Automatica

This brief shows how a min–max MPC with bounded additive uncertainties and a quadratic cost function results in a piecewise affine and continuous control law. Proofs based on properties of the cost function and the optimization problem are given. The boundaries of the regions in which the state space can be partitioned are also treated. The results are illustrated by an example.

Ahatract-We investigate the existence and uniqueness of robust time-optimal control solutions of flexible structures for rest-torest motion. We show that several robust time-optimal control designs for flexible systems are equivalent to traditional nonrobust time-optimal controls for difirent systems. This equivalence implies that the robust time-optimal controllers must then have all the properties that are known about traditional timeoptimal controllers. Further, many of the numerical methods developed for generating time-optimal commands are directly applicable to designing robust time-optimal commands. 0

It has been veri"ed that a controllable series capacitor with a suitable control scheme can improve transient stability and help to damp electromechanical oscillations. A question of great importance is the selection of the input signals and a control strategy for this device in order to damp power oscillations in an e!ective and robust manner. Based on Lyapunov theory a control strategy for damping of electromechanical power oscillations in a multi-machine power system is derived. Lyapunov theory deals with dynamical systems without inputs. For this reason, it has traditionally been applied only to closed-loop control systems, that is, systems for which the input has been eliminated through the substitution of a predetermined feedback control. However, in this paper, we use Lyapunov function candidates in feedback design itself by making the Lyapunov derivative negative when choosing the control. This control strategy is called control Lyapunov function for systems with control inputs. Also, two input signals for this control strategy are used. The "rst one is based on local information and the second one on remote information derived by the single machine equivalent method. : S 0 0 0 5 -1 0 9 8 ( 0 1 ) 0 0 0 9 9 -1

Two alternative solutions to the generalized predictive control (GPC) design problem are given for the case when the output horizon is larger than or equal to the plant order. First, using multirate models of the discrete-time plant, we present a state-space solution that does not require state observers or Riccati equation iterations for its implementation. Second, it is shown, via simple algebraic manipulations, that the key prediction equation used for GPC can be easily derived from the transfer function coefficients effectively replacing the Diophantine equation recursions by the inversion of a lower triangular matrix.

A continuous finite-time control scheme for rigid robotic manipulators is proposed using a new form of terminal sliding modes. The robustness of the controller is established using the Lyapunov stability theory. Theoretical analysis and simulation results show that faster and high-precision tracking performance is obtained compared with the conventional continuous sliding mode control method.

The problem of controlling large scale systems, usually divided into subsystems controlled by different agents, is usually solved using cooperative distributed control schemes, where the agents share open-loop information in order to improve closed-loop performance, (Rawlings and Mayne 2009, Chapter 6). In this paper we proposed a cooperative distributed linear model predictive control strategy applicable to any finite number of subsystems, which is able to steer the system to any admissible set point in an admissible way. Feasibility is ensured under any changing of the target steady state. The proposed controller is applied to a four tanks system.

Non-minimum phase tracking control is studied for boost and buck-boost power converters. A sliding mode control algorithm is developed to track directly a causal voltage tracking profile given by an exogenous system. The approximate causal output non-minimum phase asymptotic tracking in non-linear boost and buck-boost power converters is addressed via sliding mode control using a dynamic sliding manifold (DSM). Use of DSM allows the stabilization of the internal dynamics when the output tracking error tends asymptotically to zero in the sliding mode. The sliding mode controller with DSM links features of conventional sliding mode control (insensitivity to matched non-linearities and disturbances) and a conventional dynamic compensator (accommodation to unmatched disturbances). Numerical examples demonstrate the effectiveness of the sliding mode controller even for a known time-varying load. Copyright © 2003 John Wiley & Sons, Ltd.

The maneuvering problem involves two tasks. The first, called the geometric task, is to force the system output to converge to a desired path continuously parametrized by a scalar θ. The second task, called the dynamic task, is to satisfy a desired dynamic behavior along the path. In this paper, this dynamic behavior is further specified as a speed assignment for θ(t). While the main concern is to satisfy the geometric task, the dynamic task ensures that the system output follows the path with the desired speed. An adaptive recursive design technique is developed for a parametrically uncertain nonlinear plant describing the dynamics of a ship. First the geometric part of the problem is solved. Then an update law is constructed that bridges the geometric design with the dynamic task. The design procedure is performed and tested by several experiments for a model ship in a marine control laboratory. c°2004 Elsevier Science Ltd. All rights reserved.

