

5.3.2 On the Systematic Use of Budget‐Based Design

Abstract: In the majority of the engineering projects, the most important design decisions are taken at the early stages of the design. As these decisions have a considerable impact on the final implementation of the product, they ought to be made in a well-considered manner. The usage of higher-level methods to support making balanced decisions in initial stages of a design is considered very helpful. This paper deals with one of these methods: budget-based design. It is claimed that the systematic usage of budgets helps to speed-up the development process, to better assess project risks and results in better-founded design tradeoffs.

Squaring the circle: an algorithm for generating polyhedral invariant sets from ellipsoidal ones

Abstract: This paper presents a new (geometrical) approach to the computation of polyhedral positively invariant sets for general (possibly discontinuous) nonlinear systems, possibly affected by disturbances. Given a /spl beta/-contractive ellipsoidal set E, the key idea is to construct a polyhedral set that lies between the ellipsoidal sets /spl beta/E and E. A proof that the resulting polyhedral set is positively invariant (and contractive under an additional assumption) is given, and a new algorithm is developed to construct the desired polyhedral set. An advantage of the proposed method is that the problem of computing polyhedral invariant sets is formulated as a number of quadratic programming (QP) problems. The number of QP problems is guaranteed to be finite and therefore, the algorithm has finite termination. An important application of the proposed algorithm is the computation of polyhedral terminal constraint sets for model predictive control based on quadratic costs.

The use of the key driver technique in the design of copiers

Abstract: In the design of many of the complex products we encounter today it is important to remain focused on the essential customer objectives, which can be captured in terms of customer key drivers. In order to obtain a successful product these key drivers need to be related to the system requirements. A structured overview of the relationships between key drivers and system requirements is an effective means to support the design. This paper proposes the key driver technique and its use to create such an overview that is also highly convenient in requirements tracing. A stepwise approach is presented together with guidelines on how to obtain a key driver model. An industrial case study for a high-volume copier demonstrates the application and serves as a proof-of-concept for the key driver technique. The benefits, limitations and lessons learned are presented.

Stabilizing output feedback nonlinear model predictive control : an extended observer approach

Abstract: —Nonlinear Model Predictive Control (NMPC), generally based on nonlinear state space models, needs knowledge of the full state for feedback. However, in practice knowledge of the full state is usually not available. Therefore, an asymptotically stabilizing MPC scheme for a class of nonlinear discrete-time systems is proposed, which only requires knowledge of the output of the system for feedback. The presented output based NMPC scheme consists of an extended observer interconnected with an NMPC controller which represents a possibly discontinuous state feedback control law. Sufficient conditions for asymptotic stability of the system in closed-loop with the NMPC observer interconnection are derived using the discrete-time input-tostate stability framework. Moreover, it is shown that there always exist NMPC tuning parameters and observer gains, such that the derived sufficient stabilization conditions can be satisfied.

Convex Polyhedral Invariant Sets for Closed-Loop Linear MPC Systems

Abstract: Given an asymptotically stabilizing linear MPC controller, this paper proposes an algorithm to construct invariant polyhedral sets for the closed-loop system. Rather than exploiting an explicit form of the MPC controller, the approach exploits a recently developed DC (Difference of Convex functions) programming technique developed by the authors to construct a polyhedral set in between two convex sets. Here, the inner convex set is any given level set V(x) les gamma of the MPC value function (implicitly defined by the quadratic programming problem associated with MPC or explicitly computed via multiparametric quadratic programming), while the outer convex set is the level set of a the value function of a modified multiparametric quadratic program (implicitly or explicitly defined). The level gamma acts as a tuning parameter for deciding the size of the polyhedral invariant containing the inner set, ranging from the origin (gamma = 0) to the maximum invariant set around the origin where the solution to the unconstrained MPC problem remains feasible, up to the whole domain of definition of the controller (possibly the whole state space Ropfn) (gamma = inf). Potential applications of the technique include reachability analysis of MPC systems and generation of constraints to supervisory decision algorithms on top of MPC loops

The key driver method

Abstract: This chapter is a re-worked version of a paper for the International Conference on System Engineering and Applications (ICSSEA) 2006.

A Stabilizing Output Based Nonlinear Model Predictive Control Scheme

Abstract: In this paper we present an asymptotically stabilizing output feedback control scheme for a class of nonlinear discrete-time systems. The presented scheme consists of an extended observer interconnected with an NMPC controller which represents a possible discontinuous state feedback control law. Local asymptotic stability of the resulting closed-loop system is proven.

Practical stability of perturbed event-driven controlled linear systems

Abstract: Many plants are regulated by digital controllers that run at a constant sampling frequency, thereby requiring a high processor load for the computations. To guarantee a good control performance, such a high sampling frequency might be required at some periods of time, but not necessarily continuously. By using an event-driven control scheme that triggers the update of the control value only when the (tracking or stabilization) error is large, the average processor load can be reduced considerably. Although event-driven control can be effective from a CPU-load perspective, the analysis of such control schemes is much more involved than that of conventional schemes and is a widely open research area. This paper investigates the control performance of an event-driven controlled continuous-time linear system with additive disturbances in terms of practical stability (ultimate boundedness). By using the derived results, the event-driven controller can be tuned to get satisfactorily transient behavior and desirable ultimate bounds, while reducing the required average processor load for its implementation. Several examples illustrate the theory.