High level control of dynamic positioning systems on marine vessels using hybrid controller are developed to extend the operational weather window for marine operations to harsh environments. The types of hybrid controller considered are multi-output PID controllers with position measurements, and multi-output PID and acceleration feedback controllers with position and acceleration measurements. Numerical simulations and experiments in addition to stability

The output maneuvering problem involves two tasks. The first, which is the geometric task, is to force the output to converge to a desired path parametrized by a continuous scalar variable θ. The second task is to satisfy a desired speed assignment along the path. The main concern is to satisfy the geometric task. However, the speed assignment will ensure that the output follows the path with sufficient speed. A recursive control design technique is developed for nonlinear plants in vectorial strict feedback form of any relative degree. First the geometric part of the problem is solved. Then an update law is constructed that bridges the geometric design with the speed assignment. An extra degree of freedom is provided for an operator to specify the speedθ. A computer simulation with a marine vessel is performed to illustrate the design. Copyright c°2002 IFAC

This paper deals with the problem of synthesizing or designing a feedback controller of xxed dynamic order for a linear time-invariant plant for a "xed plant, as well as for an uncertain family of plants containing parameter uncertainty, so that stability, robust stability and robust performance are attained. The desired closed-loop speci"cations considered here are given in terms of a target performance vector representing a desired closed-loop design. In general, these point targets are unattainable with a "xed-order controller. By enlarging the target from a "xed-point set to an interval set the solvability conditions are relaxed and a solution is enabled. Results from the parametric robust control literature can be used to design the interval target family so that the poles and zeros of the closed-loop system are guaranteed to remain in a prescribed region of the complex plane, and closed-loop performance, measured for instance in the H norm are attained, even when plant uncertainty is present. It is shown that it is possible to devise a computationally simple linear programming approach that attempts to meet the desired closed-loop speci"cations. The approach developed here gives the entire set of controllers attaining the speci"cations as a convex set and also can be recast to give the lowest-order controller attaining speci"cations. 0005-1098/99/$ -see front matter 1999 Elsevier Science Ltd. All rights reserved. PII: S 0 0 0 5 -1 0 9 8 ( 9 9 ) 0 0 0 8 0 -1

In this paper, several instrumental variable (IV) and instrumental variable-related methods for closed-loop system identification are considered and set in an extended IV framework. Extended IV methods require the appropriate choice of particular design variables, as the number and type of instrumental signals, data prefiltering and the choice of an appropriate norm of the extended IV-criterion. The optimal IV estimator achieves minimum variance, but requires the exact knowledge of the noise model. For the closed-loop situation several IV methods are put in an extended IV framework and characterized by different choices of design variables. Their variance properties are considered and illustrated with a simulation example.

The widely used cascade speed control scheme for thyristor driven DC-motors can be significantly improved by applying adaptive and robust control methods to compensate for unmeasurable variations of their mechanical and electrical characteristics.

This paper presents a new method to perform fault diagnosis for data-correlation based process monitoring. As alternative to the traditional contribution plot method, reconstruction-based contribution of fault detection indices is proposed. The monitored indices are SP E, T 2 and a combined index ϕ. The lack of diagnosability of traditional contributions is analyzed for the case of single sensor faults with large fault magnitudes, whereas for the same case the proposed reconstruction-based contributions guarantee correct diagnosis. Monte Carlo simulation results are provided for the case of modest fault magnitudes by randomly assigning fault sensors and fault magnitudes.

In Part I of this paper, we presented the fundamentals of the theory of IDA-PBC. In this part, we discuss the main new results and the practical applications of this control design approach as well as the current open problems and future directions.

A coordinate-free description for dynamic systems described by explicit (nonlinear) difference equations in one independent variable via a differential geometric framework is presented. Based on this covariant approach suitable geometric objects for discrete-time dynamics are introduced. Especially, the observability along a trajectory is discussed and transformations to normal forms are derived. In addition, the obtained (local) observability criteria can be checked by computer algebra algorithms. Some examples illustrate the proposed approach.

We consider stochastic discrete-time systems with multiplicative noise which are controlled by dynamic output feedback and subjected to blockdiagonal stochastic parameter perturbations. Stability radii for these systems are characterized via scaling techniques and it is shown that for real data, the real and the complex stability radii coincide. In a second part of the paper we investigate the problem of maximizing the stability radii by dynamic output feedback. Necessary and su cient conditions are derived for the existence of a stabilizing compensator which ensures that the stability radius is above a prespeci ed level. These conditions consist of parametrized matrix inequalities and a coupling condition.

We propose a class of discrete-time dynamic average consensus algorithms that allow a group of agents to track the average of their reference inputs. The convergence results rely on the input-to-output stability properties of static average consensus algorithms and require that the union of communication graphs over a bounded period of time be strongly connected. The only requirement on the set of reference inputs is that the maximum relative deviation between the nth-order differences of any two reference inputs be bounded for some integer n ≥ 1.

In classical time domain Box-Jenkins identification discrete-time plant and noise models are estimated using sampled input/output signals. The frequency content of the input/output samples covers uniformly the whole unit circle in a natural way, even in case of prefiltering. Recently, the classical time domain Box-Jenkins framework has been extended to frequency domain data captured in open loop. The proposed frequency domain maximum likelihood (ML) solution can handle (i) discrete-time models using data that only covers a part of the unit circle, and (ii) continuous-time models. Part I of this series of two papers (i) generalizes the frequency domain ML solution to the closed loop case, and (ii) proves the properties of the ML estimator under non-standard conditions. Contrary to the classical time domain case it is shown that the controller should be either known or estimated. The proposed ML estimators are applicable to frequency domain data as well as time domain data. ᭧

Nonminimum phase tracking control is studied for boost and buck-boost power converters. The sliding mode controller is designed to track directly a causal voltage tracking proÿle given by an exogenous system. The nonminimum phase output tracking problem is reduced to a state tracking problem. Bounded state tracking proÿles are generated by equations of stable system centre. Numerical examples demonstrate the e ectiveness of the sliding mode control design. ?

This paper presents the development of a nonlinear model and of a nonlinear control strategy for a VARIO scale model helicopter. Our global interest is a 7-DOF (degree-of-freedom) general model to be used for the autonomous forward-ight of helicopter drones. However, in this paper we focus on the particular case of a reduced-order model (3-DOF) representing the scale model helicopter mounted on an experimental platform. Both cases represent underactuated systems (u ∈ R 4 for the 7-DOF model and u ∈ R 2 for the 3-DOF model studied in this paper). The proposed nonlinear model possesses quite speciÿc features which make its study an interesting challenge, even in the 3-DOF case. In particular aerodynamical forces result in input signals and matrices which signiÿcantly di er from what is usually considered in the literature on mechanical systems control. Numerical results and experiments on a scale model helicopter illustrate the theoretical developments, and robustness with respect to parameter uncertainties is studied. ?

This note improves the results of Zheng, Wang, and Lee (Automatica 38 (2002) 517) on the design of multivariable PID controllers via LMI approach. The idea of the improvement is to transform the problem of PID controller design to that of static output feedback (SOF) controller design for a system in descriptor form. The merits of the present result are: (1) The present condition removes the invertibility constraint on the controllers in and incorporates it to the matrix inequality to be solved. (2) Once the SOF matrix is obtained, the PID gains are ready in hand and no additional computation is needed. (3) The present approach can deal with the case of some system parameters subject to perturbations. ?

A robust MPC for constrained nonlinear systems with uncertainties is presented. Outer bounds of the reachable sets of the system are used to predict the evolution of the system under uncertainty. A method that uses zonotopes to represent the approximated reachable sets is proposed. The closed-loop system is ultimately bounded thanks to a contractive constraint that drives the system to a robust invariant set. ᭧

In robot constrained motion problems on planar surfaces with frictional contacts, uncertainties on the contacted surface not only affect the control system performance but also distort control targets. The surface normal direction cosines are in this case uncertain parameters that are involved in both the control law and the control targets. This work proposes an adaptive learning controller that uses force and joint position/velocity measurements to simultaneously learn the surface orientation and achieve the desired goal. Simulation examples for a 6 dof robot are used to illustrate the theoretical results and the performance of the proposed controller in practical cases.