Observer design for an experimental rotor system with discontinuous friction

Abstract: In this paper we present an experimental observer design for a rotor system with friction. The model of the system exhibits set-valued static friction law with the Stribeck effect. As the model of the setup is non-smooth and non-Lipschitz, observer has to be designed using mathematical tools from convex analysis and the theory of differential inclusions. The designed observer guarantees that there exists a unique solution to the observer dynamics and that the estimated state converges to the true state of the system. Simulation and experimental results illustrate the design and performance of the observer in practice.

Min-max nonlinear model predictive control with guaranteed input-to-state stability

Abstract: —In this paper we consider discrete-time nonlinear systems that are affected, possibly simultaneously, by parametric uncertainties and disturbance inputs. The min-max model predictive control (MPC) methodology is employed to obtain a controller that robustly steers the state of the system towards a desired equilibrium. The aim is to provide a priori sufficient conditions for robust stability of the resulting closed-loop system via the input-to-state stability framework. First, we show that only input-to-state practical stability can be ensured in general for perturbed nonlinear systems in closed-loop with min-max MPC schemes and we provide explicit bounds on the evolution of the closed-loop system state. Then, we derive new sufficient conditions that guarantee input-to-state stability of the min-max MPC closedloop system, via a dual-mode approach. Keywords—Min-max, Nonlinear model predictive control, Input-to-state stability, Input-to-state practical stability

Threads of reasoning : a case study in printer control

Abstract: . In the design of technology intensive products like copiers, wafer steppers and televisions, one searches for a product that satisfies the product requirements as well as the business drivers. The main need in an early design phase is to bring structure in the typical chaos of uncertainty and the huge amount of realization options present. Potential realization choices all have advantages and disadvantages, which cause tensions and conflicts. The earlier the (essential) conflicts and tensions are identified, the better it is. Turning them from implicit to explicit helps the system architect in making the trade-off consciously or at least in selecting the most important tensions and conflicts that require further in-depth investigation. In this respect we demonstrate the effectiveness of a technique called "threads of reasoning". The illustrative case study is the design of the paper flow control (sensors, actuators, control architecture, etc.) in a high-volume copier/printer.

Robust control of networked control systems, with uncertain time-varying delays (draft)

Abstract: • A submitted manuscript is the author's version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers.

Threads of reasoning : a case study

Abstract: In the design of technology intensive products like copiers, wafer steppers and televisions, one searches for a product that satisfies the product requirements as well as the business drivers. The main need in an early design phase is to bring structure in the typical chaos of uncertainty and the huge amount of realization options present. Potential realization choices all have advantages and disadvantages, which cause tensions and conflicts. The earlier the (essential) conflicts and tensions are identified, the better it is. Turning them from implicit to explicit helps the system architect in making the trade-off consciously or at least in selecting the most important tensions and conflicts that require further in-depth investigation. In this respect we demonstrate the effectiveness of a technique called "threads of reasoning". The illustrative case study is the design of the paper flow control (sensors, actuators, control architecture, etc.) in a high-volume copier/printer.

An example of Zero robustness in Piecewise Affine Systems

Abstract: An example is presented in order to illustrate that nominally exponentially stable discrete-time PieceWise Affine (PWA) systems can have zero robustness [1] to arbitrarily small additive disturbances. It is shown that this is mainly due to the absence of a continuous Lyapunov function. The importance of this issue cannot be overstated since nominally stabilizing controllers are affected by perturbations when applied in practice. Moreover, many of the methods for synthesizing stabilizing state-feedback controllers for discrete-time PWA systems employ discontinuous (piecewise quadratic) Lyapunov functions, for example see [2, 3]. The discrete-time input-to-state stability framework [4] is used in order to develop an a posteriori robustness test, which boils down to solving a finite number of linear programming problems. The test can be used to check whether a specific nominally stable PWA system, possibly with a discontinuous Lyapunov function, has some (inherent) robustness to additive disturbances or not.

6.3.1 Threads of Reasoning: A Case Study

Abstract: In the design of technology intensive products like copiers, wafer steppers and televisions, one searches for a product that satisfies the product requirements as well as the business drivers. The main need in an early design phase is to bring structure in the typical chaos of uncertainty and the huge amount of realization options present. Potential realization choices all have advantages and disadvantages, which cause tensions and conflicts. The earlier the (essential) conflicts and tensions are identified, the better it is. Turning them from implicit to explicit helps the system architect in making the trade-off consciously or at least in selecting the most important tensions and conflicts that require further in-depth investigation. In this respect we demonstrate the effectiveness of a technique called “threads of reasoning”. The illustrative case study is the design of the paper flow control (sensors, actuators, control architecture, etc.) in a high-volume copier/printer.