The paper concerns Drag-Free and Attitude Control of the European satellite Gravity field and steady-state Ocean Circulation Explorer (GOCE) during the science phase. Design has followed Embedded Model Control, where a spacecraft/environment discrete-time model becomes the realtime control core and is interfaced to actuators and sensors via tuneable feedback laws. Drag-free control implies cancelling non-gravitational forces and all torques, leaving the satellite to free fall subject only to gravity. In addition, for reasons of science, the spacecraft must be carefully aligned to the local orbital frame, retrieved from range and rate of a Global Positioning System receiver. Accurate drag-free and attitude control requires proportional and low-noise thrusting, which in turn raises the problem of propellant saving. Six-axis drag-free control is driven by accurate acceleration measurements provided by the mission payload. Their angular components must be combined with the star-tracker attitude so as to compensate accelerometer drift. Simulated results are presented and discussed. he contributed to data reduction of the European astrometric mission Hipparcos. Technological studies in view of scientific and drag-free space missions, like Gaia and GOCE provided the opportunity of applying Embedded Model Control to drag-free satellites and to electro-optics. He contributed to the conception, design and implementation of the interferometric thrust-stand Nanobalance, capable of sub-micro-Newton accuracy. His research interests cover the entire field of control problems that are challenging because of complexity, uncertainty and precision.

In this paper a method is presented for deriving the explicit robust model-based optimal control law for constrained linear dynamic systems. The controller is derived o -line via parametric programming before any actual process implementation takes place. The proposed control scheme guarantees feasible operation in the presence of bounded input uncertainties by (i) explicitly incorporating in the controller design stage a set of feasibility constraints and (ii) minimizing the nominal performance, or the expectation of the performance over the uncertainty space. An extension of the method to problems involving target point tracking in the presence of persistent disturbances is also discussed. The general concept is illustrated with two examples. ?

This article addresses the optimal (minimum-input-energy) output-transition problem for linear systems. The goal is to transfer the output from an initial value y(t) = y (for all time t 6 t i) to a ÿnal output value y(t) = y (for all time t ¿ t f). Previous methods solve this output-transition problem by transforming it into a state-transition problem; the initial and ÿnal states (x(t i); x(t f), respectively) are chosen and a minimum-energy state-to-state transition problem is solved. However, the choice of the initial and ÿnal states can be ad hoc and the resulting output-transition cost (input energy) may not be minimal. The contribution of this article is the solution of the optimal output-transition problem. An example system with elastic dynamics is studied to illustrate the proposed method. Simulation results are presented that show substantial reduction of transition costs with the use of the proposed method when compared to the use of minimum-energy state-to-state transitions.

A survey of advanced control applications in the pulp and paper industry indicates that very jew industrial control schemes use advanced control methods, although there are some encouraging applications of adaptive control and signs of Jrui(ful cooperation between academia, industry and suppliers.

This paper addresses predictive state regulation of linear discrete-time systems subject to persistent bounded disturbances and to state and/or control constraints. It is well known that the joint presence of constraints and disturbances can drive a predictive controller to infeasibility and instability. Here it is shown how robustness against persistent bounded disturbances can be enforced by inserting in the predictive controller suitable constraint restrictions. The robust predictive controller obtained in this way guarantees, for all admissible disturbances, constraint ful"llment and asymptotic state regulation, i.e. convergence of the state to a minimal robust invariant set, provided that the initial state is feasible. Simulation results demonstrate the e!ectiveness of the proposed approach.

A generalized minimum variance control law is derived for the control of nonlinear, possibly time-varying, multi-variable systems. The solution for the tracking and feedback/feedforward control law was obtained in the time-domain using a nonlinear operator representation of the process. The cost index involves both error and control signal costing terms and is normally quadratic but may also involve nonlinear functions. The feedback controller obtained is simple to implement and includes an internal model of the process. The tracking controller can include future reference change information, providing a predictive control capability. In one form the compensator might be considered a nonlinear version of the Smith Predictor that has feedforward action.

The goal of this paper is to provide a Lyapunov statement and proof of the recent nonlinear small-gain theorem for interconnected input/state stable (iss) systems. An iss-Lyapunov function for the overall system is obtained from the corresponding Lyapunov functions for both the subsystems.

This new edition combines a thorough, balanced treatment of theory and practice with a complete package of CLIPS 6.0 software tools for developing expert systems. It features a balanced blend of expert systems theory and practice; a detailed presentation of CLIPS Version 6.0, a ...

The value of the time delay in linear sampled systems is recursively updated by inspection of the phase contribution of the zero arising from a delay or anticipation shorter than one sampling time in continuous model. Absirat~--This paper presents a new identification method, based on standard Recursive Least Squares, for the estimation of time delay in linear sampled systems. The algorithm relies on the fact that if the continuous time model has a delay or anticipation shorter than one sampling time, then a real negative zero arises in the corresponding sampled system. By inspection of the phase contribution of this zero, the value of the delay is recursively updated. A frequency domain analysis is also performed to examine the characteristics of the algorithm. Simulation results illustrate the performances of the time delay estimation algorithm. *